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YouTube-simulations/rde.c
Nils Berglund 4d6547bad0
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2024-10-12 18:19:46 +02:00

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/*********************************************************************************/
/* */
/* Animation of reaction-diffusion equation in a planar domain */
/* */
/* N. Berglund, January 2022 */
/* */
/* Feel free to reuse, but if doing so it would be nice to drop a */
/* line to nils.berglund@univ-orleans.fr - Thanks! */
/* */
/* compile with */
/* gcc -o rde rde.c */
/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
/* */
/* OMP acceleration may be more effective after executing */
/* export OMP_NUM_THREADS=2 in the shell before running the program */
/* */
/* To make a video, set MOVIE to 1 and create subfolder tif_bz */
/* It may be possible to increase parameter PAUSE */
/* */
/* create movie using */
/* ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4 */
/* */
/*********************************************************************************/
/*********************************************************************************/
/* */
/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
/* One could make it much faster by using a GPU */
/* */
/*********************************************************************************/
#include <math.h>
#include <string.h>
#include <GL/glut.h>
#include <GL/glu.h>
#include <unistd.h>
#include <sys/types.h>
#include <tiffio.h> /* Sam Leffler's libtiff library. */
#include <omp.h>
#include <time.h>
#define MOVIE 0 /* set to 1 to generate movie */
#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
#define SAVE_MEMORY 1 /* set to 1 to save memory when writing tiff images */
#define NO_EXTRA_BUFFER_SWAP 1 /* some OS require one less buffer swap when recording images */
/* General geometrical parameters */
#define WINWIDTH 1920 /* window width */
#define WINHEIGHT 1150 /* window height */
#define NX 960 /* number of grid points on x axis */
#define NY 575 /* number of grid points on y axis */
#define HRES 4 /* factor for high resolution plots */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
#define YMIN -1.041666667
#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
/* Choice of simulated equation */
#define RDE_EQUATION 8 /* choice of reaction term, see list in global_3d.c */
#define NFIELDS 3 /* number of fields in reaction-diffusion equation */
#define NLAPLACIANS 0 /* number of fields for which to compute Laplacian */
#define SPHERE 1 /* set to 1 to simulate equation on sphere */
#define DPOLE 0 /* safety distance to poles */
#define DSMOOTH 1 /* size of neighbourhood of poles that are smoothed */
#define SMOOTHPOLE 0.05 /* smoothing coefficient at poles */
#define SMOOTHCOTPOLE 0.05 /* smoothing coefficient of cotangent at poles */
#define PHISHIFT 0.0 /* shift of phi in 2D plot (in degrees) */
#define SMOOTHBLOCKS 1 /* set to 1 to use blocks of points near the poles */
#define BLOCKDIST 64 /* distance to poles where points are blocked */
#define ZERO_MERIDIAN 190.0 /* choice of zero meridian (will be at left/right boundary of 2d plot) */
#define POLE_NODRAW 2 /* distance around poles where wave is not drawn */
#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
#define ADD_FORCE_FIELD 1 /* set to 1 to add a foce field (for compressible Euler equation) */
#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */
#define FORCE_FIELD 6 /* type of force field, see list in global_3d.c */
#define ADD_CORIOLIS_FORCE 1 /* set to 1 to add Coriolis force (quasigeostrophic Euler equations) */
#define VARIABLE_DEPTH 1 /* set to 1 for variable depth in shallow water equation */
#define SWATER_DEPTH 10 /* variable depth in shallow water equation */
#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */
#define ADAPT_STATE_TO_BC 1 /* to smoothly adapt initial state to obstacles */
#define OBSTACLE_GEOMETRY 84 /* geometry of obstacles, as in B_DOMAIN */
#define BC_STIFFNESS 0.25 /* controls region of boundary condition control */
#define CHECK_INTEGRAL 1 /* set to 1 to check integral of first field */
#define JULIA_SCALE 0.5 /* scaling for Julia sets */
#define JULIA_ROT -20.0 /* rotation of Julia set, in degrees */
#define JULIA_RE 0.5
#define JULIA_IM 0.462 /* parameters for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 999 /* choice of domain shape, see list in global_pdes.c */
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
#define PDISC_FACTOR 3.25 /* controls density of Poisson disc process (default: 3.25) */
#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
#define MU 1.0 /* parameter controlling the dimensions of domain */
#define NPOLY 5 /* number of sides of polygon */
#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */
#define MDEPTH 7 /* depth of computation of Menger gasket */
#define MRATIO 5 /* ratio defining Menger gasket */
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NGRIDX 6 /* number of grid point for grid of disks */
#define NGRIDY 8 /* number of grid point for grid of disks */
#define REVERSE_TESLA_VALVE 1 /* set to 1 to orient Tesla valve in blocking configuration */
#define WALL_WIDTH 0.05 /* width of wall separating lenses */
#define RADIUS_FACTOR 0.3 /* controls inner radius for C_RING arrangements */
#define X_SHOOTER -0.2
#define Y_SHOOTER -0.6
#define X_TARGET 0.4
#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
#define ISO_XSHIFT_LEFT -1.65
#define ISO_XSHIFT_RIGHT 0.4
#define ISO_YSHIFT_LEFT -0.05
#define ISO_YSHIFT_RIGHT -0.05
#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */
/* You can add more billiard tables by adapting the functions */
/* xy_in_billiard and draw_billiard in sub_wave.c */
/* Physical parameters of wave equation */
#define DT 0.00000025
#define VISCOSITY 0.02
#define POISSON_STIFFNESS 1.0 /* stiffness of Poisson equation solver for incompressible Euler */
#define DISSIPATION 0.0
#define DISSIPATION_EXT 1.0e-3 /* dissipation of shallow water eq. outside domain */
#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */
#define RPSLZB 0.0 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
#define K_AC 0.1 /* force constant in Allen-Cahn equation */
#define EPSILON 0.8 /* time scale separation */
#define DELTA 0.1 /* time scale separation */
#define FHNA 1.0 /* parameter in FHN equation */
#define FHNC -0.01 /* parameter in FHN equation */
#define K_HARMONIC 1.0 /* spring constant of harmonic potential */
#define K_COULOMB 0.5 /* constant in Coulomb potential */
#define V_MAZE 0.4 /* potential in walls of maze */
#define BZQ 0.0008 /* parameter in BZ equation */
#define BZF 1.2 /* parameter in BZ equation */
#define B_FIELD 10.0 /* magnetic field */
#define G_FIELD 0.025 /* gravity/Coriolis force */
#define BC_FIELD 1.0e-6 /* constant in repulsive field from obstacles */
#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */
#define K_EULER 50.0 /* constant in stream function integration of Euler equation */
#define K_EULER_INC 0.5 /* constant in incompressible Euler equation */
#define C_EULER_COMP 0.1 /* constant in compressible Euler equation */
#define SWATER_VARDEPTH_FACTOR 0.1 /* force constant in front of variable depth term */
#define SWATER_CORIOLIS_FORCE 0.002 /* Coriolis force for shallow water equation */
#define SMOOTHEN_VORTICITY 0 /* set to 1 to smoothen vorticity field in Euler equation */
#define SMOOTHEN_VELOCITY 1 /* set to 1 to smoothen velocity field in Euler equation */
#define SMOOTHEN_PERIOD 7 /* period between smoothenings */
#define SMOOTH_FACTOR 0.2 /* factor by which to smoothen */
#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */
#define OSCILLATING_SOURCE_PERIOD 1 /* period of oscillating source */
#define OSCILLATING_SOURCE_OMEGA 0.2 /* frequency of oscillating source */
#define ADD_TRACERS 1 /* set to 1 tof add tracer particles (for Euler equations) */
#define N_TRACERS 2000 /* number of tracer particles */
#define TRACERS_STEP 0.1 /* step size in tracer evolution */
#define RESPAWN_TRACERS 1 /* set to 1 to randomly move tracer position */
#define RESPAWN_PROBABILTY 0.005 /* probability of moving tracer */
#define T_OUT 2.0 /* outside temperature */
#define T_IN 0.0 /* inside temperature */
#define SPEED 0.0 /* speed of drift to the right */
#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */
#define NOISE_INTENSITY 0.01 /* noise intensity */
#define CHANGE_NOISE 0 /* set to 1 to increase noise intensity */
#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */
#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */
#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */
#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */
#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */
#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */
#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase, for numerical stability */
#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */
#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */
#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */
#define CHANGE_FLOW_SPEED 0 /* set to 1 to change speed of laminar flow */
#define IN_OUT_FLOW_BC 0 /* type of in-flow/out-flow boundary conditions for Euler equation, 0 for no b.c. */
#define IN_OUT_BC_FACTOR 0.001 /* factor of convex combination between old and new flow */
#define BC_FLOW_TYPE 1 /* type of initial condition */
/* see list in global_pdes.c */
#define IN_OUT_FLOW_MIN_AMP 0.25 /* amplitude of in-flow/out-flow boundary conditions (for Euler equation) - min value */
#define IN_OUT_FLOW_AMP 0.25 /* amplitude of in-flow/out-flow boundary conditions (for Euler equation) - max value */
#define LAMINAR_FLOW_MODULATION 0.01 /* asymmetry of laminar flow */
#define LAMINAR_FLOW_YPERIOD 1.0 /* period of laminar flow in y direction */
