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YouTube-simulations/wave_common.c

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2021-08-15 11:49:37 +02:00
/* functions common to wave_billiard.c, wave_comparison.c, mangrove.c */
void init_xyin(short int * xy_in[NX])
/* initialise table xy_in, needed when obstacles are killed */
// short int * xy_in[NX];
//
{
int i, j;
double xy[2];
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
}
}
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void init_xyin_xrange(short int * xy_in[NX], int imin, int imax)
/* initialise table xy_in, needed when obstacles are killed */
// short int * xy_in[NX];
//
{
int i, j;
double xy[2];
for (i=imin; i<imax; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
}
}
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void init_wave(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
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if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.005)*cos(-sqrt(dist2)/0.1);
// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01);
// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.00025)*cos(-sqrt(dist2)/0.005);
else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
}
void init_circular_wave(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
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printf("Initializing wave\n");
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for (i=0; i<NX; i++)
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{
if (i%100 == 0) printf("Initializing column %i of %i\n", i, NX);
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for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
if ((xy_in[i][j])||(TWOSPEEDS))
phi[i][j] = INITIAL_AMP*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
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else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
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}
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}
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void init_wave_plus(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) for y > 0 - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
if ((xy[1] > 0.0)&&((xy_in[i][j])||(TWOSPEEDS)))
phi[i][j] = INITIAL_AMP*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
}
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void init_circular_wave_xplusminus(double xleft, double yleft, double xright, double yright,
double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with two drops, x > 0 and x < 0 do not communicate - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
if (xy[0] < 0.0) dist2 = (xy[0]-xleft)*(xy[0]-xleft) + (xy[1]-yleft)*(xy[1]-yleft);
else dist2 = (xy[0]-xright)*(xy[0]-xright) + (xy[1]-yright)*(xy[1]-yright);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
if ((xy_in[i][j])||(TWOSPEEDS))
phi[i][j] = INITIAL_AMP*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
}
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void init_planar_wave(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
/* beta version, works for vertical planar wave only so far */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
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{
// if (i%100 == 0) printf("Initializing column %i\n", i);
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for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
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if ((xy_in[i][j])||(TWOSPEEDS))
phi[i][j] = INITIAL_AMP*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
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// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.01*exp(-dist2/0.0005)*cos(-sqrt(dist2)/0.01);
// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.01*exp(-dist2/0.0005)*cos(-sqrt(dist2)/0.02);
// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.01*exp(-dist2/0.005)*cos(-sqrt(dist2)/0.02);
// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.01*exp(-dist2/0.01)*cos(-sqrt(dist2)/0.02);
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// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.01*exp(-dist2/0.0005)*cos(-sqrt(dist2)/0.01);
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// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.01*exp(-dist2/0.05)*cos(-sqrt(dist2)/0.025);
