759 lines
31 KiB
C
759 lines
31 KiB
C
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/*********************************************************************************/
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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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/* 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 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 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 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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/* 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 1 /* 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 0.002 /* 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 0.01 /* Courant number in medium B */
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// #define COURANTB 0.00666 /* Courant number in medium B */
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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 GAMMAB 5.0e-4 /* damping factor in wave equation */
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// #define GAMMAB 1.0e-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 1000 /* number of frames of movie */
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#define NSTEPS 4500 /* 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 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 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 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 1.1e-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 0 /* set to 1 for mangroves to be eroded */
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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 DT_MANGROVE 0.1 /* time step for mangrove displacement */
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#define KSPRING 0.25 /* spring constant of mangroves */
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// #define KSPRING 0.75 /* spring constant of mangroves */
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// #define KSPRING 0.15 /* spring constant of mangroves */
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#define KWAVE 2.0 /* constant in force due to wave gradient */
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#define DXMAX 0.02 /* max displacement of mangrove in one time step */
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#define L_DETACH 0.2 /* spring length beyond which mangroves detach */
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#define DAMP_MANGROVE 0.2 /* damping coefficient of mangroves */
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#define MANGROVE_MASS 1.5 /* mass of mangrove of radius MU */
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// #define MANGROVE_MASS 2.0 /* mass of mangrove of radius MU */
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// #define KSPRING 0.5 /* spring constant of mangroves */
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// #define KWAVE 2.0 /* constant in force due to wave gradient */
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// #define DXMAX 0.02 /* max displacement of mangrove in one time step */
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// #define L_DETACH 0.4 /* spring length beyond which mangroves detach */
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// #define DAMP_MANGROVE 0.3 /* damping coefficient of mangroves */
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//
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// #define KSPRING 1.0 /* spring constant of mangroves */
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// #define KWAVE 2.0 /* constant in force due to wave gradient */
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// #define DXMAX 0.02 /* max displacement of mangrove in one time step */
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// #define L_DETACH 0.4 /* spring length beyond which mangroves detach */
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// #define DAMP_MANGROVE 0.3 /* damping coefficient of mangroves */
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//
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// #define KSPRING 2.0 /* spring constant of mangroves */
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// #define KWAVE 5.0 /* constant in force due to wave gradient */
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// #define DXMAX 0.02 /* max displacement of mangrove in one time step */
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// #define L_DETACH 0.2 /* spring length beyond which mangroves detach */
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// #define DAMP_MANGROVE 0.2 /* damping coefficient of mangroves */
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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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#include "global_pdes.c"
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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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double circle_energy[NMAXCIRCLES]; /* energy dissipated by the circles */