#define PRESSURE_GRADIENT 0.2 /* amplitude of pressure gradient for Euler equation */
#define SWATER_MIN_HEIGHT 0.05 /* min height of initial condition for shallow water equation */
#define DEPTH_FACTOR 0.00002 /* proportion of min height in variable depth */
#define TANH_FACTOR 5.0 /* steepness of variable depth */
#define EULER_GRADIENT_YSHIFT 0.0 /* y-shift in computation of gradient in Euler equation */
#define ADD_MOON_FORCING 1 /* set to 1 to simulate tidal forces from Moon */
#define FORCING_AMP 5.0e-6 /* amplitude of periodic forcing */
#define FORCING_CONST_AMP 0.0 /* amplitude of periodic forcing */
#define FORCING_PERIOD 1600 /* period of forcing */
#define FORCING_SHIFT 1.5 /* phase shift of forcing in units of Pi */
/* Boundary conditions, see list in global_pdes.c */
#define B_COND 1
#define B_COND_LEFT 0
#define B_COND_RIGHT 0
#define B_COND_TOP 0
#define B_COND_BOTTOM 0
/* Parameters for length and speed of simulation */
#define NSTEPS 1400 /* number of frames of movie */
#define NVID 80 /* number of iterations between images displayed on screen */
#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */
#define MAX_DT 0.024 /* maximal value of integration step */
#define NSEG 999 /* number of segments of boundary */
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
#define PAUSE 100 /* number of frames after which to pause */
#define PSLEEP 2 /* sleep time during pause */
#define SLEEP1 2 /* initial sleeping time */
#define SLEEP2 1 /* final sleeping time */
#define INITIAL_TIME 0 /* initial still time */
#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */
#define END_FRAMES 250 /* number of still frames at end of movie */
#define FADE 1 /* set to 1 to fade at end of movie */
/* Visualisation */
#define PLOT_3D 1 /* controls whether plot is 2D or 3D */
#define PLOT_SPHERE 1 /* draws fields on a sphere */
#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */
#define ROTATE_ANGLE -45.0 /* total angle of rotation during simulation */
#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */
#define SHADE_2D 0 /* set to 1 to change luminosity according to normal vector */
#define VIEWPOINT_TRAJ 1 /* type of viewpoint trajectory */
#define MAX_LATITUDE 45.0 /* maximal latitude for viewpoint trajectory VP_ORBIT2 */
#define DRAW_PERIODICISED 0 /* set to 1 to repeat wave periodically in x and y directions */
#define DRAW_MOON_POSITION 0 /* set to 1 to draw vertical lines for tidal sim */
/* Plot type - color scheme */
#define CPLOT 70
#define CPLOT_B 74
/* Plot type - height of 3D plot */
#define ZPLOT 70 /* z coordinate in 3D plot */
#define ZPLOT_B 71 /* z coordinate in second 3D plot */
#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */
#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */
#define FADE_WATER_DEPTH 0 /* set to 1 to make wave color depth-dependent */
#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */
#define ADD_POTENTIAL_TO_Z 0 /* set to 1 to add the external potential to z-coordinate of plot */
#define ADD_POT_CONSTANT 0.35 /* constant added to wave height */
#define DRAW_DEPTH 0 /* set to 1 to draw water depth */
#define DEPTH_SCALE 0.75 /* vertical scaling of depth plot */
#define DEPTH_SHIFT -0.015 /* vertical shift of depth plot */
#define FLOODING 1 /* set to 1 for drawing water when higher than continents */
// #define FLOODING_VSHIFT 0.51 /* controls when wave is considered higher than land */
#define FLOODING_VSHIFT 0.56 /* controls when wave is considered higher than land */
#define FLOODING_VSHIFT_2D 0.61 /* controls when wave is considered higher than land */
#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */
#define PRINT_TIME 0 /* set to 1 to print running time */
#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */
#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */
#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
#define PRINT_NOISE 0 /* set to 1 to print noise intensity */
#define PRINT_FLOW_SPEED 0 /* set to 1 to print speed of flow */
#define PRINT_AVERAGE_SPEED 0 /* set to 1 to print average speed of flow */
#define PRINT_LEFT 1 /* set to 1 to print parameters at left side */
#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */
#define FIELD_LINE_WIDTH 1 /* width of field lines */
#define N_FIELD_LINES 120 /* number of field lines */
#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */
#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */
#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */
/* 3D representation */
#define REPRESENTATION_3D 1 /* choice of 3D representation */
#define REP_AXO_3D 0 /* linear projection (axonometry) */
#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */
/* Color schemes, see list in global_pdes.c */
#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */
#define COLOR_PALETTE_B 16 /* Color palette, see list in global_pdes.c */
#define BLACK 1 /* black background */
#define COLOR_OUT_R 1.0 /* color outside domain */
#define COLOR_OUT_G 1.0
#define COLOR_OUT_B 1.0
#define COLOR_SCHEME 3 /* choice of color scheme */
#define PHASE_SHIFT -0.25 /* phase shift of color scheme, in units of Pi (formerly COLOR_PHASE_SHIFT) */
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
#define VSHIFT_AMPLITUDE 0.0 /* additional shift for wave amplitude */
#define VSCALE_AMPLITUDE 15.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
#define CURL_SCALE 1.0 /* scaling factor for curl representation */
#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
#define SLOPE_SCHROD_LUM 10.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
#define MIN_SCHROD_LUM 0.1 /* minimal luminosity in color scheme Z_ARGUMENT*/
#define VSCALE_PRESSURE 2.0 /* additional scaling factor for color scheme Z_EULER_PRESSURE */
#define PRESSURE_SHIFT 10.0 /* shift for color scheme Z_EULER_PRESSURE */
#define PRESSURE_LOG_SHIFT -2.5 /* shift for color scheme Z_EULER_PRESSURE */
#define VSCALE_WATER_HEIGHT 15.0 /* vertical scaling of water height */
#define ADD_HEIGHT_CONSTANT -0.016 /* constant added to wave height */
#define SHADE_SCALE_2D 0.25 /* controls "depth" of 2D shading */
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
#define HUEMEAN 359.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */
#define E_SCALE 100.0 /* scaling factor for energy representation */
#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
#define LOG_SCALE 0.5 /* scaling factor for energy log representation */
#define LOG_SHIFT 1.0
#define LOG_MIN 1.0e-3 /* floor value for log vorticity plot */
#define VSCALE_SPEED 50.0 /* additional scaling factor for color scheme Z_EULER_SPEED */
#define VMEAN_SPEED 0.0 /* mean value around which to scale for color scheme Z_EULER_SPEED */
#define SHIFT_DENSITY 1.0 /* shift for color scheme Z_EULER_DENSITY */
#define VSCALE_DENSITY 30.0 /* additional scaling factor for color scheme Z_EULER_DENSITY */
#define VSCALE_VORTICITY 15.0 /* additional scaling factor for color scheme Z_EULERC_VORTICITY */
#define VORTICITY_SHIFT 0.0 /* vertical shift of vorticity */
#define ZSCALE_SPEED 300.0 /* additional scaling factor for z-coord Z_EULER_SPEED and Z_SWATER_SPEED */
#define ZSHIFT_SPEED 0.0 /* additional shift of z-coord Z_EULER_SPEED and Z_SWATER_SPEED */
#define ZSCALE_NORMGRADIENT -0.0001 /* vertical scaling for Z_NORM_GRADIENT */
#define VSCALE_SWATER 60.0 /* additional scaling factor for color scheme Z_EULER_DENSITY */
#define NXMAZE 7 /* width of maze */
#define NYMAZE 7 /* height of maze */
#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */
#define RAND_SHIFT 3 /* seed of random number generator */
#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
#define MAZE_WIDTH 0.04 /* half width of maze walls */
#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */
#define COLORBAR_RANGE_B 2.5 /* scale of color scheme bar for 2nd part */
#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
#define CIRC_COLORBAR 0 /* set to 1 to draw circular color scheme */
#define CIRC_COLORBAR_B 1 /* set to 1 to draw circular color scheme */
/* only for compatibility with wave_common.c */
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */
#define IOR 4 /* choice of index of refraction, see list in global_pdes.c */
#define IOR_TOTAL_TURNS 1.5 /* total angle of rotation for IOR_PERIODIC_WELLS_ROTATING */
#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */
#define OMEGA 0.005 /* frequency of periodic excitation */
#define OSCIL_YMAX 0.2 /* defines oscillation range */
#define COURANT 0.08 /* Courant number */
#define COURANTB 0.03 /* Courant number in medium B */
#define INITIAL_AMP 0.5 /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */
#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */
#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */
#define AVRG_E_FACTOR 0.99 /* controls time window size in P_AVERAGE_ENERGY scheme */
#define OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */
#define AMPLITUDE 0.8 /* amplitude of periodic excitation */
#define ACHIRP 0.2 /* acceleration coefficient in chirp */
#define DAMPING 0.0 /* damping of periodic excitation */
#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */
#define B_DOMAIN_B 20 /* second domain shape, for comparisons */
#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */
#define FLUX_WINDOW 20 /* averaging window for energy flux */
#define ADD_WAVE_PACKET_SOURCES 0 /* set to 1 to add several sources emitting wave packets */
#define WAVE_PACKET_SOURCE_TYPE 1 /* type of wave packet sources */
#define N_SOURCES 1 /* number of wave sources */
#define N_WAVE_PACKETS 15 /* number of wave packets */
#define WAVE_PACKET_RADIUS 20 /* radius of wave packets */
#define OSCIL_LEFT_YSHIFT 25.0 /* y-dependence of left oscillation (for non-horizontal waves) */
#define INITIAL_SHIFT 20.0 /* time shift of initial wave packet (in oscillation periods) */
