1277 lines
51 KiB
C
1277 lines
51 KiB
C
/*********************************************************************************/
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/* */
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/* Animation of reaction-diffusion equation in a planar domain */
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/* */
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/* N. Berglund, January 2022 */
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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 rde rde.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_bz */
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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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#include <time.h>
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#define MOVIE 0 /* set to 1 to generate movie */
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#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */
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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 1920 /* window width */
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#define WINHEIGHT 1000 /* window height */
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#define NX 960 /* number of grid points on x axis */
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#define NY 500 /* number of grid points on y axis */
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// #define NX 480 /* number of grid points on x axis */
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// #define NY 250 /* 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 -1.041666667
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#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
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// #define WINWIDTH 1280 /* window width */
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// #define WINHEIGHT 720 /* window height */
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//
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// // #define NX 320 /* number of grid points on x axis */
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// // #define NY 180 /* number of grid points on y axis */
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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 960 /* number of grid points on x axis */
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// // #define NY 540 /* number of grid points on y axis */
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//
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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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//
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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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/* Choice of simulated equation */
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#define RDE_EQUATION 6 /* choice of reaction term, see list in global_3d.c */
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#define NFIELDS 2 /* number of fields in reaction-diffusion equation */
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#define NLAPLACIANS 1 /* number of fields for which to compute Laplacian */
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#define ADD_POTENTIAL 0 /* set to 1 to add a potential (for Schrodinger equation) */
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#define ADD_MAGNETIC_FIELD 0 /* set to 1 to add a magnetic field (for Schrodinger equation) - then set POTENTIAL 1 */
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#define POTENTIAL 7 /* type of potential or vector potential, see list in global_3d.c */
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#define ANTISYMMETRIZE_WAVE_FCT 0 /* set tot 1 to make wave function antisymmetric */
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#define JULIA_SCALE 0.5 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 197 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 99 /* 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 300 /* 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 0.7 /* parameter controlling the dimensions of domain */
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#define MU 0.15 /* parameter controlling the dimensions of domain */
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#define NPOLY 5 /* number of sides of polygon */
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#define APOLY 2.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 7 /* depth of computation of Menger gasket */
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#define MRATIO 5 /* 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 in sub_wave.c */
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/* Physical patameters of wave equation */
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// #define DT 0.00000002
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// #define DT 0.00000003
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// #define DT 0.000000011
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#define DT 0.0000012
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// #define DT 0.000001
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#define VISCOSITY 2.0
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#define RPSA 0.75 /* parameter in Rock-Paper-Scissors-type interaction */
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#define RPSLZB 0.75 /* second parameter in Rock-Paper-Scissors-Lizard-Spock type interaction */
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#define EPSILON 0.8 /* time scale separation */
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#define DELTA 0.1 /* time scale separation */
