1351 lines
58 KiB
C
1351 lines
58 KiB
C
/*********************************************************************************/
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/* */
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/* Animation of wave equation in a planar domain */
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/* */
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/* N. Berglund, december 2012, may 2021 */
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/* */
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/* UPDATE 24/04: distinction between damping and "elasticity" parameters */
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/* UPDATE 27/04: new billiard shapes, bug in color scheme fixed */
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/* UPDATE 28/04: code made more efficient, with help of Marco Mancini */
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/* */
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/* Feel free to reuse, but if doing so it would be nice to drop a */
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/* line to nils.berglund@univ-orleans.fr - Thanks! */
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/* */
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/* compile with */
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/* gcc -o wave_billiard wave_billiard.c */
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/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
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/* */
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/* OMP acceleration may be more effective after executing */
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/* export OMP_NUM_THREADS=2 in the shell before running the program */
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/* */
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/* To make a video, set MOVIE to 1 and create subfolder tif_wave */
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/* It may be possible to increase parameter PAUSE */
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/* */
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/* create movie using */
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/* ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4 */
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/* */
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/*********************************************************************************/
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/*********************************************************************************/
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/* */
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/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
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/* One could make it much faster by using a GPU */
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/* */
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/*********************************************************************************/
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#include <math.h>
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#include <string.h>
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#include <GL/glut.h>
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#include <GL/glu.h>
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#include <unistd.h>
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#include <sys/types.h>
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#include <tiffio.h> /* Sam Leffler's libtiff library. */
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#include <omp.h>
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#define MOVIE 0 /* set to 1 to generate movie */
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#define SAVE_MEMORY 0 /* set to 1 to save memory when writing tiff images */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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// #define NX 1280 /* number of grid points on x axis */
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// #define NY 720 /* number of grid points on y axis */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 1.0 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */
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// #define CIRCLE_PATTERN 1 /* pattern of circles, see list in global_pdes.c */
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#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
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#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
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#define NPOISSON 340 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define RANDOM_POLY_ANGLE 0 /* set to 1 to randomize angle of polygons */
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#define LAMBDA 0.85 /* parameter controlling the dimensions of domain */
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#define MU 0.03 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 4 /* depth of computation of Menger gasket */
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#define MRATIO 3 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NGRIDX 15 /* number of grid point for grid of disks */
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#define NGRIDY 20 /* number of grid point for grid of disks */
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#define X_SHOOTER -0.2
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#define Y_SHOOTER -0.6
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#define X_TARGET 0.4
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#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
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#define ISO_XSHIFT_LEFT -1.65
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#define ISO_XSHIFT_RIGHT 0.4
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#define ISO_YSHIFT_LEFT -0.05
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#define ISO_YSHIFT_RIGHT -0.05
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#define ISO_SCALE 0.85 /* coordinates for isospectral billiards */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical parameters of wave equation */
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#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */
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#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */
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#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
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#define X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */
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#define OMEGA 0.00133333333 /* frequency of periodic excitation */
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#define K_BC 3.0 /* spatial period of periodic excitation in y direction */
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#define KX_BC 10.0 /* spatial period of periodic excitation in x direction */
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#define KY_BC 3.3333 /* spatial period of periodic excitation in y direction */