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double circley_wrapped[NMAXCIRCLES]; /* position of circle centers wrapped vertically */
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double anchor_x[NMAXCIRCLES]; /* points moving circles are attached to */
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double anchor_y[NMAXCIRCLES]; /* points moving circles are attached to */
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double vx[NMAXCIRCLES]; /* x velocity of circles */
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double vy[NMAXCIRCLES]; /* y velocity of circles */
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double circlerad_initial[NMAXCIRCLES]; /* initial circle radii */
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double mass_inverse[NMAXCIRCLES]; /* inverse of mangrove mass */
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short int circle_attached[NMAXCIRCLES]; /* has value 1 if the circle is attached to its anchor */
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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(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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time++;
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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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#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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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)
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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) % 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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/* imposing linear wave on top and bottom by making Laplacian 1d */
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if ((OSCILLATE_TOPBOT)&&(i < tb_shift))
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{
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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(double *phi[NX], double *psi[NX], double *phi_tmp[NX], double *psi_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, phi_tmp, psi_tmp, xy_in);
|
||
|
|
evolve_wave_half(phi_tmp, psi_tmp, phi, psi, xy_in);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
void animation()
|
||
|
|
{
|
||
|
|
double time, scale, diss, rgb[3], hue, y, dissip, ej, gradient[2], dx, dy, dt, xleft, xright, length;
|
||
|
|
double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX];
|
||
|
|
short int *xy_in[NX], redraw = 0;
|
||
|
|
int i, j, s, ij[2];
|
||
|
|
static int imin, imax;
|
||
|
|
static short int first = 1;
|
||
|
|
|
||
|
|
/* 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));
|
||
|
|
phi_tmp[i] = (double *)malloc(NY*sizeof(double));
|
||
|
|
psi_tmp[i] = (double *)malloc(NY*sizeof(double));
|
||
|
|
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
|
||
|
|
}
|
||
|
|
|
||
|
|
/* initialise positions and radii of circles */
|
||
|
|
if (B_DOMAIN == D_CIRCLES) init_circle_config();
|
||
|
|
|
||
|
|
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);
|
||
|
|
|
||
|
|
// init_planar_wave(XMIN + 0.01, 0.0, phi, psi, xy_in);
|
||
|
|
// init_planar_wave(XMIN + 0.02, 0.0, phi, psi, xy_in);
|
||
|
|
// init_planar_wave(XMIN + 1.0, 0.0, phi, psi, xy_in);
|
||
|
|
// init_wave(-1.5, 0.0, phi, psi, xy_in);
|
||
|
|
// init_wave(0.0, 0.0, phi, psi, xy_in);
|
||
|
|
|
||
|
|
/* add a drop at another point */
|
||
|
|
// add_drop_to_wave(1.0, 0.7, 0.0, phi, psi);
|
||
|
|
// add_drop_to_wave(1.0, -0.7, 0.0, phi, psi);
|
||
|
|
// add_drop_to_wave(1.0, 0.0, -0.7, phi, psi);
|
||
|
|
|
||
|
|
/* initialise mangroves */
|
||
|
|
for (i=0; i < ncircles; i++)
|
||
|
|
{
|
||
|
|
circle_energy[i] = 0.0;
|
||
|
|
y = circley[i];
|
||
|
|
if (y >= YMAX) y -= circlerad[i];
|
||
|
|
if (y <= YMIN) y += circlerad[i];
|
||
|
|
// if (y >= YMAX) y -= (YMAX - YMIN);
|
||
|
|
// if (y <= YMIN) y += (YMAX - YMIN);
|
||
|
|
circley_wrapped[i] = y;
|
||
|
|
|
||
|
|
if (RANDOM_RADIUS) circlerad[i] = circlerad[i]*(0.75 + 0.5*((double)rand()/RAND_MAX));
|
||
|
|
|
||
|
|
circlerad_initial[i] = circlerad[i];
|
||
|
|
circle_attached[i] = 1;
|
||
|
|
mass_inverse[i] = MU*MU/(MANGROVE_MASS*circlerad[i]*circlerad[i]);
|
||
|
|
|
||
|
|
if (MOVE_MANGROVES)
|
||
|
|
{
|
||
|
|
anchor_x[i] = circlex[i];
|
||
|
|
anchor_y[i] = circley_wrapped[i];
|
||
|
|
// anchor_y[i] = circley[i];
|
||
|
|
}
|
||
|
|
|
||
|
|
if (INERTIA)
|
||
|
|
{
|
||
|
|
vx[i] = 0.0;
|
||
|
|
vy[i] = 0.0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if (first) /* compute box limits where circles are reset */
|
||
|
|
{
|
||
|
|
/* find leftmost and rightmost circle */
|
||
|
|
for (i=0; i<ncircles; i++)
|
||
|
|
if ((circleactive[i])&&(circlex[i] - circlerad[i] < xleft)) xleft = circlex[i] - circlerad[i];
|
||
|
|
for (i=0; i<ncircles; i++)
|
||
|
|
if ((circleactive[i])&&(circlex[i] + circlerad[i] > xright)) xright = circlex[i] + circlerad[i];
|
||
|
|
|
||
|
|
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();
|
||
|
|
|
||
|
|
glutSwapBuffers();