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#define FHNA 1.0 /* parameter in FHN equation */
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#define FHNC -0.01 /* parameter in FHN equation */
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#define K_HARMONIC 1.0 /* spring constant of harmonic potential */
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#define K_COULOMB 0.5 /* constant in Coulomb potential */
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#define V_MAZE 0.4 /* potential in walls of maze */
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#define BZQ 0.0008 /* parameter in BZ equation */
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#define BZF 1.2 /* parameter in BZ equation */
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#define B_FIELD 10.0 /* magnetic field */
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#define AB_RADIUS 0.2 /* radius of region with magnetic field for Aharonov-Bohm effect */
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#define K_EULER 50.0 /* constant in stream function integration of Euler equation */
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#define SMOOTHEN_VORTICITY 1 /* set to 1 to smoothen vorticity field in Euler equation */
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#define SMOOTHEN_PERIOD 10 /* period between smoothenings */
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// #define SMOOTH_FACTOR 0.05 /* factor by which to smoothen */
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#define SMOOTH_FACTOR 0.03 /* factor by which to smoothen */
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// #define SMOOTH_FACTOR 0.015 /* factor by which to smoothen */
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// #define SMOOTH_FACTOR 0.01 /* factor by which to smoothen */
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#define ADD_TRACERS 1 /* set to 1 to add tracer particles (for Euler equations) */
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#define N_TRACERS 1000 /* number of tracer particles */
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#define T_OUT 2.0 /* outside temperature */
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#define T_IN 0.0 /* inside temperature */
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#define SPEED 0.0 /* speed of drift to the right */
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#define ADD_NOISE 0 /* set to 1 to add noise, set to 2 to add noise in right half */
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#define NOISE_INTENSITY 0.005 /* noise intensity */
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#define CHANGE_NOISE 1 /* set to 1 to increase noise intensity */
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#define NOISE_FACTOR 40.0 /* factor by which to increase noise intensity */
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#define NOISE_INITIAL_TIME 100 /* initial time during which noise remains constant */
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#define CHANGE_VISCOSITY 0 /* set to 1 to change the viscosity in the course of the simulation */
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#define ADJUST_INTSTEP 0 /* set to 1 to decrease integration step when viscosity increases */
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#define VISCOSITY_INITIAL_TIME 10 /* initial time during which viscosity remains constant */
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#define VISCOSITY_FACTOR 100.0 /* factor by which to change viscosity */
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#define VISCOSITY_MAX 2.0 /* max value of viscosity beyond which NVID is increased and integration step is decrase,
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for numerical stability */
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#define CHANGE_RPSLZB 0 /* set to 1 to change second parameter in Rock-Paper-Scissors-Lizard-Spock equation */
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#define RPSLZB_CHANGE 0.75 /* factor by which to rpslzb parameter */
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#define RPSLZB_INITIAL_TIME 0 /* initial time during which rpslzb remains constant */
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#define RPSLZB_FINAL_TIME 500 /* final time during which rpslzb remains constant */
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/* Boundary conditions, see list in global_pdes.c */
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#define B_COND 1
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#define EULER_GRADIENT_YSHIFT 0.0 /* y-shift in computation of gradient in Euler equation */
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/* Parameters for length and speed of simulation */
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#define NSTEPS 2250 /* number of frames of movie */
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// #define NSTEPS 500 /* number of frames of movie */
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// #define NVID 90 /* number of iterations between images displayed on screen */
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#define NVID 120 /* number of iterations between images displayed on screen */
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// #define NVID 1100 /* number of iterations between images displayed on screen */
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#define ACCELERATION_FACTOR 1.0 /* factor by which to increase NVID in course of simulation */
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#define DT_ACCELERATION_FACTOR 1.0 /* factor by which to increase time step in course of simulation */
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#define MAX_DT 0.024 /* maximal value of integration step */