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// #define KX_BC 20.0 /* spatial period of periodic excitation in x direction */
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// #define KY_BC 6.66666 /* spatial period of periodic excitation in y direction */
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// #define OMEGA 0.002 /* frequency of periodic excitation */
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// #define K_BC 3.0 /* spatial period of periodic excitation in y direction */
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// #define KX_BC 30.0 /* spatial period of periodic excitation in x direction */
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// #define KY_BC 10.0 /* spatial period of periodic excitation in y direction */
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#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
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#define COURANT 0.02 /* Courant number */
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#define COURANTB 0.015 /* Courant number in medium B */
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// #define COURANTB 0.00666 /* Courant number in medium B */
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#define GAMMA 3.0e-6 /* damping factor in wave equation */
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#define GAMMAB 5.0e-4 /* damping factor in wave equation */
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// #define GAMMA 2.0e-6 /* damping factor in wave equation */
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// #define GAMMAB 2.5e-4 /* damping factor in wave equation */
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#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
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#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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#define KAPPAB 1.0e-6 /* "elasticity" term enforcing oscillations */
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#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
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#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* Boundary conditions, see list in global_pdes.c */
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#define B_COND 3
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/* Parameters for length and speed of simulation */
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#define NSTEPS 2000 /* number of frames of movie */
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// #define NSTEPS 5500 /* number of frames of movie */
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#define NVID 60 /* number of iterations between images displayed on screen */
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#define NSEG 100 /* number of segments of boundary */
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#define INITIAL_TIME 100 /* time after which to start saving frames */
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#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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#define END_FRAMES 100 /* number of still frames at end of movie */
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/* Parameters of initial condition */
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#define INITIAL_AMP 0.2 /* amplitude of initial condition */
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#define INITIAL_VARIANCE 0.002 /* variance of initial condition */
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#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 0
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/* Color schemes */
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#define COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* background */
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#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
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#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
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#define PHASE_FACTOR 1.0 /* factor in computation of phase in color scheme P_3D_PHASE */
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#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define E_SCALE 2500.0 /* scaling factor for energy representation */
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#define LOG_SCALE 1.0 /* scaling factor for energy log representation */
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#define LOG_SHIFT 0.0 /* shift of colors on log scale */
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#define FLUX_SCALE 1.0e4 /* scaling factor for enegy flux represtnation */
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#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */
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/* mangrove properties */
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#define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */
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#define MANGROVE_HUE_MAX -50.0 /* color of saturated mangrove */
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// #define MANGROVE_EMAX 5.0e-3 /* max energy for mangrove to survive */
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#define MANGROVE_EMAX 1.5e-3 /* max energy for mangrove to survive */
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#define RANDOM_RADIUS 1 /* set to 1 for random circle radius */
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#define ERODE_MANGROVES 1 /* set to 1 for mangroves to be eroded */
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#define RECOVER_MANGROVES 1 /* set to 1 to allow mangroves to recover */
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#define MOVE_MANGROVES 1 /* set to 1 for mobile mangroves */
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#define DETACH_MANGROVES 1 /* set to 1 for mangroves to be able to detach */
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#define INERTIA 1 /* set to 1 for taking inertia into account */
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#define REPELL_MANGROVES 1 /* set to 1 for mangroves to repell each other */
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#define DT_MANGROVE 0.1 /* time step for mangrove displacement */
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#define KSPRING 0.05 /* spring constant of mangroves */
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#define KWAVE 4.0 /* constant in force due to wave gradient */
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#define KREPEL 5.0 /* constant in repelling force between mangroves */
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#define REPEL_RADIUS 1.1 /* radius in which repelling force acts (in units of mangrove radius) */
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#define DXMAX 0.02 /* max displacement of mangrove in one time step */
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#define L_DETACH 0.25 /* spring length beyond which mangroves detach */
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#define DAMP_MANGROVE 0.1 /* damping coefficient of mangroves */