#define WAVE_PACKET_SHIFT 200.0 /* time shift between wave packets (in oscillation periods) */
#define DRAW_WAVE_PROFILE 0 /* set to 1 to draw a profile of the wave */
#define HORIZONTAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
#define VERTICAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
#define WAVE_PROFILE_X 1.9 /* value of x to sample wave profile */
#define WAVE_PROFILE_Y -1.0 /* value of y to sample wave profile */
#define PROFILE_AT_BOTTOM 1 /* draw wave profile at bottom instead of top */
#define AVERAGE_WAVE_PROFILE 1 /* set to 1 to draw time-average of wave profile squared*/
#define MU_B 1.0 /* parameter controlling the dimensions of domain */
#define GAMMA 0.0 /* damping factor in wave equation */
#define GAMMAB 0.0 /* damping factor in wave equation */
#define VERTICAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
#define DRAW_WAVE_TIMESERIES 0 /* set to 1 to draw a time series of the wave */
#define TIMESERIES_NVALUES 400 /* number of values plotted in time series */
#define DRAW_WAVE_SOURCE 0 /* set to 1 to draw source of wave at (wave_source_x, wave_source_y) */
#define MESSAGE_LDASH 1 /* length of dash for Morse code message */
#define MESSAGE_LDOT 1 /* length of dot for Morse code message */
#define MESSAGE_LINTERVAL 1 /* length of interval between dashes/dots for Morse code message */
#define MESSAGE_LINTERLETTER 1 /* length of interval between letters for Morse code message */
#define MESSAGE_LSPACE 1 /* length of space for Morse code message */
#define MESSAGE_INITIAL_TIME 1 /* initial time before starting message for Morse code message */
/* end of constants added only for compatibility with wave_common.c */
double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */
double v_3d[2] = {-0.75, -0.45};
double w_3d[2] = {0.0, 0.015};
double light[3] = {-0.816496581, 0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */
double observer[3] = {-6.0, -6.0, 4.5}; /* location of observer for REP_PROJ_3D representation */
int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
/* constants for simulations on planets */
#define ADD_DEM 1 /* add DEM (digital elevation model) */
#define ADD_NEGATIVE_DEM 1 /* add DEM with bathymetric data */
#define RSCALE_DEM 0.075 /* scaling factor of radial component for DEM */
#define SMOOTH_DEM 1 /* set to 1 to smoothen DEM (to make altitude less constant) */
#define DEM_SMOOTH_STEPS 10 /* number of smoothening steps */
#define DEM_SMOOTH_HEIGHT 2.0 /* relative height below which to smoothen */
#define DEM_MAXHEIGHT 9000.0 /* max height of DEM (estimated from Everest/Olympus Mons) */
#define DEM_MAXDEPTH -10000 /* max depth of DEM */
#define PLANET_SEALEVEL 0.0 /* sea level for flooded planet */
#define VENUS_NODATA_FACTOR 0.5 /* altitude to assign to DEM points without data (fraction of mean altitude) */
#define Z_SCALING_FACTOR 0.8 /* overall scaling factor of z axis for REP_PROJ_3D representation */
#define XY_SCALING_FACTOR 2.1 /* overall scaling factor for on-screen (x,y) coordinates after projection */
#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */
#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */
#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */
#define BORDER_PADDING 0 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
#define DRAW_ARROW 0 /* set to 1 to draw arrow above sphere */
#define RSCALE 0.15 /* scaling factor of radial component */
#define RSHIFT -0.075 /* shift in radial component */
#define RMAX 2.0 /* max value of radial component */
#define RMIN 0.5 /* min value of radial component */
#define COS_VISIBLE -0.35 /* limit on cosine of normal to shown facets */
/* For debugging purposes only */
#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */
#define VMAX 100.0 /* max value of wave amplitude */
#define TEST_GRADIENT 0 /* print norm squared of gradient */
#define REFRESH_B (ZPLOT_B != ZPLOT)||(CPLOT_B != CPLOT) /* to save computing time, to be improved */
#define COMPUTE_WRAP_ANGLE ((WRAP_ANGLE)&&((cplot == Z_ANGLE_GRADIENT)||(cplot == Z_ANGLE_GRADIENTX)||(cplot == Z_ARGUMENT)||(cplot == Z_ANGLE_GRADIENTX)||(cplot == Z_EULER_DIRECTION_SPEED)||(cplot == Z_SWATER_DIRECTION_SPEED)))
#define PRINT_PARAMETERS ((PRINT_TIME)||(PRINT_VISCOSITY)||(PRINT_RPSLZB)||(PRINT_PROBABILITIES)||(PRINT_NOISE)||(PRINT_FLOW_SPEED)||(PRINT_AVERAGE_SPEED))
#define COMPUTE_PRESSURE ((ZPLOT == Z_EULER_PRESSURE)||(CPLOT == Z_EULER_PRESSURE)||(ZPLOT_B == Z_EULER_PRESSURE)||(CPLOT_B == Z_EULER_PRESSURE))
#define ASYM_SPEED_COLOR (VMEAN_SPEED == 0.0)
#define XYIN_INITIALISED (B_DOMAIN == D_IMAGE)
int block_sizes[NY]; /* table of block sizes for blocking around poles */
int block_numbers[NY]; /* table of block numbers for blocking around poles */
#include "global_pdes.c"
#include "global_3d.c" /* constants and global variables */
#include "sub_maze.c"
#include "sub_wave.c"
#include "wave_common.c" /* common functions for wave_billiard, wave_comparison, etc */
#include "sub_wave_3d_rde.c" /* should be later replaced by sub_wave_rde.c */
#include "sub_rde.c"
double f_aharonov_bohm(double r2)
/* radial part of Aharonov-Bohm vector potential */
{
double r02 = AB_RADIUS*AB_RADIUS;
if (r2 > r02) return(-0.25*r02/r2);
else return(0.25*(r2 - 2.0*r02)/r02);
// if (r2 > r02) return(1.0/r2);
// else return((2.0*r02 - r2)/(r02*r02));
}
double potential(int i, int j)
/* compute potential (e.g. for Schrödinger equation), or potential part if there is a magnetic field */
{
double x, y, xy[2], r, small = 1.0e-1, kx, ky, lx = XMAX - XMIN, r1, r2, r3, f;
int rect;
ij_to_xy(i, j, xy);
x = xy[0];
y = xy[1];
switch (POTENTIAL) {
case (POT_HARMONIC):
{
return (K_HARMONIC*(x*x + y*y));
}
case (POT_COULOMB):
{
// r = module2(x, y);
r = sqrt(x*x + y*y + small*small);
// if (r < small) r = small;
return (-K_COULOMB/r);
}
case (POT_PERIODIC):
{
kx = 4.0*DPI/(XMAX - XMIN);
ky = 2.0*DPI/(YMAX - YMIN);
return(-K_HARMONIC*cos(kx*x)*cos(ky*y));
}
case (POT_FERMIONS):
{
r = sqrt((x-y)*(x-y) + small*small);
return (-K_COULOMB/r);
}
case (POT_FERMIONS_PERIODIC):
{
r1 = sqrt((x-y)*(x-y) + small*small);
r2 = sqrt((x-lx-y)*(x-lx-y) + small*small);
r3 = sqrt((x+lx-y)*(x+lx-y) + small*small);
// r = r/3.0;
return (-0.5*K_COULOMB*(1.0/r1 + 1.0/r2 + 1.0/r3));
}
case (VPOT_CONSTANT_FIELD):
{
return (K_HARMONIC*(x*x + y*y)); /* magnetic field strength b is chosen such that b^2 = K_HARMONIC */
}
case (VPOT_AHARONOV_BOHM):
{
r2 = x*x + y*y;
f = f_aharonov_bohm(r2);
return (B_FIELD*B_FIELD*f*f*r2); /* magnetic field strength b is chosen such that b^2 = K_HARMONIC */
// return (K_HARMONIC*f); /* magnetic field strength b is chosen such that b^2 = K_HARMONIC */
}
case (POT_MAZE):
{
for (rect=0; rect<npolyrect; rect++)
if (ij_in_polyrect(i, j, polyrect[rect])) return(V_MAZE);
return(0.0);
}
default:
{
return(0.0);
}
}
}
void compute_vector_potential(int i, int j, double *ax, double *ay)
/* initialize the vector potential, for Schrodinger equation in a magnetic field */
{
double x, y, xy[2], r2, f;
ij_to_xy(i, j, xy);
x = xy[0];
y = xy[1];
switch (POTENTIAL) {
case (VPOT_CONSTANT_FIELD):
{
*ax = B_FIELD*y;
*ay = -B_FIELD*x;
break;
}
case (VPOT_AHARONOV_BOHM):
{
r2 = x*x + y*y;
f = f_aharonov_bohm(r2);
*ax = B_FIELD*y*f;
*ay = -B_FIELD*x*f;
break;
}
default:
{
*ax = 0.0;
*ay = 0.0;
}
}
}
void compute_gfield(int i, int j, double *gx, double *gy)
/* initialize the exterior field, for the compressible Euler equation */
{
double x, y, xy[2], r, f, a = 0.4, x1, y1, hx, hy, h;
ij_to_xy(i, j, xy);
x = xy[0];
y = xy[1];
switch (FORCE_FIELD) {
case (GF_VERTICAL):
{
*gx = 0.0;
*gy = -G_FIELD;
break;
}
case (GF_CIRCLE):
{
r = module2(x,y) + 1.0e-2;
f = 0.5*(1.0 - tanh(BC_STIFFNESS*(r - LAMBDA)));
*gx = BC_FIELD*f*x/r;
*gy = BC_FIELD*f*y/r;
break;
}
case (GF_ELLIPSE):
{
r = module2(x/LAMBDA,y/MU) + 1.0e-2;
f = 0.5*(1.0 - tanh(BC_STIFFNESS*(r - 1.0)));
*gx = BC_FIELD*f*x/(LAMBDA*LAMBDA);
*gy = BC_FIELD*f*y/(MU*MU);
break;
}
case (GF_AIRFOIL):
{
y1 = y + a*x*x;
r = module2(x/LAMBDA,y1/MU) + 1.0e-2;
f = 0.5*(1.0 - tanh(BC_STIFFNESS*(r - 1.0)));
*gx = BC_FIELD*f*(x/(LAMBDA*LAMBDA) + a*y1/(MU*MU));
*gy = BC_FIELD*f*y1/(MU*MU);
break;
}
case (GF_WING):
{
if (x >= LAMBDA)
{
*gx = 0.0;
*gy = 0.0;
}
else
{
x1 = 1.0 - x/LAMBDA;
if (x1 < 0.1) x1 = 0.1;
y1 = y + a*x*x;
r = module2(x/LAMBDA,y1/(MU*x1)) + 1.0e-2;
f = 0.5*(1.0 - tanh(BC_STIFFNESS*(r - 1.0)));
*gx = BC_FIELD*f*(x/(LAMBDA*LAMBDA) + 2.0*a*x*y1/(MU*MU*x1*x1) - y1*y1/(MU*MU*x1*x1*x1));
*gy = BC_FIELD*f*y1/(MU*MU*x1*x1);
// *gx = 0.1*G_FIELD*f*(x/(LAMBDA*LAMBDA) + 2.0*a*x*y1/(MU*MU*x1*x1) - y1*y1/(MU*MU*x1*x1*x1));
// *gy = 0.1*G_FIELD*f*y1/(MU*MU*x1*x1);
// hx = x/(LAMBDA*LAMBDA) + 2.0*a*x*y1/(MU*MU*x1*x1) - y1*y1/(MU*MU*x1*x1*x1);
// hy = y1/(MU*MU*x1*x1);
// h = module2(hx, hy) + 1.0e-2;
// *gx = G_FIELD*f*hx/h;
// *gy = G_FIELD*f*hy/h;
}
break;
}
default:
{
*gx = 0.0;
*gy = 0.0;
}
}
}
void initialize_potential(double potential_field[NX*NY])
/* initialize the potential field, e.g. for the Schrödinger equation */
{
int i, j;
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
potential_field[i*NY+j] = potential(i,j);
}
}
}
void initialize_vector_potential(double vpotential_field[2*NX*NY])
/* initialize the potential field, e.g. for the Schrödinger equation */
{
int i, j;
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
compute_vector_potential(i, j, &vpotential_field[i*NY+j], &vpotential_field[NX*NY+i*NY+j]);
}
}
}
void initialize_gfield(double gfield[2*NX*NY], double bc_field[NX*NY], double bc_field2[NX*NY], t_wave_sphere *wsphere, t_wave_sphere *wsphere_hr)
/* initialize the exterior field, e.g. for the compressible Euler equation */
{
int i, j;
double dx, dy;
switch (FORCE_FIELD)
{
case (GF_COMPUTE_FROM_BC):
{
dx = (XMAX - XMIN)/(double)NX;
dy = (YMAX - YMIN)/(double)NY;
#pragma omp parallel for private(i,j)
for (i=1; i<NX-1; i++){