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#define NSEG 100 /* number of segments of boundary */
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#define BOUNDARY_WIDTH 5 /* width of billiard boundary */
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#define PAUSE 100 /* number of frames after which to pause */
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#define PSLEEP 2 /* sleep time during pause */
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#define SLEEP1 2 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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#define INITIAL_TIME 0 /* initial still time */
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#define MID_FRAMES 50 /* number of still frames between parts of two-part movie */
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#define END_FRAMES 50 /* number of still frames at end of movie */
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#define FADE 1 /* set to 1 to fade at end of movie */
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/* Visualisation */
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#define PLOT_3D 0 /* controls whether plot is 2D or 3D */
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#define ROTATE_VIEW 0 /* set to 1 to rotate position of observer */
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#define ROTATE_ANGLE 360.0 /* total angle of rotation during simulation */
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#define DRAW_PERIODICISED 1 /* set to 1 to repeat wave periodically in x and y directions */
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/* Plot type - color scheme */
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#define CPLOT 52
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#define CPLOT_B 51
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/* Plot type - height of 3D plot */
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#define ZPLOT 52 /* z coordinate in 3D plot */
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// #define ZPLOT 32 /* z coordinate in 3D plot */
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#define ZPLOT_B 51 /* z coordinate in second 3D plot */
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#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of P_3D_AMPLITUDE plot */
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#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */
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#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */
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#define WRAP_ANGLE 1 /* experimental: wrap angle to [0, 2Pi) for interpolation in angle schemes */
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#define FADE_IN_OBSTACLE 0 /* set to 1 to fade color inside obstacles */
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#define DRAW_OUTSIDE_GRAY 0 /* experimental - draw outside of billiard in gray */
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#define ADD_POTENTIAL_TO_Z 1 /* set to 1 to add the external potential to z-coordinate of plot */
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#define ADD_POT_CONSTANT 0.35 /* constant in front of added potential */
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#define PLOT_SCALE_ENERGY 0.05 /* vertical scaling in energy plot */
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#define PRINT_TIME 0 /* set to 1 to print running time */
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#define PRINT_VISCOSITY 0 /* set to 1 to print viscosity */
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#define PRINT_RPSLZB 0 /* set to 1 to print rpslzb parameter */
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#define PRINT_PROBABILITIES 0 /* set to 1 to print probabilities (for Ehrenfest urn configuration) */
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#define PRINT_NOISE 0 /* set to 1 to print noise intensity */
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#define DRAW_FIELD_LINES 0 /* set to 1 to draw field lines */
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#define FIELD_LINE_WIDTH 1 /* width of field lines */
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#define N_FIELD_LINES 120 /* number of field lines */
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#define FIELD_LINE_FACTOR 120 /* factor controlling precision when computing origin of field lines */
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#define DRAW_BILLIARD 1 /* set to 1 to draw boundary */
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#define DRAW_BILLIARD_FRONT 1 /* set to 1 to draw boundary */
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#define FILL_BILLIARD_COMPLEMENT 1 /* set to 1 to fill complement of billiard (for certain shapes only) */
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/* 3D representation */
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#define REPRESENTATION_3D 1 /* choice of 3D representation */
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#define REP_AXO_3D 0 /* linear projection (axonometry) */
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#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */
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/* Color schemes, see list in global_pdes.c */
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#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */
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#define COLOR_PALETTE_B 13 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* black background */
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#define COLOR_SCHEME 3 /* choice of color scheme */
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#define COLOR_PHASE_SHIFT 0.0 /* phase shift of color scheme, in units of Pi */