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
sleep(SLEEP1);
|
||
|
|
|
||
|
|
for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
|
||
|
|
{
|
||
|
|
//printf("%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;
|
||
|
|
|
||
|
|
draw_wave(phi, psi, xy_in, scale, i, PLOT);
|
||
|
|
for (j=0; j<NVID; j++)
|
||
|
|
{
|
||
|
|
evolve_wave(phi, psi, phi_tmp, 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);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* compute energy dissipated in obstacles */
|
||
|
|
if (ERODE_MANGROVES) for (j=0; j<ncircles; j++)
|
||
|
|
{
|
||
|
|
dissip = compute_dissipation(phi, psi, xy_in, circlex[j], circley_wrapped[j]);
|
||
|
|
|
||
|
|
/* 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 (circleactive[j])
|
||
|
|
{
|
||
|
|
circle_energy[j] += dissip;
|
||
|
|
ej = circle_energy[j];
|
||
|
|
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(circlex[j], circley[j], circlerad[j], NSEG, rgb);
|
||
|
|
|
||
|
|
/* shrink mangrove */
|
||
|
|
if (ej > 0.0)
|
||
|
|
{
|
||
|
|
// circlerad[j] -= MU*ej*ej/(MANGROVE_EMAX*MANGROVE_EMAX);
|
||
|
|
// if (circlerad[j] < 0.0) circlerad[j] = 0.0;
|
||
|
|
circlerad[j] = circlerad_initial[j]*(1.0 - ej*ej/(MANGROVE_EMAX*MANGROVE_EMAX));
|
||
|
|
redraw = 1;
|
||
|
|
}
|
||
|
|
else circlerad[j] = circlerad_initial[j];
|
||
|
|
}
|
||
|
|
else /* remove mangrove */
|
||
|
|
{
|
||
|
|
circleactive[j] = 0;
|
||
|
|
/* reinitialize table xy_in */
|
||
|
|
redraw = 1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else /* allow disabled mangroves to recover */
|
||
|
|
{
|
||
|
|
circle_energy[j] -= 0.15*dissip;
|
||
|
|
// circlerad[j] += 0.005*MU;
|
||
|
|
// if (circlerad[j] > MU) circlerad[j] = MU;
|
||
|
|
// if ((circle_energy[j] < 0.0)&&(circlerad[j] > 0.0))
|
||
|
|
if (circle_energy[j] < 0.0)
|
||
|
|
{
|
||
|
|
circleactive[j] = 1;
|
||
|
|
// circlerad[j] = circlerad[j]*(0.75 + 0.5*((double)rand()/RAND_MAX));
|
||
|
|
circlerad[j] = circlerad_initial[j];
|
||
|
|
circle_energy[j] = -MANGROVE_EMAX;
|
||
|
|
/* reinitialize table xy_in */
|
||
|
|
redraw = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
// printf("Circle %i, energy %.5lg\n", j, circle_energy[j]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* move mangroves */
|
||
|
|
if (MOVE_MANGROVES) for (j=0; j<ncircles; j++) if (circleactive[j])
|
||
|
|
{
|
||
|
|
compute_gradient(phi, psi, circlex[j], circley_wrapped[j], gradient);
|
||
|
|
|
||
|
|
// if (j%NGRIDY == 0) printf("gradient (%.3lg, %.3lg)\n", gradient[0], gradient[1]);
|
||
|
|
// if (j%NGRIDY == 0) printf("circle %i (%.3lg, %.3lg) -> ", j, circlex[j], circley[j]);
|
||
|
|
|
||
|
|
/* compute force of wave */
|
||
|
|
dx = DT_MANGROVE*KWAVE*gradient[0];
|
||
|
|
dy = DT_MANGROVE*KWAVE*gradient[1];
|
||
|
|
|
||
|
|
/* compute force of spring */
|
||
|
|
if (circle_attached[j])
|
||
|
|
{
|
||
|
|
dx += DT_MANGROVE*(-KSPRING*(circlex[j] - anchor_x[j]));
|
||
|
|
dy += DT_MANGROVE*(-KSPRING*(circley_wrapped[j] - anchor_y[j]));
|
||
|
|
}
|
||
|
|
|
||
|
|
/* detach mangrove if spring is too long */
|
||
|
|
if (DETACH_MANGROVES)
|
||
|
|
{
|
||
|
|
length = module2(circlex[j] - anchor_x[j], circley_wrapped[j] - anchor_y[j]);
|
||
|
|
if (j%NGRIDY == 0) printf("spring length %.i: %.3lg\n", j, length);
|
||
|
|
// if (length > L_DETACH) circle_attached[j] = 0;
|
||
|
|
if (length*mass_inverse[j] > L_DETACH) circle_attached[j] = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (dx > DXMAX) dx = DXMAX;
|
||
|
|
if (dx < -DXMAX) dx = -DXMAX;
|
||
|
|
if (dy > DXMAX) dy = DXMAX;
|
||
|
|
if (dy < -DXMAX) dy = -DXMAX;
|
||
|
|
|
||
|
|
if (INERTIA)
|
||
|
|
{
|
||
|
|
vx[j] += (dx - DAMP_MANGROVE*vx[j])*mass_inverse[j];
|
||
|
|
vy[j] += (dy - DAMP_MANGROVE*vy[j])*mass_inverse[j];
|
||
|
|
circlex[j] += vx[j]*DT_MANGROVE;
|
||
|
|
circley[j] += vy[j]*DT_MANGROVE;
|
||
|
|
circley_wrapped[j] += vy[j]*DT_MANGROVE;
|
||
|
|
if (j%NGRIDY == 0)
|
||
|
|
printf("circle %.i: (dx,dy) = (%.3lg,%.3lg), (vx,vy) = (%.3lg,%.3lg)\n",
|
||
|
|
j, circlex[j]-anchor_x[j], circley[j]-anchor_y[j], vx[j], vy[j]);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
circlex[j] += dx*mass_inverse[j]*DT_MANGROVE;
|
||
|
|
circley[j] += dy*mass_inverse[j]*DT_MANGROVE;
|
||
|
|
circley_wrapped[j] += dy*mass_inverse[j]*DT_MANGROVE;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (circlex[j] <= XMIN) circlex[j] = XMIN;
|
||
|
|
if (circlex[j] >= XMAX) circlex[j] = XMAX;
|
||
|
|
if (circley_wrapped[j] <= YMIN) circley_wrapped[j] = YMIN;
|
||
|
|
if (circley_wrapped[j] >= YMAX) circley_wrapped[j] = YMAX;
|
||
|
|
|
||
|
|
// if (j%NGRIDY == 0) printf("(%.3lg, %.3lg)\n", circlex[j], circley[j]);
|
||
|
|
|
||
|
|
redraw = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
draw_billiard();
|
||
|
|
|
||
|
|
glutSwapBuffers();
|
||
|
|
|
||
|
|
if (redraw)
|
||
|
|
{
|
||
|
|
printf("Reinitializing xy_in\n");
|
||
|
|
init_xyin_xrange(xy_in, imin, NX-1);
|
||
|
|
// 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(phi_tmp[i]);
|
||
|
|
free(psi_tmp[i]);
|
||
|
|
free(xy_in[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
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;
|
||
|
|
}
|
||
|
|
|