for (j=1; j<NY-1; j++){
gfield[i*NY+j] = BC_FIELD*(bc_field2[(i+1)*NY+j] - bc_field2[(i-1)*NY+j])/dx;
gfield[NX*NY+i*NY+j] = BC_FIELD*(bc_field2[i*NY+j+1] - bc_field2[i*NY+j-1])/dy;
// printf("gfield at (%i,%i): (%.3lg, %.3lg)\n", i, j, gfield[i*NY+j], gfield[NX*NY+i*NY+j]);
}
}
/* boundaries */
for (i=0; i<NX; i++)
{
gfield[i*NY] = 0.0;
gfield[NX*NY+i*NY] = 0.0;
gfield[i*NY+NY-1] = 0.0;
gfield[NX*NY+i*NY+NY-1] = 0.0;
}
for (j=0; j<NY; j++)
{
gfield[j] = 0.0;
gfield[NX*NY+j] = 0.0;
gfield[(NX-1)*NY+j] = 0.0;
gfield[NX*NY+(NX-1)*NY+j] = 0.0;
}
break;
}
case (GF_EARTH):
{
dx = (XMAX - XMIN)/(double)NX;
dy = (YMAX - YMIN)/(double)NY;
init_earth_map_rde(wsphere, 1);
init_earth_map_rde(wsphere_hr, HRES);
#pragma omp parallel for private(i,j)
for (i=1; i<NX-1; i++){
for (j=1; j<NY-1; j++)
{
if (wsphere[i*NY+j].altitude > 0.0)
{
gfield[i*NY+j] = -BC_FIELD*(wsphere[(i+1)*NY+j].altitude - wsphere[(i-1)*NY+j].altitude)/dx;
gfield[NX*NY+i*NY+j] = -BC_FIELD*(wsphere[i*NY+j+1].altitude - wsphere[i*NY+j-1].altitude)/dy;
}
else
{
gfield[i*NY+j] = 0.0;
gfield[NX*NY+i*NY+j] = 0.0;
}
}
}
/* boundaries TODO */
for (i=0; i<NX; i++)
{
gfield[i*NY] = 0.0;
gfield[NX*NY+i*NY] = 0.0;
gfield[i*NY+NY-1] = 0.0;
gfield[NX*NY+i*NY+NY-1] = 0.0;
}
for (j=0; j<NY; j++)
{
gfield[j] = 0.0;
gfield[NX*NY+j] = 0.0;
gfield[(NX-1)*NY+j] = 0.0;
gfield[NX*NY+(NX-1)*NY+j] = 0.0;
}
break;
}
case (GF_MARS):
{
dx = (XMAX - XMIN)/(double)NX;
dy = (YMAX - YMIN)/(double)NY;
init_planet_map_rde(wsphere, D_SPHERE_MARS, 1);
init_planet_map_rde(wsphere_hr, D_SPHERE_MARS, HRES);
#pragma omp parallel for private(i,j)
for (i=1; i<NX-1; i++){
for (j=1; j<NY-1; j++){
gfield[i*NY+j] = BC_FIELD*(wsphere[(i+1)*NY+j].altitude - wsphere[(i-1)*NY+j].altitude)/dx;
gfield[NX*NY+i*NY+j] = BC_FIELD*(wsphere[i*NY+j+1].altitude - wsphere[i*NY+j-1].altitude)/dy;
}
}
/* boundaries TODO */
for (i=0; i<NX; i++)
{
gfield[i*NY] = 0.0;
gfield[NX*NY+i*NY] = 0.0;
gfield[i*NY+NY-1] = 0.0;
gfield[NX*NY+i*NY+NY-1] = 0.0;
}
for (j=0; j<NY; j++)
{
gfield[j] = 0.0;
gfield[NX*NY+j] = 0.0;
gfield[(NX-1)*NY+j] = 0.0;
gfield[NX*NY+(NX-1)*NY+j] = 0.0;
}
break;
}
case (GF_VENUS):
{
dx = (XMAX - XMIN)/(double)NX;
dy = (YMAX - YMIN)/(double)NY;
init_planet_map_rde(wsphere, D_SPHERE_VENUS, 1);
init_planet_map_rde(wsphere_hr, D_SPHERE_VENUS, HRES);
#pragma omp parallel for private(i,j)
for (i=1; i<NX-1; i++){
for (j=1; j<NY-1; j++){
gfield[i*NY+j] = BC_FIELD*(wsphere[(i+1)*NY+j].altitude - wsphere[(i-1)*NY+j].altitude)/dx;
gfield[NX*NY+i*NY+j] = BC_FIELD*(wsphere[i*NY+j+1].altitude - wsphere[i*NY+j-1].altitude)/dy;
}
}
/* boundaries TODO */
for (i=0; i<NX; i++)
{
gfield[i*NY] = 0.0;
gfield[NX*NY+i*NY] = 0.0;
gfield[i*NY+NY-1] = 0.0;
gfield[NX*NY+i*NY+NY-1] = 0.0;
}
for (j=0; j<NY; j++)
{
gfield[j] = 0.0;
gfield[NX*NY+j] = 0.0;
gfield[(NX-1)*NY+j] = 0.0;
gfield[NX*NY+(NX-1)*NY+j] = 0.0;
}
break;
}
default:
{
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
compute_gfield(i, j, &gfield[i*NY+j], &gfield[NX*NY+i*NY+j]);
}
}
}
}
}
void compute_water_depth(int i, int j, t_rde *rde, t_wave_sphere wsphere[NX*NY], int ncircles)
/* initialize the vector potential, for Schrodinger equation in a magnetic field */
{
double x, y, xy[2], r0, r, z, h, h0, hh, x1, y1, z1, d, rmax, rmin, phi, vshift;
int n, nx, ny;
static double phi1, phi2, phi3, sq3, rico;
static int first = 1;
if (first)
{
phi = 0.5*(sqrt(5.0)+1.0);
phi1 = phi - 1.0;
phi2 = phi - 2.0;
phi3 = 2.0*phi - 3.0;
sq3 = 0.5/sqrt(3.0);
rico = 0.5/(2.0 + phi);
first = 0;
}
ij_to_xy(i, j, xy);
x = xy[0];
y = xy[1];
switch (SWATER_DEPTH) {
case (SH_CIRCLE):
{
r0 = module2(x,y);
r = r0/LAMBDA;
h = tanh(TANH_FACTOR*(r-1.0));
hh = 1.0 - h*h;
z = SWATER_MIN_HEIGHT*DEPTH_FACTOR*TANH_FACTOR*hh/(r0*LAMBDA);
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
rde->gradx = x*z;
rde->grady = y*z;
break;
}
case (SH_CIRCLES):
{
h = 0.0;
z = 0.0;
r = 10.0;
/* compute minimal distance to circles */
for (n = 0; n < ncircles; n++)
for (nx = -1; nx < 2; nx++)
for (ny = -1; ny < 2; ny++)
{
x1 = circles[n].xc + (double)nx*(XMAX-XMIN);
y1 = circles[n].yc + (double)ny*(YMAX-YMIN);
r0 = module2(x - x1,y - y1)/circles[n].radius;
if (r0 < r) r = r0;
}
h = tanh(TANH_FACTOR*(r-1.0));
h = 0.5*(h + 1.0);
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
case (SH_COAST):
{
x1 = PI*(x + 0.1 - 0.1*cos(PI*y/YMAX))/XMAX;
d = 3.0*sin(x1);
h = tanh(-TANH_FACTOR*d);
h = 0.5*(h + 1.0);
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
case (SH_COAST_MONOTONE):
{
x1 = PI*(x + 0.1 - 0.2*cos(PI*y/YMAX))/XMAX;
h = tanh(-TANH_FACTOR*x1);
h = 0.5*(h + 1.0);
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
case (SH_SPHERE_CUBE):
{
rmax = 0.0;
/* compute distance from cube to origin, given by 0.5/rmax */
if (vabs(wsphere[i*NY+j].x) > rmax) rmax = vabs(wsphere[i*NY+j].x);
if (vabs(wsphere[i*NY+j].y) > rmax) rmax = vabs(wsphere[i*NY+j].y);
if (vabs(wsphere[i*NY+j].z) > rmax) rmax = vabs(wsphere[i*NY+j].z);
h = 1.0 - 0.5/rmax;
// printf("h = %.3lg\n", h);
if (h < 0.0) h = 0.0;
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
case (SH_SPHERE_OCTAHEDRON):
{
rmax = 0.0;
/* compute distance from octahedron to origin, given by 0.5/rmax */
rmax = 1.0/(vabs(wsphere[i*NY+j].x) + vabs(wsphere[i*NY+j].y) + vabs(wsphere[i*NY+j].z));
h = 1.0 - 0.5/rmax;
printf("h = %.3lg\n", h);
if (h < 0.0) h = 0.0;
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
case (SH_SPHERE_DODECAHEDRON):
{
rmax = 0.0;
x1 = wsphere[i*NY+j].x;
y1 = wsphere[i*NY+j].y;
z1 = wsphere[i*NY+j].z;
/* compute distance from dodecahedron */
d = vabs(phi1*y1 - phi2*z1) - sq3;
if (d > rmax) rmax = d;
d = vabs(-phi2*x1 + phi1*z1) - sq3;
if (d > rmax) rmax = d;
d = vabs(phi1*x1 - phi2*y1) - sq3;
if (d > rmax) rmax = d;
d = vabs(phi1*y1 + phi2*z1) - sq3;
if (d > rmax) rmax = d;
d = vabs(phi2*x1 + phi1*z1) - sq3;
if (d > rmax) rmax = d;
d = vabs(phi1*x1 + phi2*y1) - sq3;
if (d > rmax) rmax = d;
h = rmax;
printf("h = %.3lg\n", h);
if (h < 0.0) h = 0.0;
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
case (SH_SPHERE_ICOSAHEDRON):
{
rmax = 0.0;
x1 = wsphere[i*NY+j].x;
y1 = wsphere[i*NY+j].y;
z1 = wsphere[i*NY+j].z;
/* compute distance from dodecahedron */
d = vabs(phi2*(x1+y1+z1)) - rico;
if (d > rmax) rmax = d;
d = vabs(phi2*(-x1+y1+z1)) - rico;
if (d > rmax) rmax = d;
d = vabs(phi2*(x1-y1+z1)) - rico;
if (d > rmax) rmax = d;
d = vabs(phi2*(x1+y1-z1)) - rico;
if (d > rmax) rmax = d;
d = vabs(phi3*x1 + phi1*z1) - rico;
if (d > rmax) rmax = d;
d = vabs(phi3*z1 + phi1*y1) - rico;
if (d > rmax) rmax = d;
d = vabs(phi3*y1 + phi1*x1) - rico;
if (d > rmax) rmax = d;
d = vabs(phi3*x1 - phi1*z1) - rico;
if (d > rmax) rmax = d;
d = vabs(phi3*z1 - phi1*y1) - rico;
if (d > rmax) rmax = d;
d = vabs(phi3*y1 - phi1*x1) - rico;
if (d > rmax) rmax = d;
h = rmax;
printf("h = %.3lg\n", h);
if (h < 0.0) h = 0.0;
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
case (SH_EARTH):
{
/* TODO */
vshift = PLANET_SEALEVEL/(DEM_MAXHEIGHT - DEM_MAXDEPTH);
h = 0.5 - RSCALE_DEM*(wsphere[i*NY+j].altitude - vshift);
rde->depth = SWATER_MIN_HEIGHT*DEPTH_FACTOR*h;
break;
}
}
}
double initialize_water_depth(t_rde rde[NX*NY], t_wave_sphere *wsphere, t_wave_sphere *wsphere_hr)
{
int i, j, ncircles;
double dx, dy, min, max, pscal, norm, vz = 0.01;
if (SWATER_DEPTH == SH_CIRCLES) ncircles = init_circle_config_pattern(circles, CIRCLE_PATTERN);
if (SWATER_DEPTH == SH_EARTH)
{
init_earth_map_rde(wsphere, 1);
init_earth_map_rde(wsphere_hr, HRES);
}
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
compute_water_depth(i, j, &rde[i*NY + j], wsphere, ncircles);
if (rde[i*NY + j].depth < 0.0) rde[i*NY + j].depth = 0.0;
}
}
dx = (XMAX - XMIN)/(double)NX;
dy = (YMAX - YMIN)/(double)NY;
/* compute x gradient */
#pragma omp parallel for private(i,j)
for (i=1; i<NX-1; i++){
for (j=0; j<NY; j++){
rde[i*NY + j].gradx = (rde[(i+1)*NY + j].depth - rde[(i-1)*NY + j].depth)/dx;
}
}
/* left boundary */
for (j=0; j<NY; j++){
switch (B_COND_LEFT) {
case (BC_PERIODIC):
{
rde[j].gradx = (rde[NY + j].depth - rde[(NX-1)*NY + j].depth)/dx;
break;
}
case (BC_DIRICHLET):
{
rde[j].gradx = (rde[NY + j].depth - rde[j].depth)*2.0/dx;
break;
}
}
}
/* right boundary */
for (j=0; j<NY; j++){
switch (B_COND_RIGHT) {
case (BC_PERIODIC):
{
rde[(NX-1)*NY + j].gradx = (rde[j].depth - rde[(NX-2)*NY + j].depth)/dx;
break;
}
case (BC_DIRICHLET):
{
rde[(NX-1)*NY + j].gradx = (rde[(NX-1)*NY + j].depth - rde[(NX-2)*NY + j].depth)*2.0/dx;
break;
}
}
}
/* compute y gradient */
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=1; j<NY-1; j++){
rde[i*NY + j].grady = (rde[i*NY + j+1].depth - rde[i*NY + j-1].depth)/dy;
}
}
/* bottom boundary */
for (i=0; i<NX; i++){
switch (B_COND_BOTTOM) {
case (BC_PERIODIC):
{
rde[i*NY].grady = (rde[i*NY + 1].depth - rde[i*NY + NY-1].depth)/dy;
break;
}
case (BC_DIRICHLET):
{
rde[i*NY].grady = (rde[i*NY + 1].depth - rde[i*NY].depth)*2.0/dy;
break;
}
}
}
/* top boundary */
for (i=0; i<NX; i++){
switch (B_COND_TOP) {
case (BC_PERIODIC):
{
rde[i*NY + NY-1].grady = (rde[i*NY].depth - rde[i*NY + NY-2].depth)/dy;
break;
}
case (BC_DIRICHLET):
{
rde[i*NY + NY-1].grady = (rde[i*NY + NY-1].depth - rde[i*NY + NY-2].depth)*2.0/dy;
break;
}
}
}
/* compute light angle */
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=1; j<NY-1; j++){
norm = sqrt(vz*vz + rde[i*NY + j].gradx*rde[i*NY + j].gradx + rde[i*NY + j].grady*rde[i*NY + j].grady);
pscal = -rde[i*NY + j].gradx*light[0] - rde[i*NY + j].grady*light[1] + vz;
rde[i*NY+j].cos_depth_angle = pscal/norm;
}
}
/* for monitoring */
min = 0.0;
max = 0.0;
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (rde[i*NY + j].gradx > max) max = rde[i*NY + j].gradx;
if (rde[i*NY + j].gradx < min) min = rde[i*NY + j].gradx;
}
}
printf("gradx min = %.3lg, max = %.3lg\n", min, max);
min = 0.0;
max = 0.0;
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (rde[i*NY + j].grady > max) max = rde[i*NY + j].grady;