else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
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}
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}
void init_wave_flat( double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise flat field - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
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for (i=0; i<NX; i++) {
if (i%100 == 0) printf("Wave and table xy_in - Initialising column %i of %i\n", i, NX);
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for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
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// if ((i%10 == 0)&&(j == NY/2)) printf ("xy_in[%i][%i] = %i\n", i, j, xy_in[i][j]);
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phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
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}
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}
void add_drop_to_wave(double factor, double x, double y, double *phi[NX], double *psi[NX])
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/* OLD VERSION - add drop at (x,y) to the field with given prefactor */
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{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
phi[i][j] += 0.2*factor*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01);
}
}
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void add_circular_wave(double factor, double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* add drop at (x,y) to the field with given prefactor */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
if ((xy_in[i][j])||(TWOSPEEDS))
phi[i][j] += INITIAL_AMP*factor*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
}
}
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void oscillate_linear_wave(double amplitude, double t, double x1, double y1, double x2, double y2, double *phi[NX],
double *psi[NX])
/* oscillating boundary condition at (x,y), beta version */
{
int i, j, ij1[2], ij2[2], imin, imax, jmin, jmax, d = 5;
double xy[2], dist2;
xy_to_ij(x1, y1, ij1);
xy_to_ij(x2, y2, ij2);
imin = ij1[0] - d; if (imin < 0) imin = 0;
imax = ij2[0] + d; if (imax >= NX) imax = NX-1;
jmin = ij1[1] - d; if (jmin < 0) jmin = 0;
jmax = ij2[1] + d; if (jmax >= NY) jmax = NY-1;
for (i = imin; i < imax; i++)
for (j = jmin; j < jmax; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x1)*(xy[0]-x1); /* to be improved */
// dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
// if (dist2 < 0.01)
if (dist2 < 0.001)
phi[i][j] = amplitude*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01)*cos(t*OMEGA);
// phi[i][j] += 0.2*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01)*cos(t*OMEGA);
}
}
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void compute_gradient(double *phi[NX], double *psi[NX], double x, double y, double gradient[2])
{
double velocity;
int iplus, iminus, jplus, jminus, ij[2], i, j;
xy_to_ij(x, y, ij);
i = ij[0];
j = ij[1];
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
gradient[0] = (phi[iplus][j]-phi[i][j])*(phi[iplus][j]-phi[i][j])
+ (phi[i][j] - phi[iminus][j])*(phi[i][j] - phi[iminus][j]);
gradient[1] = (phi[i][jplus]-phi[i][j])*(phi[i][jplus]-phi[i][j])
+ (phi[i][j] - phi[i][jminus])*(phi[i][j] - phi[i][jminus]);
}
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double compute_energy(double *phi[NX], double *psi[NX], short int *xy_in[NX], int i, int j)
{
double velocity, energy, gradientx2, gradienty2;
int iplus, iminus, jplus, jminus;
velocity = (phi[i][j] - psi[i][j]);
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
gradientx2 = (phi[iplus][j]-phi[i][j])*(phi[iplus][j]-phi[i][j])
+ (phi[i][j] - phi[iminus][j])*(phi[i][j] - phi[iminus][j]);
gradienty2 = (phi[i][jplus]-phi[i][j])*(phi[i][jplus]-phi[i][j])
+ (phi[i][j] - phi[i][jminus])*(phi[i][j] - phi[i][jminus]);
if (xy_in[i][j]) return(E_SCALE*E_SCALE*(velocity*velocity + 0.5*COURANT*COURANT*(gradientx2+gradienty2)));
else if (TWOSPEEDS) return(E_SCALE*E_SCALE*(velocity*velocity + 0.5*COURANTB*COURANTB*(gradientx2+gradienty2)));
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else return(0.0);
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}
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void compute_energy_flux(double *phi[NX], double *psi[NX], short int *xy_in[NX], int i, int j, double *gx, double *gy, double *arg, double *module)