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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 VSCALE_AMPLITUDE 1.5 /* additional scaling factor for color scheme P_3D_AMPLITUDE */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define CURL_SCALE 0.000015 /* scaling factor for curl representation */
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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 SLOPE_SCHROD_LUM 50.0 /* sensitivity of luminosity on module, for color scheme Z_ARGUMENT */
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#define MIN_SCHROD_LUM 0.2 /* minimal luminosity in color scheme Z_ARGUMENT*/
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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 359.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -359.0 /* amplitude of variation of hue for color scheme C_HUE */
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#define E_SCALE 100.0 /* scaling factor for energy representation */
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#define FLUX_SCALE 100.0 /* scaling factor for energy representation */
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#define LOG_SCALE 0.5 /* scaling factor for energy log representation */
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#define LOG_SHIFT 1.0
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#define LOG_MIN 1.0e-3 /* floor value for log vorticity plot */
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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 0 /* seed of random number generator */
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#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
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#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
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#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 3.0 /* 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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/* only for compatibility with wave_common.c */
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#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
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#define OMEGA 0.005 /* frequency of periodic excitation */
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#define COURANT 0.08 /* Courant number */
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#define COURANTB 0.03 /* Courant number in medium B */
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#define INITIAL_AMP 0.5 /* amplitude of initial condition */
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#define INITIAL_VARIANCE 0.0002 /* variance of initial condition */
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#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */
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#define VSCALE_ENERGY 200.0 /* additional scaling factor for color scheme P_3D_ENERGY */
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#define PHASE_FACTOR 20.0 /* 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 OSCILLATION_SCHEDULE 0 /* oscillation schedule, see list in global_pdes.c */
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#define AMPLITUDE 0.8 /* amplitude of periodic excitation */
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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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#define COMPARISON 0 /* set to 1 to compare two different patterns (beta) */
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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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/* end of constants added only for compatibility with wave_common.c */
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double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */
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double v_3d[2] = {-0.75, -0.45};
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double w_3d[2] = {0.0, 0.015};
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double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */
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double observer[3] = {8.0, 8.0, 8.0}; /* location of observer for REP_PROJ_3D representation */
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int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
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#define Z_SCALING_FACTOR 0.08 /* overall scaling factor of z axis for REP_PROJ_3D representation */
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#define XY_SCALING_FACTOR 1.7 /* overall scaling factor for on-screen (x,y) coordinates after projection */
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#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */
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#define XSHIFT_3D -0.1 /* overall x shift for REP_PROJ_3D representation */
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#define YSHIFT_3D 0.1 /* overall y shift for REP_PROJ_3D representation */
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#define BORDER_PADDING 0 /* distance from boundary at which to plot points, to avoid boundary effects due to gradient */
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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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#define TEST_GRADIENT 0 /* print norm squared of gradient */
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#define REFRESH_B (ZPLOT_B != ZPLOT)||(CPLOT_B != CPLOT) /* to save computing time, to be improved */
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#define COMPUTE_WRAP_ANGLE ((WRAP_ANGLE)&&((cplot == Z_ANGLE_GRADIENT)||(cplot == Z_ANGLE_GRADIENTX)||(cplot == Z_ARGUMENT)||(cplot == Z_ANGLE_GRADIENTX)))