if (rde[i*NY + j].grady < min) min = rde[i*NY + j].grady;
}
}
printf("grady min = %.3lg, max = %.3lg\n", min, max);
min = 0.0;
max = 0.0;
#pragma omp parallel for private(i,j)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (rde[i*NY + j].depth > max) max = rde[i*NY + j].depth;
if (rde[i*NY + j].depth < min) min = rde[i*NY + j].depth;
}
}
printf("Depth min = %.3lg, max = %.3lg\n", min, max);
// for (j=0; j<NY; j++)
// {
// for (i=0; i<2; i++){
// printf("point (%03i,%03i): depth %.03lg, gradient (%.03lg, %.03lg)\n", i, j, rde[i*NY + j].depth, rde[i*NY + j].gradx, rde[i*NY + j].grady);
// }
// for (i=NX-2; i<NX; i++){
// printf("point (%03i,%03i): depth %.03lg, gradient (%.03lg, %.03lg)\n", i, j, rde[i*NY + j].depth, rde[i*NY + j].gradx, rde[i*NY + j].grady);
// }
// }
return(max);
}
void compute_forcing_schedule(int t, t_wave_sphere wsphere[NX*NY])
/* compute periodic forcing */
{
int i, j;
double phase;
phase = DPI*(double)t/(double)FORCING_PERIOD + ZERO_MERIDIAN*PI/180.0 + FORCING_SHIFT*PID;
for (i=0; i<NX; i++) for (j=0.0; j<NY; j++)
{
wsphere[i*NY+j].force = FORCING_AMP*wsphere[i*NY+j].stheta*sin(2.0*(wsphere[i*NY+j].phi - phase));
wsphere[i*NY+j].force += FORCING_CONST_AMP*wsphere[i*NY+j].stheta*cos(2.0*(wsphere[i*NY+j].phi));
}
moon_position = (int)((double)NX*(phase/DPI + 0.625));
while (moon_position < 0) moon_position += NX;
while (moon_position >= NX) moon_position -= NX;
// i = NX/2;
i = moon_position;
printf("Phase = %.5lg, Forcing at i = %i: %.5lg, Moon position = %i\n", phase, i, wsphere[i*NY+NY/2].force, moon_position);
}
void evolve_wave_half(double *phi_in[NFIELDS], double *phi_out[NFIELDS], short int xy_in[NX*NY], double potential_field[NX*NY], double vector_potential_field[2*NX*NY],
double gfield[2*NX*NY], t_rde rde[NX*NY], t_wave_sphere wsphere[NX*NY])
/* time step of field evolution */
{
int i, j, k, iplus, iminus, jplus, jminus, ropening, w;
double x, y, z, deltax, deltay, deltaz, rho, rhox, rhoy, pot, u, v, ux, uy, vx, vy, test = 0.0, dx, dy, xy[2], padding, a, eta, etax, etay, sum;
double *delta_phi[NLAPLACIANS], *nabla_phi, *nabla_psi, *nabla_omega, *delta_vorticity, *delta_pressure, *delta_p, *delta_u, *delta_v, *nabla_rho, *nabla_u, *nabla_v, *nabla_eta;
// double u_bc[NY], v_bc[NY];
static double invsqr3 = 0.577350269; /* 1/sqrt(3) */
static int smooth = 0, y_channels, y_channels1, imin, imax, first = 1;
if (first) /* for D_MAZE_CHANNELS boundary conditions in Euler equation */
{
ropening = (NYMAZE+1)/2;
padding = 0.02;
dy = (YMAX - YMIN - 2.0*padding)/(double)(NYMAZE);
y = YMIN + 0.02 + dy*((double)ropening);
x = YMAX - padding + MAZE_XSHIFT;
xy_to_pos(x, y, xy);
if ((B_DOMAIN == D_MAZE_CHANNELS)||(OBSTACLE_GEOMETRY == D_MAZE_CHANNELS)||(OBSTACLE_GEOMETRY == D_MAZE_CHANNELS_INT))
{
imax = xy[0] + 2;
x = YMIN + padding + MAZE_XSHIFT;
xy_to_pos(x, y, xy);
imin = xy[0] - 2;
if (imin < 5) imin = 5;
}
else
{
imin = 0;
imax = NX;
}
/* average values at poles on sphere */
if (SPHERE) for (k=0; k<NFIELDS; k++)
{
sum = 0.0;
for (i=0; i<NX; i++) for (j=0; j<DPOLE; j++)
sum += phi_in[k][i*NY+j];
sum = sum/(double)(NX*DPOLE);
if (sum > 1.0) sum = 1.0;
if (sum < -1.0) sum = -1.0;
for (i=0; i<NX; i++) for (j=0; j<DPOLE; j++)
phi_in[k][i*NY+j] = sum;
sum = 0.0;
for (i=0; i<NX; i++) for (j=NY-DPOLE-1; j<NY; j++)
sum += phi_in[k][i*NY+j];
sum = sum/(double)(NX*DPOLE);
if (sum > 1.0) sum = 1.0;
if (sum < -1.0) sum = -1.0;
for (i=0; i<NX; i++) for (j=NY-DPOLE-1; j<NY; j++)
phi_in[k][i*NY+j] = sum;
}
first = 0;
}
/* smooth vector fields at poles */
if ((SPHERE)&&(!SMOOTHBLOCKS)) for (k=0; k<NFIELDS; k++) smooth_poles(phi_in[k]);
else for (k=0; k<NFIELDS; k++) block_poles(phi_in[k]);
for (i=0; i<NLAPLACIANS; i++) delta_phi[i] = (double *)malloc(NX*NY*sizeof(double));
if (COMPUTE_PRESSURE)
{
delta_pressure = (double *)malloc(NX*NY*sizeof(double));
delta_p = (double *)malloc(NX*NY*sizeof(double));
}
/* compute the Laplacian of phi */
for (i=0; i<NLAPLACIANS; i++) compute_laplacian_rde(phi_in[i], delta_phi[i], xy_in, wsphere);
if (COMPUTE_PRESSURE) compute_laplacian_rde(phi_in[2], delta_pressure, xy_in, wsphere);
/* compute the gradient of phi if there is a magnetic field */
if (ADD_MAGNETIC_FIELD)
{
nabla_phi = (double *)malloc(2*NX*NY*sizeof(double));
nabla_psi = (double *)malloc(2*NX*NY*sizeof(double));
compute_gradient_xy(phi_in[0], nabla_phi);
compute_gradient_xy(phi_in[1], nabla_psi);
}
switch (RDE_EQUATION){
/* compute gradients of stream function and vorticity for Euler equation */
case (E_EULER_INCOMP):
{
nabla_psi = (double *)malloc(2*NX*NY*sizeof(double));
nabla_omega = (double *)malloc(2*NX*NY*sizeof(double));
compute_gradient_euler(phi_in[0], nabla_psi, wsphere, EULER_GRADIENT_YSHIFT);
compute_gradient_euler(phi_in[1], nabla_omega, wsphere, 0.0);
if (COMPUTE_PRESSURE) compute_pressure_laplacian(phi_in, delta_p);
dx = (XMAX-XMIN)/((double)NX);
dy = (YMAX-YMIN)/((double)NY);
if (SMOOTHEN_VORTICITY) /* beta: try to reduce formation of ripples */
{
if (smooth == 0)
{
delta_vorticity = (double *)malloc(NX*NY*sizeof(double));
compute_laplacian_rde(phi_in[1], delta_vorticity, xy_in, wsphere);
// #pragma omp parallel for private(i,delta_vorticity)
for (i=0; i<NX*NY; i++) phi_in[1][i] += intstep*SMOOTH_FACTOR*delta_vorticity[i];
free(delta_vorticity);
}
smooth++;
if (smooth >= SMOOTHEN_PERIOD) smooth = 0;
}
break;
}
/* compute gradients of fields for compressible Euler equation */
case (E_EULER_COMP):
{
nabla_rho = (double *)malloc(2*NX*NY*sizeof(double));
compute_gradient_euler_test(phi_in[0], nabla_rho, xy_in, wsphere);
compute_velocity_gradients(phi_in, rde, xy_in, wsphere);
if (SMOOTHEN_VELOCITY) /* beta: try to reduce formation of ripples */
{
if (smooth == 0)
{
delta_u = (double *)malloc(NX*NY*sizeof(double));
delta_v = (double *)malloc(NX*NY*sizeof(double));
compute_laplacian_rde(phi_in[1], delta_u, xy_in, wsphere);
compute_laplacian_rde(phi_in[2], delta_v, xy_in, wsphere);
#pragma omp parallel for private(i)
for (i=0; i<NX*NY; i++) phi_in[1][i] += intstep*SMOOTH_FACTOR*delta_u[i];
#pragma omp parallel for private(i)
for (i=0; i<NX*NY; i++) phi_in[2][i] += intstep*SMOOTH_FACTOR*delta_v[i];
free(delta_u);
free(delta_v);
}
smooth++;
if (smooth >= SMOOTHEN_PERIOD) smooth = 0;
}
break;
}
case (E_SHALLOW_WATER):
{
nabla_eta = (double *)malloc(2*NX*NY*sizeof(double));
compute_gradient_euler_test(phi_in[0], nabla_eta, xy_in, wsphere);
compute_velocity_gradients(phi_in, rde, xy_in, wsphere);
if (VISCOSITY > 0.0)
{
delta_u = (double *)malloc(NX*NY*sizeof(double));
delta_v = (double *)malloc(NX*NY*sizeof(double));
compute_laplacian_rde(phi_in[1], delta_u, xy_in, wsphere);
compute_laplacian_rde(phi_in[2], delta_v, xy_in, wsphere);
}
break;
}
default:
{
/* do nothing */
}
}
if (TEST_GRADIENT) {
test = 0.0;
for (i=0; i<2*NX*NY; i++){
test += nabla_v[i]*nabla_v[i];
// test += nabla_omega[i]*nabla_omega[i];
// test += nabla_psi[i]*nabla_psi[i];
}
printf("nabla square = %.5lg\n", test/((double)NX*NY));
}
#pragma omp parallel for private(i,j,k,x,y,z,deltax,deltay,deltaz,rho)
for (i=imin; i<imax; i++){
for (j=0; j<NY; j++){
if (xy_in[i*NY+j]) switch (RDE_EQUATION){
case (E_HEAT):
{
deltax = viscosity*delta_phi[0][i*NY+j];
phi_out[0][i*NY+j] = phi_in[0][i*NY+j] + intstep*deltax;
break;
}
case (E_ALLEN_CAHN):
{
x = phi_in[0][i*NY+j];
deltax = viscosity*delta_phi[0][i*NY+j];
phi_out[0][i*NY+j] = phi_in[0][i*NY+j] + intstep*(deltax + K_AC*x*(1.0-x*x));
break;
}
case (E_CAHN_HILLIARD):
{
/* TO DO */
break;
}
case (E_FHN):
{
x = phi_in[0][i*NY+j];
y = phi_in[1][i*NY+j];
deltax = viscosity*delta_phi[0][i*NY+j];
phi_out[0][i*NY+j] = phi_in[0][i*NY+j] + intstep*(deltax + x*(1.0-x*x) + y);
phi_out[1][i*NY+j] = phi_in[0][i*NY+j] + intstep*EPSILON*(- invsqr3 - FHNC - FHNA*x);
break;
}
case (E_RPS):
{
x = phi_in[0][i*NY+j];
y = phi_in[1][i*NY+j];
z = phi_in[2][i*NY+j];
rho = x + y + z;
deltax = viscosity*delta_phi[0][i*NY+j];
deltay = viscosity*delta_phi[1][i*NY+j];
deltaz = viscosity*delta_phi[2][i*NY+j];
phi_out[0][i*NY+j] = x + intstep*(deltax + x*(1.0 - rho - RPSA*y));
phi_out[1][i*NY+j] = y + intstep*(deltay + y*(1.0 - rho - RPSA*z));
phi_out[2][i*NY+j] = z + intstep*(deltaz + z*(1.0 - rho - RPSA*x));
break;
}
case (E_RPSLZ):
{
rho = 0.0;
for (k=0; k<5; k++) rho += phi_in[k][i*NY+j];
for (k=0; k<5; k++)
{
x = phi_in[k][i*NY+j];
y = phi_in[(k+1)%5][i*NY+j];
z = phi_in[(k+3)%5][i*NY+j];
phi_out[k][i*NY+j] = x + intstep*(delta_phi[k][i*NY+j] + x*(1.0 - rho - RPSA*y - rpslzb*z));
}
break;
}
case (E_SCHRODINGER):
{
phi_out[0][i*NY+j] = phi_in[0][i*NY+j] - intstep*delta_phi[1][i*NY+j];
phi_out[1][i*NY+j] = phi_in[1][i*NY+j] + intstep*delta_phi[0][i*NY+j];
if ((ADD_POTENTIAL)||(ADD_MAGNETIC_FIELD))
{
pot = potential_field[i*NY+j];
phi_out[0][i*NY+j] += intstep*pot*phi_in[1][i*NY+j];
phi_out[1][i*NY+j] -= intstep*pot*phi_in[0][i*NY+j];
}
if (ADD_MAGNETIC_FIELD)
{
vx = vector_potential_field[i*NY+j];
vy = vector_potential_field[NX*NY+i*NY+j];
phi_out[0][i*NY+j] -= 2.0*intstep*(vx*nabla_phi[i*NY+j] + vy*nabla_phi[NX*NY+i*NY+j]);
phi_out[1][i*NY+j] -= 2.0*intstep*(vx*nabla_psi[i*NY+j] + vy*nabla_psi[NX*NY+i*NY+j]);
}
break;
}
case (E_EULER_INCOMP):
{
phi_out[0][i*NY+j] = phi_in[0][i*NY+j] + intstep*POISSON_STIFFNESS*(delta_phi[0][i*NY+j] + phi_in[1][i*NY+j]*dx*dx);
// phi_out[0][i*NY+j] += intstep*EULER_GRADIENT_YSHIFT;
phi_out[1][i*NY+j] = phi_in[1][i*NY+j] - intstep*K_EULER*(nabla_omega[i*NY+j]*nabla_psi[NX*NY+i*NY+j]);
phi_out[1][i*NY+j] += intstep*K_EULER*(nabla_omega[NX*NY+i*NY+j]*nabla_psi[i*NY+j]);
if (COMPUTE_PRESSURE)
{
phi_out[2][i*NY+j] = phi_in[2][i*NY+j] + intstep*POISSON_STIFFNESS*(delta_pressure[i*NY+j] - delta_p[i*NY+j]);
phi_out[2][i*NY+j] *= exp(-2.0e-3);
}
break;
}
case (E_EULER_COMP):
{
rho = phi_in[0][i*NY+j];
if (rho == 0.0) rho = 1.0e-1;
u = phi_in[1][i*NY+j];
v = phi_in[2][i*NY+j];
rhox = nabla_rho[i*NY+j];