/* computes energy flux given by c^2 norm(nabla u) du/dt*/
{
double velocity, energy, gradientx, gradienty;
int iplus, iminus, jplus, jminus;
velocity = vabs(phi[i][j] - psi[i][j]);
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
gradientx = (phi[iplus][j] - phi[iminus][j]);
gradienty = (phi[i][jplus] - phi[i][jminus]);
*arg = argument(gradientx,gradienty);
if (*arg < 0.0) *arg += DPI;
if (*arg > DPI) *arg -= DPI;
if ((xy_in[i][j])||(TWOSPEEDS))
{
*module = velocity*module2(gradientx, gradienty);
*gx = velocity*gradientx;
*gy = velocity*gradienty;
}
else
{
*module = 0.0;
*gx = 0.0;
*gy = 0.0;
}
// if (xy_in[i][j]) return(E_SCALE*E_SCALE*(velocity*COURANT*module2(gradientx,gradienty)));
// else if (TWOSPEEDS) return(E_SCALE*E_SCALE*(velocity*COURANTB*module2(gradientx,gradienty)));
}
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double compute_variance(double *phi[NX], double *psi[NX], short int *xy_in[NX])
/* compute the variance of the field, to adjust color scheme */
{
int i, j, n = 0;
double variance = 0.0;
for (i=1; i<NX; i++)
for (j=1; j<NY; j++)
{
if (xy_in[i][j])
{
n++;
variance += phi[i][j]*phi[i][j];
}
}
if (n==0) n=1;
return(variance/(double)n);
}
double compute_dissipation(double *phi[NX], double *psi[NX], short int *xy_in[NX], double x, double y)
{
double velocity;
int ij[2];
xy_to_ij(x, y, ij);
velocity = (phi[ij[0]][ij[1]] - psi[ij[0]][ij[1]]);
return(velocity*velocity);
}
void draw_wave(double *phi[NX], double *psi[NX], short int *xy_in[NX], double scale, int time, int plot)
/* draw the field */
{
int i, j, iplus, iminus, jplus, jminus;
double rgb[3], xy[2], x1, y1, x2, y2, velocity, energy, gradientx2, gradienty2;
static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
glBegin(GL_QUADS);
// printf("dtinverse = %.5lg\n", dtinverse);
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
if (plot == P_AMPLITUDE)
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{
/* make wave luminosity larger inside obstacles */
if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, phi[i][j], scale, time, 0.7, rgb);
else color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
}
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else if (plot == P_ENERGY)
color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
else if (plot == P_MIXED)
{
if (j > NY/2) color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
else color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
}
glColor3f(rgb[0], rgb[1], rgb[2]);
glVertex2i(i, j);
glVertex2i(i+1, j);
glVertex2i(i+1, j+1);
glVertex2i(i, j+1);
}
}
glEnd ();
}
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void draw_wave_e(double *phi[NX], double *psi[NX], double *total_energy[NX], double *color_scale[NX], short int *xy_in[NX],
double scale, int time, int plot)
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/* draw the field, new version with total energy option */
{
int i, j, iplus, iminus, jplus, jminus;
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double rgb[3], xy[2], x1, y1, x2, y2, velocity, field_value, energy, gradientx2, gradienty2, r2;
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static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
glBegin(GL_QUADS);
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// printf("dtinverse = %.5lg\n", dtinverse);
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
switch (plot) {
case (P_AMPLITUDE):
{
/* make wave luminosity larger inside obstacles */
field_value = phi[i][j];
if (RESCALE_COLOR_IN_CENTER)
{
field_value *= color_scale[i][j];
}
// if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, field_value, scale, time, 0.7, rgb);
// else
color_scheme(COLOR_SCHEME, field_value, scale, time, rgb);
break;
}
case (P_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (RESCALE_COLOR_IN_CENTER)
{
energy *= color_scale[i][j];
}
/* adjust energy to color palette */
if (COLOR_PALETTE >= COL_TURBO) color_scheme_asym(COLOR_SCHEME, energy, scale, time, rgb);
else color_scheme(COLOR_SCHEME, energy, scale, time, rgb);
break;
}
case (P_MIXED):
{
if (j > NY/2) color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
else color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
total_energy[i][j] += energy;
if (COLOR_PALETTE >= COL_TURBO)
color_scheme_asym(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
else color_scheme(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
break;
}