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#define PRINT_PARAMETERS ((PRINT_TIME)||(PRINT_VISCOSITY)||(PRINT_RPSLZB)||(PRINT_PROBABILITIES)||(PRINT_NOISE))
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#include "global_pdes.c"
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#include "global_3d.c" /* constants and global variables */
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#include "sub_maze.c"
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#include "sub_wave.c"
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#include "wave_common.c" /* common functions for wave_billiard, wave_comparison, etc */
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#include "sub_wave_3d_rde.c" /* should be later replaced by sub_wave_rde.c */
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#include "sub_rde.c"
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double f_aharonov_bohm(double r2)
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/* radial part of Aharonov-Bohm vector potential */
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{
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double r02 = AB_RADIUS*AB_RADIUS;
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if (r2 > r02) return(-0.25*r02/r2);
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else return(0.25*(r2 - 2.0*r02)/r02);
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// if (r2 > r02) return(1.0/r2);
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// else return((2.0*r02 - r2)/(r02*r02));
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}
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double potential(int i, int j)
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/* compute potential (e.g. for Schrödinger equation), or potential part if there is a magnetic field */
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{
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double x, y, xy[2], r, small = 1.0e-1, kx, ky, lx = XMAX - XMIN, r1, r2, r3, f;
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int rect;
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ij_to_xy(i, j, xy);
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x = xy[0];
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y = xy[1];
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switch (POTENTIAL) {
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case (POT_HARMONIC):
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{
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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 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 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])
|
|
/* time step of field evolution */
|
|
{
|
|
int i, j, k, iplus, iminus, jplus, jminus;
|
|
double x, y, z, deltax, deltay, deltaz, rho, pot, vx, vy, test = 0.0, dx;
|
|
double *delta_phi[NLAPLACIANS], *nabla_phi, *nabla_psi, *nabla_omega, *delta_vorticity;
|
|
static double invsqr3 = 0.577350269; /* 1/sqrt(3) */
|
|
static double stiffness = 2.0; /* stiffness of Poisson equation solver */
|
|
static int smooth = 0;
|
|
|
|
for (i=0; i<NLAPLACIANS; i++) delta_phi[i] = (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);
|
|
|
|
/* 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);
|
|
}
|
|
|
|
/* compute gradients of stream function and vorticity for Euler equation */
|
|
if (RDE_EQUATION == 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, EULER_GRADIENT_YSHIFT);
|
|
compute_gradient_euler(phi_in[1], nabla_omega, 0.0);
|
|
dx = (XMAX-XMIN)/((double)NX);
|
|
|
|
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);
|
|
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;
|
|
}
|
|
}
|
|
|
|
if (TEST_GRADIENT) {
|
|
for (i=0; i<2*NX*NY; 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=0; i<NX; 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 + 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):
|
|
{
|
|
// if ((j > 1)&&(j < NY - 1))
|
|
{
|
|
phi_out[0][i*NY+j] = phi_in[0][i*NY+j] + intstep*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 ((i == 0)&&(j%10 == 0)) printf("j = %i, psi = %.5lg\n", j, phi_out[0][i*NY+j]);
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
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);
|
|
}
|
|
}
|
|
|
|
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])
|
|
/* time step of field evolution */
|
|
{
|
|
evolve_wave_half(phi, phi_tmp, xy_in, potential_field, vector_potential_field);
|
|
evolve_wave_half(phi_tmp, phi, xy_in, potential_field, vector_potential_field);
|
|
}
|
|
|
|
|
|
void evolve_tracers(double *phi[NFIELDS], double tracers[2*N_TRACERS*NSTEPS], int time, int nsteps, double step)
|
|
/* time steps of tracer particle evolution (for Euler equation) */
|
|
{
|
|
int tracer, i, j, t, ij[2], iplus, jplus;
|
|
double x, y, xy[2], vx, vy;
|
|
|
|
step = 0.2;
|
|
|
|
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];
|
|
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;
|
|
|
|
// 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)
|
|
{
|
|
tracers[(time+1)*2*N_TRACERS + 2*tracer] = x;
|
|
tracers[(time+1)*2*N_TRACERS + 2*tracer + 1] = y;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
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(t_rde rde[NX*NY], short int xy_in[NX*NY], double time, short int left, double viscosity, double noise)
|
|
{
|
|
char message[100];
|
|
double density, hue, rgb[3], logratio, x, y, pos[2], probas[2];
|
|
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 - 0.39;
|
|
xtext = XMAX - 0.55;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
boxwidth = 0.3;
|
|
boxheight = 0.05;
|
|
if (left)
|
|
{
|
|
xbox = XMIN + 0.4;
|
|
xtext = XMIN + 0.1;
|
|
}
|
|
else
|
|
{
|
|
xbox = XMAX - 0.39;
|
|
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);
|
|
if (PLOT_3D) write_text(xtext, y, message);
|
|
else
|
|
{
|
|