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#define MANGROVE_MASS 1.5 /* mass of mangrove of radius MU */
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#define HASHX 25 /* size of hashgrid in x direction */
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#define HASHY 15 /* size of hashgrid in y direction */
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#define HASHMAX 10 /* maximal number of mangroves per hashgrid cell */
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#define HASHGRID_PADDING 0.1 /* padding of hashgrid outside simulation window */
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#define DRAW_COLOR_SCHEME 0 /* set to 1 to plot the color scheme */
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#define COLORBAR_RANGE 8.0 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */
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#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
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/* For debugging purposes only */
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#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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/* the following constants are only used by wave_billiard and wave_3d so far */
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#define COMPARISON 0 /* set to 1 to compare two different patterns */
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#define B_DOMAIN_B 20 /* second domain shape, for comparisons */
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#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */
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#define OSCILLATION_SCHEDULE 3 /* oscillation schedule, see list in global_pdes.c */
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#define ACHIRP 0.2 /* acceleration coefficient in chirp */
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#define DAMPING 0.0 /* damping of periodic excitation */
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/* end of constants only used by wave_billiard and wave_3d */
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/* for compatibility with sub_wave and sub_maze */
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#define NXMAZE 7 /* width of maze */
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#define NYMAZE 7 /* height of maze */
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#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */
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#define RAND_SHIFT 24 /* seed of random number generator */
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#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
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#define ADD_POTENTIAL 0
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#define POT_MAZE 7
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#define POTENTIAL 0
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#define MAZE_WIDTH 0.02 /* half width of maze walls */
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#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */
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#define IOR 7 /* choice of index of refraction, see list in global_pdes.c */
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#define IOR_TOTAL_TURNS 1.5 /* total angle of rotation for IOR_PERIODIC_WELLS_ROTATING */
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#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */
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#define WAVE_PACKET_SOURCE_TYPE 1 /* type of wave packet sources */
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#define N_WAVE_PACKETS 15 /* number of wave packets */
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#define OSCIL_LEFT_YSHIFT 0.0 /* y-dependence of left oscillation (for non-horizontal waves) */
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#define DRAW_WAVE_PROFILE 0 /* set to 1 to draw a profile of the wave */
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#define OSCILLATING_SOURCE_PERIOD 20 /* period of oscillating source */
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#define MU_B 1.0 /* parameter controlling the dimensions of domain */
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#define DRAW_WAVE_PROFILE 0 /* set to 1 to draw a profile of the wave */
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#define VERTICAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
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#define DRAW_WAVE_TIMESERIES 0 /* set to 1 to draw a time series of the wave */
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#define WALL_WIDTH 0.1 /* width of wall separating lenses */
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#define OSCIL_YMAX 0.35 /* defines oscillation range */
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#define MESSAGE_LDASH 14 /* length of dash for Morse code message */
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#define MESSAGE_LDOT 8 /* length of dot for Morse code message */
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#define MESSAGE_LINTERVAL 54 /* length of interval between dashes/dots for Morse code message */
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#define MESSAGE_LINTERLETTER 60 /* length of interval between letters for Morse code message */
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#define MESSAGE_LSPACE 48 /* length of space for Morse code message */
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#define MESSAGE_INITIAL_TIME 100 /* initial time before starting message for Morse code message */
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#define AVRG_E_FACTOR 0.95 /* controls time window size in P_AVERAGE_ENERGY scheme */
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#define HORIZONTAL_WAVE_PROFILE 0 /* set to 1 to draw wave profile vertically */
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#define WAVE_PROFILE_X 2.1 /* value of x to sample wave profile */
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#define WAVE_PROFILE_Y -1.0 /* value of y to sample wave profile */
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#define PROFILE_AT_BOTTOM 1 /* draw wave profile at bottom instead of top */
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#define AVERAGE_WAVE_PROFILE 1 /* set to 1 to draw time-average of wave profile squared*/
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#define TIMESERIES_NVALUES 400 /* number of values plotted in time series */
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#define DRAW_WAVE_SOURCE 0 /* set to 1 to draw source of wave at (wave_source_x, wave_source_y) */
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/* end of constants only used by sub_wave and sub_maze */
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#include "global_pdes.c"
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#include "sub_maze.c" /* support for generating mazes */
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#include "sub_wave.c"
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#include "wave_common.c"
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double courant2, courantb2; /* Courant parameters squared */
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typedef struct