case (P_LOG_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
color_scheme(COLOR_SCHEME, LOG_SHIFT + LOG_SCALE*log(energy), scale, time, rgb);
break;
}
case (P_LOG_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (energy == 0.0) energy = 1.0e-20;
total_energy[i][j] += energy;
energy = LOG_SHIFT + LOG_SCALE*log(total_energy[i][j]/(double)(time+1));
color_scheme(COLOR_SCHEME, energy, scale, time, rgb);
break;
}
}
glColor3f(rgb[0], rgb[1], rgb[2]);
glVertex2i(i, j);
glVertex2i(i+1, j);
glVertex2i(i+1, j+1);
glVertex2i(i, j+1);
}
}
glEnd ();
}
void draw_wave_highres(int size, double *phi[NX], double *psi[NX], double *total_energy[NX], short int *xy_in[NX], double scale, int time, int plot)
/* draw the field, new version with total energy option */
{
int i, j, iplus, iminus, jplus, jminus;
double rgb[3], xy[2], x1, y1, x2, y2, velocity, energy, gradientx2, gradienty2;
static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
glBegin(GL_QUADS);
// printf("dtinverse = %.5lg\n", dtinverse);
for (i=0; i<NX; i+=size)
for (j=0; j<NY; j+=size)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
switch (plot) {
case (P_AMPLITUDE):
{
// /* make wave luminosity larger inside obstacles */
// if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, phi[i][j], scale, time, 0.7, rgb);
// else
color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
break;
}
case (P_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
/* adjust energy to color palette */
if (COLOR_PALETTE >= COL_TURBO) color_scheme_asym(COLOR_SCHEME, energy, scale, time, rgb);
else color_scheme(COLOR_SCHEME, energy, scale, time, rgb);
break;
}
case (P_MIXED):
{
if (j > NY/2) color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
else color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
total_energy[i][j] += energy;
if (COLOR_PALETTE >= COL_TURBO)
color_scheme_asym(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
else color_scheme(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
break;
}
case (P_LOG_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
// energy = LOG_SHIFT + LOG_SCALE*log(energy);
// if (energy < 0.0) energy = 0.0;
color_scheme(COLOR_SCHEME, LOG_SHIFT + LOG_SCALE*log(energy), scale, time, rgb);
break;
}
case (P_LOG_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (energy == 0.0) energy = 1.0e-20;
total_energy[i][j] += energy;
color_scheme(COLOR_SCHEME, LOG_SHIFT + LOG_SCALE*log(total_energy[i][j]/(double)(time+1)), scale, time, rgb);
break;
}
}
glColor3f(rgb[0], rgb[1], rgb[2]);
glVertex2i(i, j);
glVertex2i(i+size, j);
glVertex2i(i+size, j+size);
glVertex2i(i, j+size);
}
}
glEnd ();
}
void draw_wave_ediss(double *phi[NX], double *psi[NX], double *total_energy[NX], double *color_scale[NX], short int *xy_in[NX],
double *gamma[NX], double gammamax, double scale, int time, int plot)
/* draw the field with luminosity depending on damping */
{
int i, j, k, iplus, iminus, jplus, jminus;
double rgb[3], xy[2], x1, y1, x2, y2, velocity, field_value, energy, gradientx2, gradienty2, r2;
static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
glBegin(GL_QUADS);
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// printf("dtinverse = %.5lg\n", dtinverse);
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
switch (plot) {
case (P_AMPLITUDE):
{
/* make wave luminosity larger inside obstacles */
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field_value = phi[i][j];
if (RESCALE_COLOR_IN_CENTER)
{
field_value *= color_scale[i][j];
}
if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, field_value, scale, time, 0.7, rgb);
else color_scheme(COLOR_SCHEME, field_value, scale, time, rgb);
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break;
}
case (P_ENERGY):
{
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energy = compute_energy(phi, psi, xy_in, i, j);
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if (RESCALE_COLOR_IN_CENTER)
{
energy *= color_scale[i][j];
}
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/* adjust energy to color palette */
if (COLOR_PALETTE >= COL_TURBO) color_scheme_asym(COLOR_SCHEME, energy, scale, time, rgb);
else color_scheme(COLOR_SCHEME, energy, scale, time, rgb);
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break;
}
case (P_MIXED):
{
if (j > NY/2) color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
else color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