rhoy = nabla_rho[NX*NY+i*NY+j];
ux = rde[i*NY+j].dxu;
uy = rde[i*NY+j].dyu;
vx = rde[i*NY+j].dxv;
vy = rde[i*NY+j].dyv;
phi_out[0][i*NY+j] = rho - intstep*C_EULER_COMP*(u*rhox + v*rhoy + rho*(ux + vy));
phi_out[1][i*NY+j] = u - intstep*(u*ux + v*uy + K_EULER_INC*rhox/rho);
phi_out[2][i*NY+j] = v - intstep*(u*vx + v*vy + K_EULER_INC*rhoy/rho);
if (ADD_FORCE_FIELD)
{
phi_out[1][i*NY+j] += intstep*gfield[i*NY+j];
phi_out[2][i*NY+j] += intstep*gfield[NX*NY+i*NY+j];
}
if (ADD_CORIOLIS_FORCE)
{
if (SPHERE)
{
phi_out[1][i*NY+j] += intstep*G_FIELD*v*wsphere[i*NY+j].ctheta;
phi_out[2][i*NY+j] -= intstep*G_FIELD*u*wsphere[i*NY+j].reg_cottheta;
// phi_out[1][i*NY+j] += intstep*G_FIELD*v;
// phi_out[2][i*NY+j] -= intstep*G_FIELD*u;
// phi_out[1][i*NY+j] -= intstep*G_FIELD*v;
// phi_out[2][i*NY+j] += intstep*G_FIELD*u;
// phi_out[1][i*NY+j] -= intstep*G_FIELD*v*wsphere[i*NY+j].ctheta;
// phi_out[2][i*NY+j] += intstep*G_FIELD*u*wsphere[i*NY+j].ctheta;
}
else
{
phi_out[1][i*NY+j] += intstep*G_FIELD*v;
phi_out[2][i*NY+j] -= intstep*G_FIELD*u;
}
}
break;
}
case (E_SHALLOW_WATER):
{
eta = phi_in[0][i*NY+j];
if (eta == 0.0) eta = 1.0e-6;
u = phi_in[1][i*NY+j];
v = phi_in[2][i*NY+j];
etax = nabla_eta[i*NY+j];
etay = nabla_eta[NX*NY+i*NY+j];
ux = rde[i*NY+j].dxu;
uy = rde[i*NY+j].dyu;
vx = rde[i*NY+j].dxv;
vy = rde[i*NY+j].dyv;
// printf("etax = %.3lg, etay = %.3lg, ux = %.3lg, uy = %.3lg, vx = %.3lg, vy = %.3lg\n", etax, etay, ux, uy, vx, vy);
/* do not evolve wave at high altitude */
if (FLOODING)
{
if (!wsphere[i*NY+j].evolve_wave)
{
phi_out[0][i*NY+j] = eta;
phi_out[1][i*NY+j] = 0.0;
phi_out[2][i*NY+j] = 0.0;
break;
}
}
if (SPHERE)
{
/* TODO */
if ((j > DSMOOTH)&&(j < NY-DSMOOTH))
{
phi_out[0][i*NY+j] = eta - intstep*(u*etax + v*etay + eta*(ux + vy));
phi_out[1][i*NY+j] = u - intstep*(u*ux + v*uy + G_FIELD*etax);
phi_out[2][i*NY+j] = v - intstep*(u*vx + v*vy + G_FIELD*etay);
}
else
{
// phi_out[0][i*NY+j] = SWATER_MIN_HEIGHT;
phi_out[0][i*NY+j] = eta;
phi_out[1][i*NY+j] = 0.0;
phi_out[2][i*NY+j] = 0.0;
}
}
else
{
phi_out[0][i*NY+j] = eta - intstep*(u*etax + v*etay + eta*(ux + vy));
phi_out[1][i*NY+j] = u - intstep*(u*ux + v*uy + G_FIELD*etax);
phi_out[2][i*NY+j] = v - intstep*(u*vx + v*vy + G_FIELD*etay);
}
if (ADD_CORIOLIS_FORCE)
{
phi_out[1][i*NY+j] += intstep*SWATER_CORIOLIS_FORCE*v*wsphere[i*NY+j].ctheta;
phi_out[2][i*NY+j] -= intstep*SWATER_CORIOLIS_FORCE*u*wsphere[i*NY+j].reg_cottheta;
}
if (VISCOSITY > 0.0)
{
phi_out[1][i*NY+j] += intstep*VISCOSITY*delta_u[i*NY+j];
phi_out[2][i*NY+j] += intstep*VISCOSITY*delta_v[i*NY+j];
}
if (DISSIPATION > 0.0)
{
phi_out[1][i*NY+j] -= intstep*DISSIPATION*u;
phi_out[2][i*NY+j] -= intstep*DISSIPATION*v;
}
if ((DISSIPATION_EXT > 0.0)&&(!wsphere[i*NY+j].indomain))
{
phi_out[1][i*NY+j] -= intstep*DISSIPATION_EXT*u;
phi_out[2][i*NY+j] -= intstep*DISSIPATION_EXT*v;
}
if (ADD_FORCE_FIELD)
{
phi_out[1][i*NY+j] += intstep*gfield[i*NY+j];
phi_out[2][i*NY+j] += intstep*gfield[NX*NY+i*NY+j];
}
if (ADD_MOON_FORCING)
{
phi_out[0][i*NY+j] += intstep*wsphere[i*NY+j].force;
}
if ((VARIABLE_DEPTH)&&(j > DSMOOTH)&&(j < NY-DSMOOTH))
{
phi_out[0][i*NY+j] -= intstep*SWATER_VARDEPTH_FACTOR*rde[i*NY+j].depth*(ux + vy);
phi_out[0][i*NY+j] -= intstep*SWATER_VARDEPTH_FACTOR*rde[i*NY+j].gradx*u;
phi_out[0][i*NY+j] -= intstep*SWATER_VARDEPTH_FACTOR*rde[i*NY+j].grady*v;
}
if ((j <= DSMOOTH)||(j >= NY-DSMOOTH))
{
// printf("Pole reset\n");
phi_out[0][i*NY+j] = SWATER_MIN_HEIGHT;
}
break;
}
}
}
}
/* in-flow/out-flow b.c. for incompressible Euler equation */
if (((RDE_EQUATION == E_EULER_INCOMP)||(RDE_EQUATION == E_EULER_COMP))&&(IN_OUT_FLOW_BC > 0))
set_in_out_flow_bc(phi_out, xy_in, flow_speed);
// if (TEST_GRADIENT) {
// test = 0.0;
// for (i=0; i<NX*NY; i++){
// test += delta_phi[0][i] + phi_out[1][i]*dx*dx;
// }
// printf("Delta psi + omega = %.5lg\n", test/((double)NX*NY));
// }
if (FLOOR) for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (xy_in[i*NY+j] != 0) for (k=0; k<NFIELDS; k++)
{
if (phi_out[k][i*NY+j] > VMAX) phi_out[k][i*NY+j] = VMAX;
if (phi_out[k][i*NY+j] < -VMAX) phi_out[k][i*NY+j] = -VMAX;
}
}
}
for (i=0; i<NLAPLACIANS; i++) free(delta_phi[i]);
if (ADD_MAGNETIC_FIELD)
{
free(nabla_phi);
free(nabla_psi);
}
if (RDE_EQUATION == E_EULER_INCOMP)
{
free(nabla_psi);
free(nabla_omega);
}
else if (RDE_EQUATION == E_EULER_COMP)
{
free(nabla_rho);
}
else if (RDE_EQUATION == E_SHALLOW_WATER)
{
free(nabla_eta);
if (VISCOSITY > 0.0)
{
free(delta_u);
free(delta_v);
}
}
if (COMPUTE_PRESSURE)
{
free(delta_pressure);
free(delta_p);
}
}
void evolve_wave(double *phi[NFIELDS], double *phi_tmp[NFIELDS], short int xy_in[NX*NY],
double potential_field[NX*NY], double vector_potential_field[2*NX*NY],
double gfield[2*NX*NY], t_rde rde[NX*NY], t_wave_sphere wsphere[NX*NY])
/* time step of field evolution */
{
evolve_wave_half(phi, phi_tmp, xy_in, potential_field, vector_potential_field, gfield, rde, wsphere);
evolve_wave_half(phi_tmp, phi, xy_in, potential_field, vector_potential_field, gfield, rde, wsphere);
}
void update_tracer_table(double tracers[2*N_TRACERS*NSTEPS], t_rde rde[NX*NY], int time)
/* update tracer information in rde */
{
int tracer, t, t1, maxtime, i, j, n, ij[2], length = 50, cell, oldcell;
double x, y, x1, y1, dist;
static double maxlength;
static int first = 1;
if (first)
{
maxlength = pow(0.01*(XMAX - XMIN), 2.0);
first = 0;
}
#pragma omp parallel for private(cell)
for (cell=0; cell<NX*NY; cell++)
{
rde[cell].tracer = 0;
rde[cell].prev_cell = cell;
rde[cell].n_tracer_pts = 0;
}
maxtime = length;
if (maxtime > time) maxtime = time;
#pragma omp parallel for private(tracer)
for (tracer = 0; tracer < N_TRACERS; tracer++)
{
x1 = XMIN;
y1 = YMIN;
for (t = 0; t < maxtime; t++)
{
t1 = time - t;
x = tracers[t1*2*N_TRACERS + 2*tracer];
y = tracers[t1*2*N_TRACERS + 2*tracer + 1];
xy_to_ij(x, y, ij);
cell = ij[0]*NY + ij[1];
n = rde[cell].n_tracer_pts;
if (n < NMAX_TRACER_PTS)
{
rde[cell].tracerx[n] = x;
rde[cell].tracery[n] = y;
rde[cell].n_tracer_pts++;
rde[cell].tracer = length - t;
}
// else printf("More than %i tracer points per cell\n", NMAX_TRACER_PTS);
dist = (x-x1)*(x-x1) + (y-y1)*(y-y1);
if ((cell != oldcell)&&(t > 0)&&(dist < maxlength))
rde[cell].prev_cell = oldcell;
oldcell = cell;
x1 = x;
y1 = y;
}
}
}
void evolve_tracers(double *phi[NFIELDS], double tracers[2*N_TRACERS*NSTEPS], t_rde rde[NX*NY], int time, int nsteps, double step)
/* time steps of tracer particle evolution (for Euler equation) */
{
int tracer, i, j, n, t, ij[2], iplus, jplus, prev_cell, new_cell;
double x, y, xy[2], vx, vy;
static int n_respawn = 0;
step = TRACERS_STEP;
for (tracer = 0; tracer < N_TRACERS; tracer++)
{
x = tracers[time*2*N_TRACERS + 2*tracer];
y = tracers[time*2*N_TRACERS + 2*tracer + 1];
// printf("Tracer %i position (%.2f, %.2f)\n", tracer, x, y);
for (t=0; t<nsteps; t++)
{
xy_to_ij_safe(x, y, ij);
i = ij[0];
j = ij[1];
switch (RDE_EQUATION) {
case (E_EULER_INCOMP):
{
iplus = i + 1; if (iplus == NX) iplus = 0;
jplus = j + 1; if (jplus == NY) jplus = 0;
vx = phi[0][i*NY+jplus] - phi[0][i*NY+j];
vy = -(phi[0][iplus*NY+j] - phi[0][i*NY+j]);
if (j == 0) vx += EULER_GRADIENT_YSHIFT;
else if (j == NY-1) vx -= EULER_GRADIENT_YSHIFT;
break;
}
case (E_EULER_COMP):
{
vx = phi[1][i*NY+j];
vy = phi[2][i*NY+j];
break;
}
case (E_SHALLOW_WATER):
{
vx = phi[1][i*NY+j];
vy = phi[2][i*NY+j];
break;
}
}
// v = module2(vx, vy);
// if ((v > 0.0)&&(v < 0.1))
// {
// vx = vx*0.1/v;
// vy = vy*0.1/v;
// }
// printf("(i, j) = (%i, %i), Tracer %i velocity (%.6f, %.6f)\n", i, j, tracer, vx, vy);
x += vx*step;
y += vy*step;
}
// printf("Tracer %i velocity (%.2f, %.2f)\n", tracer, vx, vy);
if (x > XMAX) x += (XMIN - XMAX);
if (x < XMIN) x += (XMAX - XMIN);
if (y > YMAX) y += (YMIN - YMAX);
if (y < YMIN) y += (YMAX - YMIN);
if (time+1 < NSTEPS)
{
if ((RESPAWN_TRACERS)&&((double)rand()/RAND_MAX < RESPAWN_PROBABILTY))
{
x = XMIN + 0.05 + (XMAX - XMIN - 0.1)*rand()/RAND_MAX;
y = YMIN + 0.05 + (YMAX - YMIN - 0.1)*rand()/RAND_MAX;
n_respawn++;
printf("Respawning tracer %i, %i respawns\n", tracer, n_respawn);
}
tracers[(time+1)*2*N_TRACERS + 2*tracer] = x;
tracers[(time+1)*2*N_TRACERS + 2*tracer + 1] = y;
}
}
if ((PLOT_3D)&&(time+1 < NSTEPS)) update_tracer_table(tracers, rde, time);
}
void print_level(int level)
{
double pos[2];
char message[50];
glColor3f(1.0, 1.0, 1.0);
sprintf(message, "Level %i", level);
xy_to_pos(XMIN + 0.1, YMAX - 0.2, pos);
write_text(pos[0], pos[1], message);
}
void print_parameters(double *phi[NFIELDS], t_rde rde[NX*NY], short int xy_in[NX*NY], double time, short int left, double viscosity, double noise)
{
char message[100], message2[100];
double density, hue, rgb[3], logratio, x, y, pos[2], probas[2], speed1, speed2;
static double xbox, xtext, boxwidth, boxheight;
static int first = 1;
if (first)
{
if (WINWIDTH > 1280)
{
boxheight = 0.035;
boxwidth = 0.21;
if (left)
{
xbox = XMIN + 0.4;
xtext = XMIN + 0.2;
}
else
{
xbox = XMAX - 0.49;
xtext = XMAX - 0.65;
// xbox = XMAX - 0.39;
// xtext = XMAX - 0.55;
}
}
else
{
boxwidth = 0.3;
boxheight = 0.05;
if (left)
{
xbox = XMIN + 0.4;
xtext = XMIN + 0.1;
}
else
{
xbox = XMAX - 0.49;
xtext = XMAX - 0.71;
// xbox = XMAX - 0.39;
// xtext = XMAX - 0.61;
}
}
first = 0;
}
if (PRINT_PROBABILITIES)
{
compute_probabilities(rde, xy_in, probas);
printf("pleft = %.3lg, pright = %.3lg\n", probas[0], probas[1]);
x = XMIN + 0.15*(XMAX - XMIN);
y = YMIN + 0.3*(YMAX - YMIN);
erase_area_hsl(x, y, boxwidth, boxheight, 0.0, 0.9, 0.0);
glColor3f(1.0, 1.0, 1.0);
sprintf(message, "Proba %.3f", probas[0]);
write_text(x, y, message);
x = XMIN + 0.72*(XMAX - XMIN);
y = YMIN + 0.68*(YMAX - YMIN);
erase_area_hsl(x, y, boxwidth, boxheight, 0.0, 0.9, 0.0);
glColor3f(1.0, 1.0, 1.0);
sprintf(message, "Proba %.3f", probas[1]);
write_text(x, y, message);
}
else
{
y = YMAX - 0.1;
erase_area_hsl(xbox, y + 0.02, boxwidth, boxheight, 0.0, 0.9, 0.0);
glColor3f(1.0, 1.0, 1.0);