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{
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double xc, yc, radius; /* center and radius of circle */
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short int active; /* circle is active */
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double energy; /* dissipated energy */
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double yc_wrapped; /* position of circle centers wrapped vertically */
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double anchorx; /* points moving circles are attached to */
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double anchory; /* points moving circles are attached to */
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double vx; /* x velocity of circles */
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double vy; /* y velocity of circles */
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double radius_initial; /* initial circle radii */
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double mass_inv; /* inverse of mangrove mass */
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short int attached; /* has value 1 if the circle is attached to its anchor */
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int hashx; /* hash grid positions of mangroves */
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int hashy; /* hash grid positions of mangroves */
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} t_mangrove;
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typedef struct
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{
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int number; /* total number of mangroves in cell */
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int mangroves[HASHMAX]; /* numbers of mangroves in cell */
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} t_hashgrid;
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/*********************/
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/* animation part */
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/*********************/
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void init_bc_phase(double left_bc[NY], double top_bc[NX], double bot_bc[NX])
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/* initialize boundary condition phase KX*x + KY*y */
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{
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int i, j;
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double xy[2];
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for (j=0; j<NY; j++)
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{
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ij_to_xy(0, j, xy);
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left_bc[j] = KX_BC*XMIN + KY_BC*xy[1];
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}
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for (i=0; i<NX; i++)
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{
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ij_to_xy(i, 0, xy);
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bot_bc[i] = KX_BC*xy[0] + KY_BC*YMIN;
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top_bc[i] = KX_BC*xy[0] + KY_BC*YMAX;
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}
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}
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// void evolve_wave_half_old(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX], double *psi_out[NX],
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// short int *xy_in[NX])
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// // void evolve_wave_half(phi_in, psi_in, phi_out, psi_out, xy_in)
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// /* time step of field evolution */
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// /* phi is value of field at time t, psi at time t-1 */
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// {
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// int i, j, iplus, iminus, jplus, jminus, tb_shift;
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// double delta, x, y, c, cc, gamma, kappa, phase, phasemin;
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// static long time = 0;
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// static int init_bc = 1;
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// static double left_bc[NY], top_bc[NX], bot_bc[NX];
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//
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// time++;
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//
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// /* initialize boundary condition phase KX*x + KY*y */
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// if ((OSCILLATE_LEFT)&&(init_bc))
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// {
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// init_bc_phase(left_bc, top_bc, bot_bc);
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// tb_shift = (int)((X_SHIFT - XMIN)*(double)NX/(XMAX - XMIN));
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// printf("tb_shift %i\n", tb_shift);
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// init_bc = 0;
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// }
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//
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// #pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y,c,cc,gamma,kappa)
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// for (i=0; i<NX; i++){
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// for (j=0; j<NY; j++){
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// if (xy_in[i][j])
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// {
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// c = COURANT;
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// cc = courant2;
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// gamma = GAMMA;
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// kappa = KAPPA;
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// }
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// else if (TWOSPEEDS)
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// {
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// c = COURANTB;
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// cc = courantb2;
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// gamma = GAMMAB;
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// kappa = KAPPAB;
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// }
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//
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// if ((TWOSPEEDS)||(xy_in[i][j])){
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// /* discretized Laplacian for various boundary conditions */
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// if ((B_COND == BC_DIRICHLET)||(B_COND == BC_ABSORBING))
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// {
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// iplus = (i+1); if (iplus == NX) iplus = NX-1;
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// iminus = (i-1); if (iminus == -1) iminus = 0;