total_energy[i][j] += energy;
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if (COLOR_PALETTE >= COL_TURBO)
color_scheme_asym(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
else color_scheme(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
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break;
}
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case (P_LOG_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
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color_scheme(COLOR_SCHEME, LOG_SHIFT + LOG_SCALE*log(energy), scale, time, rgb);
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break;
}
case (P_LOG_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (energy == 0.0) energy = 1.0e-20;
total_energy[i][j] += energy;
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color_scheme(COLOR_SCHEME, LOG_SHIFT + LOG_SCALE*log(total_energy[i][j]/(double)(time+1)), scale, time, rgb);
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break;
}
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}
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for (k=0; k<3; k++) rgb[k]*= 1.0 - gamma[i][j]/gammamax;
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glColor3f(rgb[0], rgb[1], rgb[2]);
glVertex2i(i, j);
glVertex2i(i+1, j);
glVertex2i(i+1, j+1);
glVertex2i(i, j+1);
}
}
glEnd ();
}
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void draw_wave_highres_diss(int size, double *phi[NX], double *psi[NX], double *total_energy[NX], short int *xy_in[NX],
double *gamma[NX], double gammamax, double scale, int time, int plot)
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/* draw the field, new version with total energy option */
{
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int i, j, k, iplus, iminus, jplus, jminus;
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double rgb[3], xy[2], x1, y1, x2, y2, velocity, energy, gradientx2, gradienty2;
static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
glBegin(GL_QUADS);
// printf("dtinverse = %.5lg\n", dtinverse);
for (i=0; i<NX; i+=size)
for (j=0; j<NY; j+=size)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
switch (plot) {
case (P_AMPLITUDE):
{
/* make wave luminosity larger inside obstacles */
if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, phi[i][j], scale, time, 0.7, rgb);
else color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
break;
}
case (P_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
/* adjust energy to color palette */
if (COLOR_PALETTE >= COL_TURBO) color_scheme_asym(COLOR_SCHEME, energy, scale, time, rgb);
else color_scheme(COLOR_SCHEME, energy, scale, time, rgb);
break;
}
case (P_MIXED):
{
if (j > NY/2) color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
else color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
total_energy[i][j] += energy;
if (COLOR_PALETTE >= COL_TURBO)
color_scheme_asym(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
else color_scheme(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
break;
}
case (P_LOG_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
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// energy = LOG_SHIFT + LOG_SCALE*log(energy);
// if (energy < 0.0) energy = 0.0;
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color_scheme(COLOR_SCHEME, LOG_SHIFT + LOG_SCALE*log(energy), scale, time, rgb);
break;
}
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case (P_LOG_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (energy == 0.0) energy = 1.0e-20;
total_energy[i][j] += energy;
color_scheme(COLOR_SCHEME, LOG_SHIFT + LOG_SCALE*log(total_energy[i][j]/(double)(time+1)), scale, time, rgb);
break;
}
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}
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for (k=0; k<3; k++) rgb[k]*= 1.0 - gamma[i][j]/gammamax;
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glColor3f(rgb[0], rgb[1], rgb[2]);
glVertex2i(i, j);
glVertex2i(i+size, j);
glVertex2i(i+size, j+size);
glVertex2i(i, j+size);
}
}
glEnd ();
}
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void draw_wave_epalette(double *phi[NX], double *psi[NX], double *total_energy[NX], double *total_flux, double *color_scale[NX],
short int *xy_in[NX], double scale, int time, int plot, int palette, int fade, double fade_value)
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/* same as draw_wave_e, but with color scheme specification */