if (PRINT_TIME) sprintf(message, "Time %.3f", time);
else if (PRINT_VISCOSITY) sprintf(message, "Viscosity %.3f", viscosity);
else if (PRINT_RPSLZB) sprintf(message, "b = %.3f", rpslzb);
else if (PRINT_NOISE) sprintf(message, "noise %.3f", noise);
else if (PRINT_FLOW_SPEED) sprintf(message, "Speed %.3f", flow_speed);
else if (PRINT_AVERAGE_SPEED)
{
compute_average_speeds(phi, rde, &speed1, &speed2);
sprintf(message, "Average vx %.3f", speed2);
sprintf(message2, "Average vx %.3f", speed1);
}
if (PLOT_3D) write_text(xtext, y, message);
else
{
xy_to_pos(xtext, y, pos);
write_text(pos[0], pos[1], message);
if (PRINT_AVERAGE_SPEED)
{
y = YMIN + 0.1;
erase_area_hsl(xbox, y + 0.02, boxwidth, boxheight, 0.0, 0.9, 0.0);
glColor3f(1.0, 1.0, 1.0);
xy_to_pos(xtext, y, pos);
write_text(pos[0], pos[1], message2);
}
}
}
}
void draw_color_bar_palette(int plot, double range, int palette, int circular, int fade, double fade_value)
{
double width = 0.14;
// double width = 0.2;
if (PLOT_3D)
{
if (ROTATE_COLOR_SCHEME)
draw_color_scheme_palette_3d(XMIN + 0.3, YMIN + 0.1, XMAX - 0.3, YMIN + 0.1 + width, plot, -range, range, palette, fade, fade_value);
else if (circular)
draw_circular_color_scheme_palette_3d(XMAX - 2.0*width, YMAX - 2.0*width, 1.0*width, plot, -range, range, palette, fade, fade_value);
else
draw_color_scheme_palette_3d(XMAX - 1.5*width, YMIN + 0.1, XMAX - 0.5*width, YMAX - 0.1, plot, -range, range, palette, fade, fade_value);
}
else
{
if (circular)
draw_circular_color_scheme_palette_fade(XMAX - 2.0*width, YMAX - 2.0*width, 1.0*width, plot, -range, range, palette, fade, fade_value);
else if (ROTATE_COLOR_SCHEME)
draw_color_scheme_palette_fade(XMIN + 0.8, YMIN + 0.05, XMAX - 0.8, YMIN + 0.05 + width, plot, -range, range, palette, fade, fade_value);
else
draw_color_scheme_palette_fade(XMAX - 1.5*width, YMIN + 0.1, XMAX - 0.5*width, YMAX - 0.1, plot, -range, range, palette, fade, fade_value);
}
}
double noise_schedule(int i)
{
double ratio;
if (i < NOISE_INITIAL_TIME) return (NOISE_INTENSITY);
else
{
ratio = (double)(i - NOISE_INITIAL_TIME)/(double)(NSTEPS - NOISE_INITIAL_TIME);
return (NOISE_INTENSITY*(1.0 + ratio*(NOISE_FACTOR - 1.0)));
}
}
double viscosity_schedule(int i)
{
double ratio;
if (i < VISCOSITY_INITIAL_TIME) return (VISCOSITY);
else
{
ratio = (double)(i - VISCOSITY_INITIAL_TIME)/(double)(NSTEPS - VISCOSITY_INITIAL_TIME);
return (VISCOSITY*(1.0 + ratio*(VISCOSITY_FACTOR - 1.0)));
}
}
double rpslzb_schedule(int i)
{
double ratio;
if (i < RPSLZB_INITIAL_TIME) return (RPSLZB);
else if (i > NSTEPS - RPSLZB_FINAL_TIME) return(RPSLZB - RPSLZB_CHANGE);
else
{
ratio = (double)(i - RPSLZB_INITIAL_TIME)/(double)(NSTEPS - RPSLZB_INITIAL_TIME - RPSLZB_FINAL_TIME);
return (RPSLZB - ratio*RPSLZB_CHANGE);
}
}
double flow_speed_schedule(int i)
{
double ratio;
ratio = (double)i/(double)NSTEPS;
return (IN_OUT_FLOW_MIN_AMP + (IN_OUT_FLOW_AMP - IN_OUT_FLOW_MIN_AMP)*ratio);
}
void viewpoint_schedule(int i)
/* change position of observer */
{
int j;
double angle, ca, sa, r1, interpolate, rho;
static double observer_initial[3], r, ratio, rho0, zmax;
static int first = 1;
if (first)
{
for (j=0; j<3; j++) observer_initial[j] = observer[j];
r1 = observer[0]*observer[0] + observer[1]*observer[1];
r = sqrt(r1 + observer[2]*observer[2]);
ratio = r/sqrt(r1);
rho0 = module2(observer[0], observer[1]);
if (vabs(rho0) < 0.001) rho0 = 0.001;
zmax = r*sin(MAX_LATITUDE*PI/180.0);
first = 0;
}
interpolate = (double)i/(double)NSTEPS;
angle = (ROTATE_ANGLE*DPI/360.0)*interpolate;
// printf("i = %i, interpolate = %.3lg, angle = %.3lg\n", i, interpolate, angle);
ca = cos(angle);
sa = sin(angle);
switch (VIEWPOINT_TRAJ)
{
case (VP_HORIZONTAL):
{
observer[0] = ca*observer_initial[0] - sa*observer_initial[1];
observer[1] = sa*observer_initial[0] + ca*observer_initial[1];
break;
}
case (VP_ORBIT):
{
observer[0] = ca*observer_initial[0] - sa*observer_initial[1]*ratio;
observer[1] = ca*observer_initial[1] + sa*observer_initial[0]*ratio;
observer[2] = ca*observer_initial[2];
break;
}
case (VP_ORBIT2):
{
observer[0] = ca*observer_initial[0] - sa*observer_initial[1]*ratio;
observer[1] = ca*observer_initial[1] + sa*observer_initial[0]*ratio;
observer[2] = sa*zmax;
break;
}
case (VP_POLAR):
{
rho = -sa*observer_initial[2] + ca*rho0;
observer[0] = observer_initial[0]*rho/rho0;
observer[1] = observer_initial[1]*rho/rho0;
observer[2] = ca*observer_initial[2] + sa*rho0;
break;
}
}
printf("Angle %.3lg, Observer position (%.3lg, %.3lg, %.3lg)\n", angle, observer[0], observer[1], observer[2]);
}
void animation()
{
double time = 0.0, scale, dx, var, jangle, cosj, sinj, sqrintstep, phishift, thetashift, amp,
intstep0, viscosity_printed, fade_value, noise = NOISE_INTENSITY, x, y, sign, phase;
double *phi[NFIELDS], *phi_tmp[NFIELDS], *potential_field, *vector_potential_field, *tracers, *gfield, *bc_field, *bc_field2;
short int *xy_in;
int i, j, k, s, nvid, field;
static int counter = 0;
t_rde *rde;
t_wave_sphere *wsphere, *wsphere_hr;
/* Since NX and NY are big, it seemed wiser to use some memory allocation here */
for (i=0; i<NFIELDS; i++)
{
phi[i] = (double *)malloc(NX*NY*sizeof(double));
phi_tmp[i] = (double *)malloc(NX*NY*sizeof(double));
}
xy_in = (short int *)malloc(NX*NY*sizeof(short int));
rde = (t_rde *)malloc(NX*NY*sizeof(t_rde));
if (SPHERE)
{
wsphere = (t_wave_sphere *)malloc(NX*NY*sizeof(t_wave_sphere));
init_wave_sphere_rde(wsphere,1);
/* high resolution version for planet simulations */
wsphere_hr = (t_wave_sphere *)malloc(HRES*HRES*NX*NY*sizeof(t_wave_sphere));
init_wave_sphere_rde(wsphere_hr,HRES);
}
npolyline = init_polyline(MDEPTH, polyline);
for (i=0; i<npolyline; i++) printf("vertex %i: (%.3f, %.3f)\n", i, polyline[i].x, polyline[i].y);
npolyrect = init_polyrect(polyrect);
for (i=0; i<npolyrect; i++) printf("polyrect vertex %i: (%.3f, %.3f) - (%.3f, %.3f)\n", i, polyrect[i].x1, polyrect[i].y1, polyrect[i].x2, polyrect[i].y2);
if (ADD_POTENTIAL)
{
potential_field = (double *)malloc(NX*NY*sizeof(double));
initialize_potential(potential_field);
}
else if (ADD_MAGNETIC_FIELD)
{
potential_field = (double *)malloc(NX*NY*sizeof(double));
vector_potential_field = (double *)malloc(2*NX*NY*sizeof(double));
initialize_potential(potential_field);
initialize_vector_potential(vector_potential_field);
}
if (VARIABLE_DEPTH)
{
// water_depth = (t_swater_depth *)malloc(NX*NY*sizeof(t_swater_depth));
max_depth = initialize_water_depth(rde, wsphere, wsphere_hr);
printf("Max depth = %.3lg\n", max_depth);
}
if (ADAPT_STATE_TO_BC)
{
bc_field = (double *)malloc(NX*NY*sizeof(double));
bc_field2 = (double *)malloc(NX*NY*sizeof(double));
initialize_bcfield(bc_field, bc_field2, polyrect, wsphere);
}
if (ADD_FORCE_FIELD)
{
if (!ADAPT_STATE_TO_BC)
{
printf("Error: if ADD_FORCE_FIELD = 1, then ADAPT_STATE_TO_BC should be 1\n");
exit(1);
}
gfield = (double *)malloc(2*NX*NY*sizeof(double));
initialize_gfield(gfield, bc_field, bc_field2, wsphere, wsphere_hr);
}
// if (ADD_TRACERS) tracers = (double *)malloc(2*NSTEPS*N_TRACERS*sizeof(double));
if (ADD_TRACERS) tracers = (double *)malloc(4*NSTEPS*N_TRACERS*sizeof(double));
dx = (XMAX-XMIN)/((double)NX);
intstep = DT/(dx*dx);
intstep0 = intstep;
intstep1 = DT/dx;
viscosity = VISCOSITY;
sqrintstep = sqrt(intstep*(double)NVID);
printf("Integration step %.3lg\n", intstep);
/* initialize field */
// init_random(0.5, 0.4, phi, xy_in);
// init_random(0.5, 0.25, phi, xy_in, wsphere);
// init_random_smoothed(1.0, 0.1, phi, xy_in, wsphere);
// init_gaussian(x, y, mean, amplitude, scalex, phi, xy_in)
// init_coherent_state(0.0, 0.0, 10.0, 0.0, 0.1, phi, xy_in);
// init_coherent_state_sphere(0, 0.0, PID, 10.0, 5.0, 0.1, phi, xy_in, wsphere);
// init_coherent_state_sphere(1, PI, PID, -10.0, 5.0, 0.1, phi, xy_in, wsphere);
// init_coherent_state_sphere(1, PID, PID, 10.0, -5.0, 0.1, phi, xy_in, wsphere);
// init_coherent_state_sphere(1, 3.0*PID, PID, -10.0, -5.0, 0.1, phi, xy_in, wsphere);
// add_coherent_state(-0.75, -0.75, 0.0, 5.0, 0.1, phi, xy_in);
// init_fermion_state(-0.5, 0.5, 2.0, 0.0, 0.1, phi, xy_in);
// init_boson_state(-0.5, 0.5, 2.0, 0.0, 0.1, phi, xy_in);
// init_laminar_flow(0.05, LAMINAR_FLOW_MODULATION, 0.015, 0.1, 1.0, 0.0, 0.1, phi, xy_in);
// for (i=0; i<5; i++)
// for (j=0; j<3; j++)
// {
// x = XMIN + ((double)i - 0.5)*(XMAX-XMIN)/4.0 + 0.15*gaussian();
// y = YMIN + ((double)j - 0.5)*(YMAX-YMIN)/2.0 + 0.15*gaussian();
// sign = (double)((i+j)%2)*2.0 - 1.0;
// add_vortex_state(0.1*sign, x, y, 0.1, -0.35*sign + 0.1*gaussian(), phi, xy_in);
// }
// add_vortex_state(0.2, 0.75, 0.1, 0.3, -0.5, phi, xy_in);
// add_vortex_state(-0.35, -0.75, -0.1, 0.4, 0.5, phi, xy_in);
// add_vortex_state(0.1, -0.3, 0.7, 0.1, -0.5, phi, xy_in);
// init_vortex_state(0.1, 0.4, 0.0, 0.3, -0.1, phi, xy_in);
// add_vortex_state(0.1, -0.4, 0.0, 0.3, 0.1, phi, xy_in);
// init_laminar_flow(double amp, double xmodulation, double ymodulation, double xperiod, double yperiod, double yshift, double density_mod, double *phi[NFIELDS], short int xy_in[NX*NY])
// init_laminar_flow_earth(0.01, phi, xy_in);
//
// add_random_onefield_smoothed(0, 0.0, 0.03, phi, xy_in, wsphere);
// add_random_onefield_smoothed(1, 0.0, 0.07, phi, xy_in, wsphere);
// add_random_onefield_smoothed(2, 0.0, 0.07, phi, xy_in, wsphere);
// init_pressure_gradient_flow(flow_speed_schedule(0), 1.0 + PRESSURE_GRADIENT, 1.0 - PRESSURE_GRADIENT, phi, xy_in, bc_field);
// init_shear_flow_sphere(1.0, 0.25, 0.25, 6, 6, 0.75, phi, xy_in, wsphere);
// phishift = 0.0;
// thetashift = 0.2*PID;
// amp = 1.0;
// init_vortex_state_sphere(0, amp, phishift, PID + thetashift, 0.15, 0.3, phi, xy_in, wsphere);
// init_gaussian_wave(0.7, 0.0, 0.0225, 0.1, SWATER_MIN_HEIGHT, phi, xy_in);
// init_gaussian_wave_sphere(4.0, PID, 0.05, 0.05, SWATER_MIN_HEIGHT, phi, xy_in, wsphere);
// init_linear_wave(-1.0, 0.01, 5.0e-8, 0.25, SWATER_MIN_HEIGHT, phi, xy_in);