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// jplus = (j+1); if (jplus == NY) jplus = NY-1;
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// jminus = (j-1); if (jminus == -1) jminus = 0;
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// }
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// else if (B_COND == BC_PERIODIC)
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// {
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// iplus = (i+1) % NX;
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// iminus = (i-1) % NX;
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// if (iminus < 0) iminus += NX;
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// jplus = (j+1) % NY;
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// jminus = (j-1) % NY;
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// if (jminus < 0) jminus += NY;
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// }
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// else if (B_COND == BC_VPER_HABS)
|
|
// {
|
|
// iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
// iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
// jplus = (j+1) % NY;
|
|
// jminus = (j-1) % NY;
|
|
// if (jminus < 0) jminus += NY;
|
|
// }
|
|
//
|
|
// /* imposing linear wave on top and bottom by making Laplacian 1d */
|
|
// if ((OSCILLATE_TOPBOT)&&(i < tb_shift))
|
|
// {
|
|
// if (j == NY-1)
|
|
// {
|
|
// jminus = NY-1;
|
|
// jplus = NY-1;
|
|
// }
|
|
// else if (j == 0)
|
|
// {
|
|
// jminus = 0;
|
|
// jplus = 0;
|
|
// }
|
|
// }
|
|
//
|
|
// delta = phi_in[iplus][j] + phi_in[iminus][j] + phi_in[i][jplus] + phi_in[i][jminus] - 4.0*phi_in[i][j];
|
|
//
|
|
// x = phi_in[i][j];
|
|
// y = psi_in[i][j];
|
|
//
|
|
// /* evolve phi */
|
|
// if ((B_COND == BC_PERIODIC)||(B_COND == BC_DIRICHLET))
|
|
// phi_out[i][j] = -y + 2*x + cc*delta - kappa*x - gamma*(x-y);
|
|
// else if (B_COND == BC_ABSORBING)
|
|
// {
|
|
// if ((i>0)&&(i<NX-1)&&(j>0)&&(j<NY-1))
|
|
// phi_out[i][j] = -y + 2*x + cc*delta - kappa*x - gamma*(x-y);
|
|
//
|
|
// /* upper border */
|
|
// else if (j==NY-1)
|
|
// phi_out[i][j] = x - c*(x - phi_in[i][NY-2]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
|
|
//
|
|
// /* lower border */
|
|
// else if (j==0)
|
|
// phi_out[i][j] = x - c*(x - phi_in[i][1]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
|
|
//
|
|
// /* right border */
|
|
// if (i==NX-1)
|
|
// phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
//
|
|
// /* left border */
|
|
// else if (i==0)
|
|
// phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
// }
|
|
// else if (B_COND == BC_VPER_HABS)
|
|
// {
|
|
// if ((i>0)&&(i<NX-1))
|
|
// phi_out[i][j] = -y + 2*x + cc*delta - kappa*x - gamma*(x-y);
|
|
//
|
|
// /* right border */
|
|
// else if (i==NX-1)
|
|
// phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
//
|
|
// /* left border */
|
|
// else if (i==0)
|
|
// phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
// }
|
|
// psi_out[i][j] = x;
|
|
//
|
|
// /* add oscillating boundary condition on the left */
|
|
// // if ((i == 0)&&(OSCILLATE_LEFT))
|
|
// // {
|
|
// // phase = (double)time*OMEGA - DPI*K_BC*(double)j/(double)NY;
|
|
// // if (phase < 0.0) phase = 0.0;
|
|
// // phi_out[i][j] = AMPLITUDE*sin(phase);
|
|
// // }
|
|
//
|
|
// /* add oscillating boundary condition on the left */
|
|
// if (OSCILLATE_LEFT)
|
|
// {
|
|
// phasemin = left_bc[0];
|
|
// if (i == 0)
|
|
// {
|
|
// phase = (double)time*OMEGA - left_bc[j] + phasemin;
|
|
// if (phase < 0.0) phase = 0.0;
|
|
// phi_out[i][j] = AMPLITUDE*sin(phase);
|
|
// }
|
|
// if ((j == 0)&&(i < tb_shift))
|
|
// {
|
|
// phase = (double)time*OMEGA - bot_bc[i] + phasemin;
|
|
// if (phase < 0.0) phase = 0.0;
|
|
// phi_out[i][j] = AMPLITUDE*sin(phase);
|
|
// }
|
|
// else if ((j == NY-1)&&(i < tb_shift))
|
|
// {
|
|
// phase = (double)time*OMEGA - top_bc[i] + phasemin;
|
|
// if (phase < 0.0) phase = 0.0;
|
|
// phi_out[i][j] = AMPLITUDE*sin(phase);
|
|
// }
|
|
// }
|
|
//
|
|
// if (FLOOR)
|
|
// {
|
|
// if (phi_out[i][j] > VMAX) phi_out[i][j] = VMAX;
|
|
// if (phi_out[i][j] < -VMAX) phi_out[i][j] = -VMAX;
|
|
// if (psi_out[i][j] > VMAX) psi_out[i][j] = VMAX;
|
|
// if (psi_out[i][j] < -VMAX) psi_out[i][j] = -VMAX;
|
|
// }
|
|
// }
|
|
// }
|
|
// }
|
|
// // printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
|
|
// }
|
|
|
|
void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX],
|
|
short int *xy_in[NX])
|
|
/* time step of field evolution */
|
|
/* phi is value of field at time t, psi at time t-1 */
|
|
/* this version of the function has been rewritten in order to minimize the number of if-branches */
|
|
{
|
|
int i, j, iplus, iminus, jplus, jminus, tb_shift;
|
|
double delta, x, y, c, cc, gamma, kappa, phase, phasemin;
|
|
static long time = 0;
|
|
static double tc[NX][NY], tcc[NX][NY], tgamma[NX][NY], left_bc[NY], top_bc[NX], bot_bc[NX];
|
|
static short int first = 1, init_bc = 1;
|
|
|
|
time++;
|
|
|
|
/* initialize boundary condition phase KX*x + KY*y */
|
|
if ((OSCILLATE_LEFT)&&(init_bc))
|
|
{
|
|
init_bc_phase(left_bc, top_bc, bot_bc);
|
|
tb_shift = (int)((X_SHIFT - XMIN)*(double)NX/(XMAX - XMIN));
|
|
printf("tb_shift %i\n", tb_shift);
|
|
init_bc = 0;
|
|
}
|
|
|
|
/* initialize tables with wave speeds and dissipation */
|
|
// if (first)
|
|
{
|
|
for (i=0; i<NX; i++){
|
|
for (j=0; j<NY; j++){
|
|
if (xy_in[i][j] != 0)
|
|
{
|
|
tc[i][j] = COURANT;
|
|
tcc[i][j] = courant2;
|
|
if (xy_in[i][j] == 1) tgamma[i][j] = GAMMA;
|
|
else tgamma[i][j] = GAMMAB;
|
|
}
|
|
else if (TWOSPEEDS)
|
|
{
|
|
tc[i][j] = COURANTB;
|
|
tcc[i][j] = courantb2;
|
|
tgamma[i][j] = GAMMAB;
|
|
}
|
|
}
|
|
}
|
|
// first = 0;
|
|
}
|
|
|
|
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y)
|
|
/* evolution in the bulk */
|
|
for (i=1; i<NX-1; i++){
|
|
for (j=1; j<NY-1; j++){
|
|
if ((TWOSPEEDS)||(xy_in[i][j] != 0)){
|
|
x = phi_in[i][j];
|
|
y = psi_in[i][j];
|
|
|
|
/* discretized Laplacian */
|
|
delta = phi_in[i+1][j] + phi_in[i-1][j] + phi_in[i][j+1] + phi_in[i][j-1] - 4.0*x;
|
|
|
|
/* evolve phi */
|
|
phi_out[i][j] = -y + 2*x + tcc[i][j]*delta - KAPPA*x - tgamma[i][j]*(x-y);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* left boundary */
|
|
// if (OSCILLATE_LEFT) for (j=1; j<NY-1; j++) phi_out[0][j] = AMPLITUDE*cos((double)time*OMEGA);
|
|
if (OSCILLATE_LEFT) for (j=1; j<NY-1; j++)
|
|
{
|
|
phasemin = left_bc[0];
|
|
phase = (double)time*OMEGA - left_bc[j] + phasemin;
|
|
if (phase < 0.0) phase = 0.0;
|
|
phi_out[0][j] = AMPLITUDE*sin(phase);
|
|
}
|
|
else for (j=1; j<NY-1; j++){
|
|
if ((TWOSPEEDS)||(xy_in[0][j] != 0)){
|
|
x = phi_in[0][j];
|
|
y = psi_in[0][j];
|
|
|
|
switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
|
|
phi_out[0][j] = -y + 2*x + tcc[0][j]*delta - KAPPA*x - tgamma[0][j]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_PERIODIC):
|
|
{
|
|
delta = phi_in[1][j] + phi_in[NX-1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 4.0*x;
|
|
phi_out[0][j] = -y + 2*x + tcc[0][j]*delta - KAPPA*x - tgamma[0][j]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_ABSORBING):
|
|
{
|
|
delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
|
|
phi_out[0][j] = x - tc[0][j]*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
break;
|
|
}
|
|
case (BC_VPER_HABS):
|
|
{
|
|