xy_to_pos(xtext, y, pos);
|
|
write_text(pos[0], pos[1], message);
|
|
}
|
|
}
|
|
}
|
|
|
|
void draw_color_bar_palette(int plot, double range, int palette, 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(-1.0, -0.8, XMAX - 0.1, -1.0, 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 (ROTATE_COLOR_SCHEME)
|
|
draw_color_scheme_palette_fade(-1.0, -0.8, XMAX - 0.1, -1.0, 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);
|
|
}
|
|
}
|
|
|
|
|
|
void viewpoint_schedule(int i)
|
|
/* change position of observer */
|
|
{
|
|
int j;
|
|
double angle, ca, sa;
|
|
static double observer_initial[3];
|
|
static int first = 1;
|
|
|
|
if (first)
|
|
{
|
|
for (j=0; j<3; j++) observer_initial[j] = observer[j];
|
|
first = 0;
|
|
}
|
|
|
|
angle = (ROTATE_ANGLE*DPI/360.0)*(double)i/(double)NSTEPS;
|
|
ca = cos(angle);
|
|
sa = sin(angle);
|
|
observer[0] = ca*observer_initial[0] - sa*observer_initial[1];
|
|
observer[1] = sa*observer_initial[0] + ca*observer_initial[1];
|
|
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,
|
|
intstep0, viscosity_printed, fade_value, noise = NOISE_INTENSITY;
|
|
double *phi[NFIELDS], *phi_tmp[NFIELDS], *potential_field, *vector_potential_field, *tracers;
|
|
short int *xy_in;
|
|
int i, j, k, s, nvid, field;
|
|
static int counter = 0;
|
|
t_rde *rde;
|
|
|
|
/* 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));
|
|
|
|
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 (ADD_TRACERS) tracers = (double *)malloc(2*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(0.0, 0.4, phi, xy_in);
|
|
// init_gaussian(x, y, mean, amplitude, scalex, phi, xy_in)
|
|
// init_coherent_state(-1.2, 0.35, 5.0, -2.0, 0.1, phi, xy_in);
|
|
// 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_shear_flow(1.0, 0.02, 0.15, 1, 1, phi, xy_in);
|
|
// init_laminar_flow(1.0, 0.1, 0.5, 0.0, phi, xy_in);
|
|
|
|
init_shear_flow(-1.0, 0.0, 0.1, 1, 1, 0.0, phi, xy_in);
|
|
|
|
init_cfield_rde(phi, xy_in, CPLOT, rde, 0);
|
|
if (PLOT_3D) 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) 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;
|
|
}
|
|
|
|
blank();
|
|
glColor3f(0.0, 0.0, 0.0);
|
|
|
|
|
|
glutSwapBuffers();
|
|
|
|
printf("Drawing wave\n");
|
|
draw_wave_rde(0, phi, xy_in, rde, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
|
|
// draw_billiard();
|
|
if (PRINT_PARAMETERS) print_parameters(rde, xy_in, time, 0, VISCOSITY, noise);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, 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 (ROTATE_VIEW)
|
|
{
|
|
viewpoint_schedule(i - INITIAL_TIME);
|
|
reset_view = 1;
|
|
}
|
|
|
|
printf("Drawing wave %i\n", i);
|
|
draw_wave_rde(0, phi, xy_in, rde, 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);
|
|
|
|
if (ADD_TRACERS)
|
|
{
|
|
printf("Evolving tracer particles\n");
|
|
evolve_tracers(phi, tracers, 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]);
|
|
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][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(rde, xy_in, time, 0, viscosity_printed, noise);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, 0, 1.0);
|
|
|
|
// print_level(MDEPTH);
|
|
// print_Julia_parameters(i);
|
|
|
|
glutSwapBuffers();
|
|
|
|
/* modify Julia set */
|
|
// set_Julia_parameters(i, phi, xy_in);
|
|
|
|
if (MOVIE)
|
|
{
|
|
printf("Saving frame %i\n", i);
|
|
save_frame();
|
|
|
|
if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
|
|
{
|
|
draw_wave_rde(1, phi, xy_in, rde, potential_field, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 0, 1.0, REFRESH_B);
|
|
if (ADD_TRACERS) draw_tracers(phi, tracers, i, 0, 1.0);
|
|
// draw_billiard();
|
|
if (PRINT_PARAMETERS) print_parameters(rde, xy_in, time, 0, viscosity_printed, noise);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, 0, 1.0);
|
|
glutSwapBuffers();
|
|
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
|
|
counter++;
|
|
}
|
|
|
|
/* 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, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
|
|
if (ADD_TRACERS) draw_tracers(phi, tracers, NSTEPS, 0, 1.0);
|
|
// draw_billiard();
|
|
if (PRINT_PARAMETERS) print_parameters(rde, xy_in, time, 0, viscosity_printed, noise);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, 0, 1.0);
|
|
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, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 1, fade_value, 0);
|
|
if (ADD_TRACERS) draw_tracers(phi, tracers, NSTEPS, 1, fade_value);
|
|
// draw_billiard();
|
|
if (PRINT_PARAMETERS) print_parameters(rde, xy_in, time, 0, viscosity_printed, noise);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, 1, fade_value);
|
|
glutSwapBuffers();
|
|
save_frame_counter(NSTEPS + i + 1);
|
|
}
|
|
draw_wave_rde(1, phi, xy_in, rde, potential_field, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 0, 1.0, REFRESH_B);
|
|
if (ADD_TRACERS) draw_tracers(phi, tracers, NSTEPS, 0, 1.0);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_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, potential_field, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 1, fade_value, 0);
|
|
if (ADD_TRACERS) draw_tracers(phi, tracers, NSTEPS, 1, fade_value);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_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, potential_field, ZPLOT, CPLOT, COLOR_PALETTE, 1, fade_value, 0);
|
|
if (ADD_TRACERS) draw_tracers(phi, tracers, NSTEPS, 1, fade_value);
|
|
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, 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 (ADD_POTENTIAL) free(potential_field);
|
|
else if (ADD_MAGNETIC_FIELD)
|
|
{
|
|
free(potential_field);
|
|
free(vector_potential_field);
|
|
}
|
|
if (ADD_TRACERS) free(tracers);
|
|
|
|
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();
|
|
|
|
glutDisplayFunc(display);
|
|
|
|
glutMainLoop();
|
|
|
|
return 0;
|
|
}
|
|
|