// init_swater_laminar_flow_sphere(0, 0.25, 0.00075, 4, 4, 0.0025, SWATER_MIN_HEIGHT, phi, xy_in, wsphere);
// init_tidal_state(1, 0.0015, SWATER_MIN_HEIGHT, phi, xy_in, wsphere);
// init_linear_blob_sphere(0, 1.3*PI, 0.65*PI, 0.0, 0.0, 0.3, 0.1, 0.1, SWATER_MIN_HEIGHT, phi, xy_in, wsphere);
init_expanding_blob_sphere(0, (220.0/180.0)*PI, (140.0/180.0)*PI, 1.0, 0.075, 0.1, SWATER_MIN_HEIGHT, phi, xy_in, wsphere);
// add_gaussian_wave(-1.6, -0.5, 0.015, 0.25, SWATER_MIN_HEIGHT, phi, xy_in);
if (SMOOTHBLOCKS) for (k=0; k<NFIELDS; k++) block_poles(phi[k]);
if (ADAPT_STATE_TO_BC) adapt_state_to_bc(phi, bc_field, xy_in);
init_cfield_rde(phi, xy_in, CPLOT, rde, 0);
if ((PLOT_3D)||(SHADE_2D)) init_zfield_rde(phi, xy_in, ZPLOT, rde, 0);
if (DOUBLE_MOVIE)
{
init_cfield_rde(phi, xy_in, CPLOT_B, rde, 1);
if ((PLOT_3D)||(SHADE_2D)) init_zfield_rde(phi, xy_in, ZPLOT_B, rde, 1);
}
if (ADD_TRACERS) for (i=0; i<N_TRACERS; i++)
{
tracers[2*i] = XMIN + 0.05 + (XMAX - XMIN - 0.1)*rand()/RAND_MAX;
tracers[2*i+1] = YMIN + 0.05 + (YMAX - YMIN - 0.1)*rand()/RAND_MAX;
}
if (ADD_MOON_FORCING) compute_forcing_schedule(0, wsphere);
blank();
glColor3f(0.0, 0.0, 0.0);
glutSwapBuffers();
printf("Drawing wave\n");
draw_wave_rde(0, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
// draw_billiard();
if (PRINT_PARAMETERS) print_parameters(phi, rde, xy_in, time, PRINT_LEFT, VISCOSITY, noise);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 0, 1.0);
glutSwapBuffers();
sleep(SLEEP1);
// printf("Saving frame %i\n", i);
if (MOVIE) for (i=0; i<INITIAL_TIME; i++) save_frame();
for (i=0; i<=NSTEPS; i++)
{
nvid = NVID;
if (CHANGE_VISCOSITY)
{
viscosity = viscosity_schedule(i);
viscosity_printed = viscosity;
printf("Viscosity = %.3lg\n", viscosity);
if ((ADJUST_INTSTEP)&&(viscosity > VISCOSITY_MAX))
{
nvid = (int)((double)NVID*viscosity/VISCOSITY_MAX);
// viscosity = VISCOSITY_MAX;
intstep = intstep0*VISCOSITY_MAX/viscosity;
printf("Nvid = %i, intstep = %.3lg\n", nvid, intstep);
}
}
if (CHANGE_RPSLZB) rpslzb = rpslzb_schedule(i);
if (CHANGE_FLOW_SPEED) flow_speed = flow_speed_schedule(i);
else flow_speed = IN_OUT_FLOW_AMP;
if (ADD_MOON_FORCING) compute_forcing_schedule(i, wsphere);
if (ROTATE_VIEW)
{
viewpoint_schedule(i - INITIAL_TIME);
reset_view = 1;
}
printf("Drawing wave %i\n", i);
draw_wave_rde(0, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
// nvid = (int)((double)NVID*(1.0 + (ACCELERATION_FACTOR - 1.0)*(double)i/(double)NSTEPS));
/* increase integration step */
// intstep = intstep0*exp(log(DT_ACCELERATION_FACTOR)*(double)i/(double)NSTEPS);
// if (intstep > MAX_DT)
// {
// nvid *= intstep/MAX_DT;
// intstep = MAX_DT;
// }
// printf("Steps per frame: %i\n", nvid);
// printf("Integration step %.5lg\n", intstep);
printf("Evolving wave\n");
for (j=0; j<nvid; j++) evolve_wave(phi, phi_tmp, xy_in, potential_field, vector_potential_field, gfield, rde, wsphere);
if (ADAPT_STATE_TO_BC) adapt_state_to_bc(phi, bc_field, xy_in);
if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == 0))
{
phase = (double)i*OSCILLATING_SOURCE_OMEGA;
printf("Adding vibration with phase %.3lg\n", phase);
add_elliptical_vibration(0.0, 0.0, 0.00007*cos(phase), LAMBDA, 1.0, 0.00004*cos(phase), 0.1, 1.0, SWATER_MIN_HEIGHT, phi, xy_in);
}
if (ADD_TRACERS)
{
printf("Evolving tracer particles\n");
evolve_tracers(phi, tracers, rde, i, 10, 0.1);
// for (j=0; j<N_TRACERS; j++)
// printf("Tracer %i position (%.2f, %.2f)\n", j, tracers[2*N_TRACERS*i + 2*j], tracers[2*N_TRACERS*i + 2*j + 1]);
if (!PLOT_3D)
{
printf("Drawing tracer particles\n");
draw_tracers(phi, tracers, i, 0, 1.0);
}
}
if (ANTISYMMETRIZE_WAVE_FCT) antisymmetrize_wave_function(phi, xy_in);
for (j=0; j<NFIELDS; j++) printf("field[%i] = %.3lg\t", j, phi[j][NY/2]);
// for (j=0; j<NFIELDS; j++) printf("field[%i] = %.3lg\t", j, phi[j][NX*NY/2]);
// for (j=0; j<NFIELDS; j++) printf("field[%i] = %.3lg\t", j, phi[j][0]);
printf("\n");
if (ADD_NOISE == 1)
{
// #pragma omp parallel for private(field,j,k)
for (field=0; field<NFIELDS; field++)
for (j=0; j<NX; j++)
for (k=0; k<NY; k++)
phi[field][j*NY+k] += sqrintstep*NOISE_INTENSITY*gaussian();
}
else if (ADD_NOISE == 2)
{
if (CHANGE_NOISE)
{
noise = noise_schedule(i);
// #pragma omp parallel for private(field,j,k)
for (field=0; field<NFIELDS; field++)
for (j=NX/2; j<NX; j++)
for (k=0; k<NY; k++)
phi[field][j*NY+k] += sqrintstep*noise*gaussian();
}
else
{
// #pragma omp parallel for private(field,j,k)
for (field=0; field<NFIELDS; field++)
for (j=NX/2; j<NX; j++)
for (k=0; k<NY; k++)
phi[field][j*NY+k] += sqrintstep*NOISE_INTENSITY*gaussian();
}
}
time += nvid*intstep;
// draw_billiard();
if (PRINT_PARAMETERS) print_parameters(phi, rde, xy_in, time, PRINT_LEFT, viscosity_printed, noise);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 0, 1.0);
// print_level(MDEPTH);
// print_Julia_parameters(i);
if (!((NO_EXTRA_BUFFER_SWAP)&&(MOVIE))) glutSwapBuffers();
// glutSwapBuffers();
// save_frame();
/* modify Julia set */
// set_Julia_parameters(i, phi, xy_in);
if (MOVIE)
// if (0)
{
printf("Saving frame %i\n", i);
// if (NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
save_frame();
if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
{
draw_wave_rde(1, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 0, 1.0, REFRESH_B);
if ((ADD_TRACERS)&&(!PLOT_3D)) draw_tracers(phi, tracers, i, 0, 1.0);
// draw_billiard();
if (PRINT_PARAMETERS) print_parameters(phi, rde, xy_in, time, PRINT_LEFT, viscosity_printed, noise);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 0, 1.0);
glutSwapBuffers();
// if (NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
counter++;
}
else if (NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
/* TEST */
// if (ADAPT_STATE_TO_BC) adapt_state_to_bc(phi, bc_field, xy_in);
/* it seems that saving too many files too fast can cause trouble with the file system */
/* so this is to make a pause from time to time - parameter PAUSE may need adjusting */
if (i % PAUSE == PAUSE - 1)
{
printf("Making a short pause\n");
sleep(PSLEEP);
s = system("mv wave*.tif tif_bz/");
}
}
else printf("Computing frame %i\n", i);
}
if (MOVIE)
{
if (DOUBLE_MOVIE)
{
draw_wave_rde(0, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
if ((ADD_TRACERS)&&(!PLOT_3D)) draw_tracers(phi, tracers, NSTEPS, 0, 1.0);
// draw_billiard();
if (PRINT_PARAMETERS) print_parameters(phi, rde, xy_in, time, PRINT_LEFT, viscosity_printed, noise);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 0, 1.0);
// if (!NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
glutSwapBuffers();
if (!FADE) for (i=0; i<MID_FRAMES; i++) save_frame();
else for (i=0; i<MID_FRAMES; i++)
{
fade_value = 1.0 - (double)i/(double)MID_FRAMES;
draw_wave_rde(0, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 1, fade_value, 0);
if ((ADD_TRACERS)&&(!PLOT_3D)) draw_tracers(phi, tracers, NSTEPS, 1, fade_value);
// draw_billiard();
if (PRINT_PARAMETERS) print_parameters(phi, rde, xy_in, time, PRINT_LEFT, viscosity_printed, noise);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 1, fade_value);
if (!NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
save_frame_counter(NSTEPS + i + 1);
}
draw_wave_rde(1, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 0, 1.0, REFRESH_B);
if ((ADD_TRACERS)&&(!PLOT_3D)) draw_tracers(phi, tracers, NSTEPS, 0, 1.0);
if (PRINT_PARAMETERS) print_parameters(phi, rde, xy_in, time, PRINT_LEFT, viscosity_printed, noise);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 0, 1.0);
glutSwapBuffers();
if (!FADE) for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
else for (i=0; i<END_FRAMES; i++)
{
fade_value = 1.0 - (double)i/(double)END_FRAMES;
draw_wave_rde(1, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 1, fade_value, 0);
if ((ADD_TRACERS)&&(!PLOT_3D)) draw_tracers(phi, tracers, NSTEPS, 1, fade_value);
if (PRINT_PARAMETERS) print_parameters(phi, rde, xy_in, time, PRINT_LEFT, viscosity_printed, noise);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 1, fade_value);
glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
}
}
else
{
if (!FADE) for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
else for (i=0; i<END_FRAMES; i++)
{
fade_value = 1.0 - (double)i/(double)END_FRAMES;
draw_wave_rde(0, phi, xy_in, rde, wsphere, wsphere_hr, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 1, fade_value, 0);
if ((ADD_TRACERS)&&(!PLOT_3D)) draw_tracers(phi, tracers, NSTEPS, 1, fade_value);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 1, fade_value);
glutSwapBuffers();
save_frame_counter(NSTEPS + 1 + counter + i);
}
}
s = system("mv wave*.tif tif_bz/");
}
for (i=0; i<NFIELDS; i++)
{
free(phi[i]);
free(phi_tmp[i]);
}
free(xy_in);
if (SPHERE)
{
free(wsphere);
free(wsphere_hr);
}
if (ADD_POTENTIAL) free(potential_field);
else if (ADD_MAGNETIC_FIELD)
{
free(potential_field);
free(vector_potential_field);
}
// if (VARIABLE_DEPTH) free(water_depth);
if (ADD_TRACERS) free(tracers);
if (ADD_FORCE_FIELD) free(gfield);
if (ADAPT_STATE_TO_BC)
{
free(bc_field);
free(bc_field2);
}
printf("Time %.5lg\n", time);
}
void display(void)
{
time_t rawtime;
struct tm * timeinfo;
time(&rawtime);
timeinfo = localtime(&rawtime);
glPushMatrix();
blank();
glutSwapBuffers();
blank();
glutSwapBuffers();
animation();
sleep(SLEEP2);
glPopMatrix();
glutDestroyWindow(glutGetWindow());
printf("Start local time and date: %s", asctime(timeinfo));
time(&rawtime);
timeinfo = localtime(&rawtime);
printf("Current local time and date: %s", asctime(timeinfo));
}
int main(int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
glutInitWindowSize(WINWIDTH,WINHEIGHT);
glutCreateWindow("FitzHugh-Nagumo equation in a planar domain");
if (PLOT_3D) init_3d();
else init_hres(HRES);
// else init();
glutDisplayFunc(display);
glutMainLoop();
return 0;
}
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