delta = phi_in[1][j] + phi_in[0][j+1] + phi_in[0][j-1] - 3.0*x;
|
|
phi_out[0][j] = x - tc[0][j]*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* right boundary */
|
|
for (j=1; j<NY-1; j++){
|
|
if ((TWOSPEEDS)||(xy_in[NX-1][j] != 0)){
|
|
x = phi_in[NX-1][j];
|
|
y = psi_in[NX-1][j];
|
|
|
|
switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
|
|
phi_out[NX-1][j] = -y + 2*x + tcc[NX-1][j]*delta - KAPPA*x - tgamma[NX-1][j]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_PERIODIC):
|
|
{
|
|
delta = phi_in[NX-2][j] + phi_in[0][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 4.0*x;
|
|
phi_out[NX-1][j] = -y + 2*x + tcc[NX-1][j]*delta - KAPPA*x - tgamma[NX-1][j]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_ABSORBING):
|
|
{
|
|
delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
|
|
phi_out[NX-1][j] = x - tc[NX-1][j]*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
break;
|
|
}
|
|
case (BC_VPER_HABS):
|
|
{
|
|
delta = phi_in[NX-2][j] + phi_in[NX-1][j+1] + phi_in[NX-1][j-1] - 3.0*x;
|
|
phi_out[NX-1][j] = x - tc[NX-1][j]*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* top boundary */
|
|
for (i=0; i<NX; i++){
|
|
if ((TWOSPEEDS)||(xy_in[i][NY-1] != 0)){
|
|
x = phi_in[i][NY-1];
|
|
y = psi_in[i][NY-1];
|
|
|
|
if ((OSCILLATE_TOPBOT)&&(i < tb_shift))
|
|
{
|
|
iplus = i+1;
|
|
iminus = i-1; if (iminus < 0) iminus = 0;
|
|
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + - 2.0*x;
|
|
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
|
|
}
|
|
else if ((OSCILLATE_LEFT)&&(i < tb_shift))
|
|
{
|
|
phasemin = left_bc[0];
|
|
phase = (double)time*OMEGA - top_bc[i] + phasemin;
|
|
if (phase < 0.0) phase = 0.0;
|
|
phi_out[i][NY-1] = AMPLITUDE*sin(phase);
|
|
}
|
|
else switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
|
|
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] - 3.0*x;
|
|
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_PERIODIC):
|
|
{
|
|
iplus = (i+1) % NX;
|
|
iminus = (i-1) % NX;
|
|
if (iminus < 0) iminus += NX;
|
|
|
|
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] + phi_in[i][0] - 4.0*x;
|
|
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_ABSORBING):
|
|
{
|
|
iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
|
|
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] - 3.0*x;
|
|
phi_out[i][NY-1] = x - tc[i][NY-1]*(x - phi_in[i][NY-2]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
|
|
break;
|
|
}
|
|
case (BC_VPER_HABS):
|
|
{
|
|
iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
|
|
delta = phi_in[iplus][NY-1] + phi_in[iminus][NY-1] + phi_in[i][NY-2] + phi_in[i][0] - 4.0*x;
|
|
phi_out[i][NY-1] = -y + 2*x + tcc[i][NY-1]*delta - KAPPA*x - tgamma[i][NY-1]*(x-y);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* bottom boundary */
|
|
for (i=0; i<NX; i++){
|
|
if ((TWOSPEEDS)||(xy_in[i][0] != 0)){
|
|
x = phi_in[i][0];
|
|
y = psi_in[i][0];
|
|
|
|
if ((OSCILLATE_TOPBOT)&&(i < tb_shift))
|
|
{
|
|
iplus = i+1;
|
|
iminus = i-1; if (iminus < 0) iminus = 0;
|
|
delta = phi_in[iplus][0] + phi_in[iminus][0] + - 2.0*x;
|
|
phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
|
|
}
|
|
else if ((OSCILLATE_LEFT)&&(i < tb_shift))
|
|
{
|
|
phasemin = left_bc[0];
|
|
phase = (double)time*OMEGA - bot_bc[i] + phasemin;
|
|
if (phase < 0.0) phase = 0.0;
|
|
phi_out[i][0] = AMPLITUDE*sin(phase);
|
|
}
|
|
else switch (B_COND) {
|
|
case (BC_DIRICHLET):
|
|
{
|
|
iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
|
|
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] - 3.0*x;
|
|
phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_PERIODIC):
|
|
{
|
|
iplus = (i+1) % NX;
|
|
iminus = (i-1) % NX;
|
|
if (iminus < 0) iminus += NX;
|
|
|
|
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] + phi_in[i][NY-1] - 4.0*x;
|
|
phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
|
|
break;
|
|
}
|
|
case (BC_ABSORBING):
|
|
{
|
|
iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
|
|
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] - 3.0*x;
|
|
phi_out[i][0] = x - tc[i][0]*(x - phi_in[i][1]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
|
|
break;
|
|
}
|
|
case (BC_VPER_HABS):
|
|
{
|
|
iplus = (i+1); if (iplus == NX) iplus = NX-1;
|
|
iminus = (i-1); if (iminus == -1) iminus = 0;
|
|
|
|
delta = phi_in[iplus][0] + phi_in[iminus][0] + phi_in[i][1] + phi_in[i][NY-1] - 4.0*x;
|
|
phi_out[i][0] = -y + 2*x + tcc[i][0]*delta - KAPPA*x - tgamma[i][0]*(x-y);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* add oscillating boundary condition on the left corners - NEEDED ? */
|
|
if ((i == 0)&&(OSCILLATE_LEFT))
|
|
{
|
|
phi_out[i][0] = AMPLITUDE*cos((double)time*OMEGA);
|
|
phi_out[i][NY-1] = AMPLITUDE*cos((double)time*OMEGA);
|
|
}
|
|
|
|
/* for debugging purposes/if there is a risk of blow-up */
|
|
if (FLOOR) for (i=0; i<NX; i++){
|
|
for (j=0; j<NY; j++){
|
|
if (xy_in[i][j] != 0)
|
|
{
|
|
if (phi_out[i][j] > VMAX) phi_out[i][j] = VMAX;
|
|
if (phi_out[i][j] < -VMAX) phi_out[i][j] = -VMAX;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void evolve_wave(double *phi[NX], double *psi[NX], double *tmp[NX], short int *xy_in[NX])
|
|
/* time step of field evolution */
|
|
/* phi is value of field at time t, psi at time t-1 */
|
|
{
|
|
evolve_wave_half(phi, psi, tmp, xy_in);
|
|
evolve_wave_half(tmp, phi, psi, xy_in);
|
|
evolve_wave_half(psi, tmp, phi, xy_in);
|
|
}
|
|
|
|
|
|
void hash_xy_to_ij(double x, double y, int ij[2])
|
|
{
|
|
static int first = 1;
|
|
static double lx, ly;
|
|
int i, j;
|
|
|
|
if (first)
|
|
{
|
|
lx = XMAX - XMIN + 2.0*HASHGRID_PADDING;
|
|
ly = YMAX - YMIN + 2.0*HASHGRID_PADDING;
|
|
first = 0;
|
|
}
|
|
|
|
i = (int)((double)HASHX*(x - XMIN + HASHGRID_PADDING)/lx);
|
|
j = (int)((double)HASHY*(y - YMIN + HASHGRID_PADDING)/ly);
|
|
|
|
if (i<0) i = 0;
|
|
if (i>=HASHX) i = HASHX-1;
|
|
if (j<0) j = 0;
|
|
if (j>=HASHY) j = HASHY-1;
|
|
|
|
ij[0] = i;
|
|
ij[1] = j;
|
|
|
|
// printf("Mapped (%.3f,%.3f) to (%i, %i)\n", x, y, ij[0], ij[1]);
|
|
}
|
|
|
|
|
|
void compute_repelling_force(int i, int j, double force[2], t_mangrove* mangrove)
|
|
/* compute repelling force of mangrove j on mangrove i */
|
|
{
|
|
double x1, y1, x2, y2, distance, r, f;
|
|
|
|
x1 = mangrove[i].xc;
|
|
y1 = mangrove[i].yc;
|
|
x2 = mangrove[j].xc;
|
|
y2 = mangrove[j].yc;
|
|
|
|
distance = module2(x2 - x1, y2 - y1);
|
|
r = mangrove[i].radius + mangrove[j].radius;
|
|
if (r <= 0.0) r = 0.001*MU;
|
|
f = KREPEL/(0.001 + distance*distance);
|
|
|
|
if ((distance > 0.0)&&(distance < REPEL_RADIUS*r))
|
|
{
|
|
force[0] = f*(x1 - x2)/distance;
|
|
force[1] = f*(y1 - y2)/distance;
|
|
}
|
|
else
|
|
{
|
|
force[0] = 0.0;
|
|
force[1] = 0.0;
|
|
}
|
|
}
|
|
|
|
|
|
void update_hashgrid(t_mangrove* mangrove, int* hashgrid_number, int* hashgrid_mangroves)
|
|
{
|
|
int i, j, k, n, m, ij[2], max = 0;
|
|
|
|
printf("Updating hashgrid_number\n");
|
|
for (i=0; i<HASHX*HASHY; i++) hashgrid_number[i] = 0;
|
|
printf("Updated hashgrid_number\n");
|
|
|
|
/* place each mangrove in hash grid */
|
|
for (k=1; k<ncircles; k++)
|
|
// if (circleactive[k])
|
|
{
|
|
// printf("placing circle %i\t", k);
|
|
hash_xy_to_ij(mangrove[k].xc, mangrove[k].yc, ij);
|
|
i = ij[0]; j = ij[1];
|
|
// printf("ij = (%i, %i)\t", i, j);
|
|
n = hashgrid_number[i*HASHY + j];
|
|
m = i*HASHY*HASHMAX + j*HASHMAX + n;
|
|
// printf("n = %i, m = %i\n", n, m);
|
|
if (m < HASHX*HASHY*HASHMAX) hashgrid_mangroves[m] = k;
|
|
else printf("Too many mangroves in hash cell, try increasing HASHMAX\n");
|
|
hashgrid_number[i*HASHY + j]++;
|
|
mangrove[k].hashx = i;
|
|
mangrove[k].hashy = j;
|
|
|
|
if (n > max) max = n;
|
|
// printf("Placed mangrove %i at (%i,%i) in hashgrid\n", k, ij[0], ij[1]);
|
|
// printf("%i mangroves at (%i,%i)\n", hashgrid_number[ij[0]][ij[1]], ij[0], ij[1]);
|
|
}
|
|
|
|
printf("Maximal number of mangroves per hash cell: %i\n", max);
|
|
}
|
|
|
|
|
|
void animation()
|
|
{
|
|
double time, scale, diss, rgb[3], hue, y, dissip, ej, gradient[2], dx, dy, dt, xleft, xright,
|
|
length, fx, fy, force[2];
|
|
double *phi[NX], *psi[NX], *tmp[NX];
|
|
short int *xy_in[NX], redraw = 0;
|
|
int i, j, k, n, s, ij[2], i0, iplus, iminus, j0, jplus, jminus, p, q;
|
|
static int imin, imax;
|
|
static short int first = 1;
|
|
t_mangrove *mangrove;
|
|
int *hashgrid_number, *hashgrid_mangroves;
|
|
t_hashgrid *hashgrid;
|
|
|
|
/* Since NX and NY are big, it seemed wiser to use some memory allocation here */
|
|
for (i=0; i<NX; i++)
|
|
{
|
|
phi[i] = (double *)malloc(NY*sizeof(double));
|
|
psi[i] = (double *)malloc(NY*sizeof(double));
|
|
tmp[i] = (double *)malloc(NY*sizeof(double));
|
|
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
|
|
}
|
|
mangrove = (t_mangrove *)malloc(NMAXCIRCLES*sizeof(t_mangrove)); /* mangroves */
|
|
|
|
hashgrid = (t_hashgrid *)malloc(HASHX*HASHY*sizeof(t_hashgrid)); /* hashgrid */
|
|
|
|
hashgrid_number = (int *)malloc(HASHX*HASHY*sizeof(int)); /* total number of mangroves in each hash grid cell */
|
|
hashgrid_mangroves = (int *)malloc(HASHX*HASHY*HASHMAX*sizeof(int)); /* numbers of mangroves in each hash grid cell */
|
|
|
|
/* initialise positions and radii of circles */
|
|
if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN == D_CIRCLES_IN_RECT)) ncircles = init_circle_config(circles);
|
|
else if (B_DOMAIN == D_POLYGONS) ncircles = init_polygon_config(polygons);
|
|
|
|
|
|
|
|
courant2 = COURANT*COURANT;
|
|
courantb2 = COURANTB*COURANTB;
|
|
// dt = 0.01;
|
|
|
|
/* initialize wave with a drop at one point, zero elsewhere */
|
|
init_wave_flat(phi, psi, xy_in);
|
|
|
|
/* initialise mangroves */
|
|
for (i=0; i < ncircles; i++)
|
|
{
|
|
/* to avoid having to recode init_circle_config, would be more elegant in C++ */
|
|
mangrove[i].xc = circles[i].xc;
|
|
mangrove[i].yc = circles[i].yc;
|
|
mangrove[i].radius = circles[i].radius;
|
|
mangrove[i].active = circles[i].active;
|
|
|
|
mangrove[i].energy = 0.0;
|
|
y = mangrove[i].yc;
|
|
if (y >= YMAX) y -= mangrove[i].radius;
|
|
if (y <= YMIN) y += mangrove[i].radius;
|
|
// if (y >= YMAX) y -= (YMAX - YMIN);
|
|
// if (y <= YMIN) y += (YMAX - YMIN);
|
|
mangrove[i].yc_wrapped = y;
|
|
// mangrove[i].active = 1;
|
|
|
|
if (RANDOM_RADIUS) mangrove[i].radius = mangrove[i].radius*(0.75 + 0.5*((double)rand()/RAND_MAX));
|
|
|
|
mangrove[i].radius_initial = mangrove[i].radius;
|
|
mangrove[i].attached = 1;
|
|
mangrove[i].mass_inv = MU*MU/(MANGROVE_MASS*mangrove[i].radius*mangrove[i].radius);
|
|
|
|
if (MOVE_MANGROVES)
|
|
{
|
|
mangrove[i].anchorx = mangrove[i].xc;
|
|
mangrove[i].anchory = mangrove[i].yc_wrapped;
|
|
// mangrove[i].anchory = mangrove[i].yc;
|
|
}
|
|
|
|
if (INERTIA)
|
|
{
|
|
mangrove[i].vx = 0.0;
|
|
mangrove[i].vy = 0.0;
|
|
}
|
|
}
|
|
|
|
/* initialise hash table for interacting mangroves */
|
|
if (REPELL_MANGROVES) update_hashgrid(mangrove, hashgrid_number, hashgrid_mangroves);
|
|
|
|
if (first) /* compute box limits where circles are reset */
|
|
{
|
|
/* find leftmost and rightmost circle */
|
|
for (i=0; i<ncircles; i++)
|
|
if ((mangrove[i].active)&&(mangrove[i].xc - mangrove[i].radius < xleft)) xleft = mangrove[i].xc - mangrove[i].radius;
|
|
for (i=0; i<ncircles; i++)
|
|
if ((mangrove[i].active)&&(mangrove[i].xc + mangrove[i].radius > xright)) xright = mangrove[i].xc + mangrove[i].radius;
|
|
|
|
xy_to_ij(xleft, 0.0, ij);
|
|
imin = ij[0] - 10;
|
|
if (imin < 0) imin = 0;
|
|
xy_to_ij(xright, 0.0, ij);
|
|
imax = ij[0];
|
|
if (imax >= NX) imax = NX-1;
|
|
first = 0;
|
|
|
|
printf("xleft = %.3lg, xright = %.3lg, imin = %i, imax = %i\n", xleft, xright, imin, imax);
|
|
}
|
|
|
|
blank();
|
|
glColor3f(0.0, 0.0, 0.0);
|
|
draw_wave(phi, psi, xy_in, 1.0, 0, PLOT);
|
|
draw_billiard(0, 1.0);
|
|
|
|
glutSwapBuffers();
|
|
|
|
|
|
|
|
sleep(SLEEP1);
|
|
|
|
for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
|
|
{
|
|
printf("Computing frame %d\n",i);
|
|
/* compute the variance of the field to adjust color scheme */
|
|
/* the color depends on the field divided by sqrt(1 + variance) */
|
|
if (SCALE)
|
|
{
|
|
scale = sqrt(1.0 + compute_variance(phi,psi, xy_in));
|
|
// printf("Scaling factor: %5lg\n", scale);
|
|
}
|
|
else scale = 1.0;
|
|
|
|
printf("Drawing wave\n");
|
|
draw_wave(phi, psi, xy_in, scale, i, PLOT);
|
|
|
|
|
|
printf("Evolving wave\n");
|
|
for (j=0; j<NVID; j++)
|
|
{
|
|
// printf("%i ", j);
|
|
evolve_wave(phi, psi, tmp, xy_in);
|
|
// if (i % 10 == 9) oscillate_linear_wave(0.2*scale, 0.15*(double)(i*NVID + j), -1.5, YMIN, -1.5, YMAX, phi, psi);
|
|
}
|
|
|
|
|
|
/* move mangroves */
|
|
if (MOVE_MANGROVES) for (j=0; j<ncircles; j++) if (mangrove[j].active)
|
|
{
|
|
compute_gradient(phi, psi, mangrove[j].xc, mangrove[j].yc_wrapped, gradient);
|
|
// printf("gradient = (%.3lg, %.3lg)\t", gradient[0], gradient[1]);
|
|
|
|
// if (j%NGRIDY == 0) printf("gradient (%.3lg, %.3lg)\n", gradient[0], gradient[1]);
|
|
// if (j%NGRIDY == 0) printf("circle %i (%.3lg, %.3lg) -> ", j, mangrove[j].xc, mangrove[j].yc);
|
|
|
|
/* compute force of wave */
|
|
dx = DT_MANGROVE*KWAVE*gradient[0];
|
|
dy = DT_MANGROVE*KWAVE*gradient[1];
|
|
|
|
/* compute force of spring */
|
|
if (mangrove[j].attached)
|
|
{
|
|
dx += DT_MANGROVE*(-KSPRING*(mangrove[j].xc - mangrove[j].anchorx));
|
|
dy += DT_MANGROVE*(-KSPRING*(mangrove[j].yc_wrapped - mangrove[j].anchory));
|
|
}
|
|
|
|
/* compute repelling force from other mangroves */
|
|
if (REPELL_MANGROVES)
|
|
{
|
|
/* determine neighboring grid points */
|
|
i0 = mangrove[j].hashx;
|
|
iminus = i0 - 1; if (iminus < 0) iminus = 0;
|
|
iplus = i0 + 1; if (iplus >= HASHX) iplus = HASHX-1;
|
|
|
|
j0 = mangrove[j].hashy;
|
|
jminus = j0 - 1; if (jminus < 0) jminus = 0;
|
|
jplus = j0 + 1; if (jplus >= HASHY) jplus = HASHY-1;
|
|
|
|
fx = 0.0;
|
|
fy = 0.0;
|
|
for (p=iminus; p<= iplus; p++)
|
|
for (q=jminus; q<= jplus; q++)
|
|
for (k=0; k<hashgrid_number[p*HASHY+q]; k++)
|
|
if (mangrove[hashgrid_mangroves[p*HASHY*HASHMAX + q*HASHMAX + k]].active)
|
|
{
|
|
compute_repelling_force(j, hashgrid_mangroves[p*HASHY*HASHMAX + q*HASHMAX + k], force, mangrove);
|
|
fx += force[0];
|
|
fy += force[1];
|
|
}
|
|
|
|
// if (fx*fx + fy*fy > 0.001) printf("Force on mangrove %i: (%.3f, %.3f)\n", j, fx, fy);
|
|
|
|
dx += DT_MANGROVE*fx;
|
|
dy += DT_MANGROVE*fy;
|
|
}
|
|
|
|
/* detach mangrove if spring is too long */
|
|
if (DETACH_MANGROVES)
|
|
{
|
|
length = module2(mangrove[j].xc - mangrove[j].anchorx, mangrove[j].yc_wrapped - mangrove[j].anchory);
|
|
// if (j%NGRIDY == 0) printf("spring length %.i: %.3lg\n", j, length);
|
|
// if (length > L_DETACH) mangrove[j].attached = 0;
|
|
if (length*mangrove[j].mass_inv > L_DETACH) mangrove[j].attached = 0;
|
|
}
|
|
|
|
if (dx > DXMAX) dx = DXMAX;
|
|
if (dx < -DXMAX) dx = -DXMAX;
|
|
if (dy > DXMAX) dy = DXMAX;
|
|
if (dy < -DXMAX) dy = -DXMAX;
|
|
|
|
if (INERTIA)
|
|
{
|
|
mangrove[j].vx += (dx - DAMP_MANGROVE*mangrove[j].vx)*mangrove[j].mass_inv;
|
|
mangrove[j].vy += (dy - DAMP_MANGROVE*mangrove[j].vy)*mangrove[j].mass_inv;
|
|
mangrove[j].xc += mangrove[j].vx*DT_MANGROVE;
|
|
mangrove[j].yc += mangrove[j].vy*DT_MANGROVE;
|
|
mangrove[j].yc_wrapped += mangrove[j].vy*DT_MANGROVE;
|
|
// if (j%NGRIDY == 0)
|
|
// printf("circle %.i: (dx,dy) = (%.3lg,%.3lg), (vx,vy) = (%.3lg,%.3lg)\n",
|
|
// j, mangrove[j].xc-mangrove[j].anchorx, mangrove[j].yc-mangrove[j].anchory, mangrove[j].vx, mangrove[j].vy);
|
|
}
|
|
else
|
|
{
|
|
mangrove[j].xc += dx*mangrove[j].mass_inv*DT_MANGROVE;
|
|
mangrove[j].yc += dy*mangrove[j].mass_inv*DT_MANGROVE;
|
|
mangrove[j].yc_wrapped += dy*mangrove[j].mass_inv*DT_MANGROVE;
|
|
}
|
|
|
|
if (mangrove[j].xc <= XMIN) mangrove[j].xc = XMIN;
|
|
if (mangrove[j].xc >= XMAX) mangrove[j].xc = XMAX;
|
|
if (mangrove[j].yc_wrapped <= YMIN) mangrove[j].yc_wrapped = YMIN;
|
|
if (mangrove[j].yc_wrapped >= YMAX) mangrove[j].yc_wrapped = YMAX;
|
|
|
|
// if (j%NGRIDY == 0) printf("(%.3lg, %.3lg)\n", mangrove[j].xc, mangrove[j].yc);
|
|
|
|
redraw = 1;
|
|
}
|
|
|
|
/* test for debugging */
|
|
if (1) for (j=0; j<ncircles; j++)
|
|
{
|
|
dissip = compute_dissipation(phi, psi, xy_in, mangrove[j].xc, mangrove[j].yc_wrapped);
|
|
|
|
/* make sure the dissipation does not grow too fast because of round-off/blow-up */
|
|
if (dissip > 0.1*MANGROVE_EMAX)
|
|
{
|
|
dissip = 0.1*MANGROVE_EMAX;
|
|
printf("Flooring dissipation!\n");
|
|
}
|
|
|
|
if (mangrove[j].active)
|
|
{
|
|
mangrove[j].energy += dissip;
|
|
ej = mangrove[j].energy;
|
|
// printf("ej = %.3f\n", ej);
|
|
if (ej <= MANGROVE_EMAX)
|
|
{
|
|
if (ej > 0.0)
|
|
{
|
|
hue = MANGROVE_HUE_MIN + (MANGROVE_HUE_MAX - MANGROVE_HUE_MIN)*ej/MANGROVE_EMAX;
|
|
if (hue < 0.0) hue += 360.0;
|
|
}
|
|
else hue = MANGROVE_HUE_MIN;
|
|
hsl_to_rgb(hue, 0.9, 0.5, rgb);
|
|
// if (j%NGRIDY == 0) printf("Circle %i, energy %.5lg, hue %.5lg\n", j, ej, hue);
|
|
draw_colored_circle(mangrove[j].xc, mangrove[j].yc, mangrove[j].radius, NSEG, rgb);
|
|
|
|
/* shrink mangrove */
|
|
if ((ERODE_MANGROVES)&&(ej > 0.0))
|
|
{
|
|
mangrove[j].radius = mangrove[j].radius_initial*(1.0 - ej*ej/(MANGROVE_EMAX*MANGROVE_EMAX));
|
|
redraw = 1;
|
|
}
|
|
else mangrove[j].radius = mangrove[j].radius_initial;
|
|
|
|
}
|
|
else /* remove mangrove */
|
|
{
|
|
mangrove[j].active = 0;
|
|
/* reinitialize table xy_in */
|
|
redraw = 1;
|
|
}
|
|
}
|
|
else if (RECOVER_MANGROVES) /* allow disabled mangroves to recover */
|
|
{
|
|
mangrove[j].energy -= 0.15*dissip;
|
|
printf("Circle %i energy %.3lg\n", j, mangrove[j].energy);
|
|
if (mangrove[j].energy < 0.0)
|
|
{
|
|
printf("Reactivating circle %i?\n", j);
|
|
/* THE PROBLEM occurs when circleactive[0] is set to 1 again */
|
|
if (j>0) mangrove[j].active = 1;
|
|
mangrove[j].radius = mangrove[j].radius_initial;
|
|
mangrove[j].energy = -MANGROVE_EMAX;
|
|
/* reinitialize table xy_in */
|
|
redraw = 1;
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
/* for compatibility with draw_billiard, may be improvable */
|
|
for (j=0; j<ncircles; j++)
|
|
{
|
|
circles[j].xc = mangrove[j].xc;
|
|
circles[j].yc = mangrove[j].yc;
|
|
circles[j].radius = mangrove[j].radius;
|
|
}
|
|
|
|
/* compute energy dissipated in obstacles */
|
|
/* if (ERODE_MANGROVES) for (j=0; j<ncircles; j++)
|
|
{
|
|
// printf("j = %i\t", j);
|
|
dissip = compute_dissipation(phi, psi, xy_in, mangrove[j].xc, mangrove[j].yc_wrapped);
|
|
printf("dissip = %.3f\t", dissip);
|
|
|
|
/* make sure the dissipation does not grow too fast because of round-off/blow-up */
|
|
// if (dissip > 0.1*MANGROVE_EMAX)
|
|
// {
|
|
// dissip = 0.1*MANGROVE_EMAX;
|
|
// printf("Flooring dissipation!\n");
|
|
// }
|
|
//
|
|
// if (mangrove[j].active)
|
|
// {
|
|
// mangrove[j].energy += dissip;
|
|
// ej = mangrove[j].energy;
|
|
// printf("ej = %.3f\n", ej);
|
|
// if (ej <= MANGROVE_EMAX)
|
|
// {
|
|
// if (ej > 0.0)
|
|
// {
|
|
// hue = MANGROVE_HUE_MIN + (MANGROVE_HUE_MAX - MANGROVE_HUE_MIN)*ej/MANGROVE_EMAX;
|
|
// if (hue < 0.0) hue += 360.0;
|
|
// }
|
|
// else hue = MANGROVE_HUE_MIN;
|
|
// hsl_to_rgb(hue, 0.9, 0.5, rgb);
|
|
// if (j%NGRIDY == 0) printf("Circle %i, energy %.5lg, hue %.5lg\n", j, ej, hue);
|
|
// draw_colored_circle(mangrove[j].xc, mangrove[j].yc, mangrove[j].radius, NSEG, rgb);
|
|
//
|
|
// /* shrink mangrove */
|
|
// if (ej > 0.0)
|
|
// {
|
|
// mangrove[j].radius -= MU*ej*ej/(MANGROVE_EMAX*MANGROVE_EMAX);
|
|
// if (mangrove[j].radius < 0.0) mangrove[j].radius = 0.0;
|
|
// mangrove[j].radius = mangrove[j].radius_initial*(1.0 - ej*ej/(MANGROVE_EMAX*MANGROVE_EMAX));
|
|
// redraw = 1;
|
|
// }
|
|
// else mangrove[j].radius = mangrove[j].radius_initial;
|
|
// }
|
|
// else /* remove mangrove */
|
|
// {
|
|
// mangrove[j].active = 0;
|
|
/* reinitialize table xy_in */
|
|
// redraw = 1;
|
|
// }
|
|
// }
|
|
// else /* allow disabled mangroves to recover */
|
|
// {
|
|
// mangrove[j].energy -= 0.15*dissip;
|
|
// printf("ej = %.3f\n", mangrove[j].energy);
|
|
// mangrove[j].radius += 0.005*MU;
|
|
// if (mangrove[j].radius > MU) mangrove[j].radius = MU;
|
|
// if ((mangrove[j].energy < 0.0)&&(mangrove[j].radius > 0.0))
|
|
// if (mangrove[j].energy < 0.0)
|
|
// {
|
|
// mangrove[j].active = 1;
|
|
// mangrove[j].radius = mangrove[j].radius*(0.75 + 0.5*((double)rand()/RAND_MAX));
|
|
// mangrove[j].radius = mangrove[j].radius_initial;
|
|
// mangrove[j].energy = -MANGROVE_EMAX;
|
|
/* reinitialize table xy_in */
|
|
// redraw = 1;
|
|
// }
|
|
|
|
// }
|
|
|
|
// printf("Circle %i, energy %.5lg\n", j, mangrove[j].energy);
|
|
// }
|
|
|
|
printf("Updating hashgrid\n");
|
|
if (REPELL_MANGROVES) update_hashgrid(mangrove, hashgrid_number, hashgrid_mangroves);
|
|
|
|
|
|
printf("Drawing billiard\n");
|
|
draw_billiard(0, 1.0);
|
|
|
|
glutSwapBuffers();
|
|
|
|
if (redraw)
|
|
{
|
|
printf("Reinitializing xy_in\n");
|
|
init_xyin_xrange(xy_in, imin, NX);
|
|
// init_xyin_xrange(xy_in, imin, imax);
|
|
}
|
|
redraw = 0;
|
|
|
|
if (MOVIE)
|
|
{
|
|
if (i >= INITIAL_TIME) save_frame();
|
|
else printf("Initial phase time %i of %i\n", i, INITIAL_TIME);
|
|
|
|
/* 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_wave/");
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
if (MOVIE)
|
|
{
|
|
for (i=0; i<END_FRAMES; i++) save_frame();
|
|
s = system("mv wave*.tif tif_wave/");
|
|
}
|
|
for (i=0; i<NX; i++)
|
|
{
|
|
free(phi[i]);
|
|
free(psi[i]);
|
|
free(tmp[i]);
|
|
free(xy_in[i]);
|
|
}
|
|
free(mangrove);
|
|
|
|
free(hashgrid_number);
|
|
free(hashgrid_mangroves);
|
|
}
|
|
|
|
|
|
void display(void)
|
|
{
|
|
glPushMatrix();
|
|
|
|
blank();
|
|
glutSwapBuffers();
|
|
blank();
|
|
glutSwapBuffers();
|
|
|
|
animation();
|
|
sleep(SLEEP2);
|
|
|
|
glPopMatrix();
|
|
|
|
glutDestroyWindow(glutGetWindow());
|
|
|
|
}
|
|
|
|
|
|
int main(int argc, char** argv)
|
|
{
|
|
glutInit(&argc, argv);
|
|
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
|
|
glutInitWindowSize(WINWIDTH,WINHEIGHT);
|
|
glutCreateWindow("Wave equation in a planar domain");
|
|
|
|
init();
|
|
|
|
glutDisplayFunc(display);
|
|
|
|
glutMainLoop();
|
|
|
|
return 0;
|
|
}
|