{
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int i, j, k, iplus, iminus, jplus, jminus;
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double rgb[3], xy[2], x1, y1, x2, y2, velocity, field_value, energy, gradientx2, gradienty2, r2, arg, mod, flux_factor, gx, gy, mgx, mgy, ffactor;
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static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
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glBegin(GL_QUADS);
// printf("dtinverse = %.5lg\n", dtinverse);
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for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
switch (plot) {
case (P_AMPLITUDE):
{
/* make wave luminosity larger inside obstacles */
field_value = phi[i][j];
if (RESCALE_COLOR_IN_CENTER)
{
field_value *= color_scale[i][j];
}
// if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, field_value, scale, time, 0.7, rgb);
// else
color_scheme_palette(COLOR_SCHEME, palette, field_value, scale, time, rgb);
break;
}
case (P_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (RESCALE_COLOR_IN_CENTER)
{
energy *= color_scale[i][j];
}
/* adjust energy to color palette */
if (COLOR_PALETTE >= COL_TURBO) color_scheme_asym_palette(COLOR_SCHEME, palette, energy, scale, time, rgb);
else color_scheme_palette(COLOR_SCHEME, palette, energy, scale, time, rgb);
break;
}
case (P_MIXED):
{
if (j > NY/2) color_scheme_palette(COLOR_SCHEME, palette, phi[i][j], scale, time, rgb);
else color_scheme_palette(COLOR_SCHEME, palette, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
total_energy[i][j] += energy;
if (COLOR_PALETTE >= COL_TURBO)
color_scheme_asym_palette(COLOR_SCHEME, palette, total_energy[i][j]/(double)(time+1), scale, time, rgb);
else color_scheme_palette(COLOR_SCHEME, palette, total_energy[i][j]/(double)(time+1), scale, time, rgb);
break;
}
case (P_LOG_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
color_scheme_palette(COLOR_SCHEME, palette, LOG_SHIFT + LOG_SCALE*log(energy), scale, time, rgb);
break;
}
case (P_LOG_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (energy == 0.0) energy = 1.0e-20;
total_energy[i][j] += energy;
energy = LOG_SHIFT + LOG_SCALE*log(total_energy[i][j]/(double)(time+1));
color_scheme_palette(COLOR_SCHEME, palette, energy, scale, time, rgb);
break;
}
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case (P_ENERGY_FLUX):
{
compute_energy_flux(phi, psi, xy_in, i, j, &gx, &gy, &arg, &mod);
// color_scheme_palette(C_ONEDIM_LINEAR, palette, arg/DPI, 1.0, 1, rgb);
// flux_factor = tanh(mod*E_SCALE);
// for (k=0; k<3; k++) rgb[k] *= flux_factor;
color_scheme_asym_palette(COLOR_SCHEME, palette, mod*FLUX_SCALE, scale, time, rgb);
break;
}
case (P_TOTAL_ENERGY_FLUX):
{
// ffactor = 1.0;
compute_energy_flux(phi, psi, xy_in, i, j, &gx, &gy, &arg, &mod);
total_flux[2*NX*NY + 2*j*NX + 2*i] += gx;
total_flux[2*NX*NY + 2*j*NX + 2*i + 1] += gy;
total_flux[2*j*NX + 2*i] += total_flux[2*NX*NY + 2*j*NX + 2*i];
total_flux[2*j*NX + 2*i + 1] += total_flux[2*NX*NY + 2*j*NX + 2*i + 1];
// total_flux[2*j*NX + 2*i] *= 1.0 + 1.0/(double)(time+1);
// total_flux[2*j*NX + 2*i + 1] *= 1.0 + 1.0/(double)(time+1);
// total_flux[2*j*NX + 2*i] *= ffactor;
// total_flux[2*j*NX + 2*i + 1] *= ffactor;
// total_flux[2*j*NX + 2*i] += gx;
// total_flux[2*j*NX + 2*i + 1] += gy;
// total_flux[2*j*NX + 2*i] *= 1.0/ffactor;
// total_flux[2*j*NX + 2*i + 1] *= 1.0/ffactor;
// total_flux[2*j*NX + 2*i] += 0.1*gx;
// total_flux[2*j*NX + 2*i + 1] += 0.1*gy;
mgx = total_flux[2*j*NX + 2*i];
mgy = total_flux[2*j*NX + 2*i + 1];
// mgx = total_flux[2*j*NX + 2*i]/sqrt((double)(time+1));
// mgy = total_flux[2*j*NX + 2*i + 1]/sqrt((double)(time+1));
// mgx = total_flux[2*j*NX + 2*i]/(1.0 + 0.1*log((double)(time+2)));
// mgy = total_flux[2*j*NX + 2*i + 1]/(1.0 + 0.1*log((double)(time+2)));
mod = module2(mgx, mgy);
arg = argument(mgx, mgy);
if (arg < 0.0) arg += DPI;
color_scheme_palette(C_ONEDIM_LINEAR, palette, arg/DPI, 1.0, 1, rgb);
flux_factor = tanh(mod*FLUX_SCALE);
for (k=0; k<3; k++) rgb[k] *= flux_factor;
// color_scheme_asym_palette(COLOR_SCHEME, palette, mod, scale, time, rgb);
break;
}
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}
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if (fade) for (k=0; k<3; k++) rgb[k] *= fade_value;
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glColor3f(rgb[0], rgb[1], rgb[2]);
glVertex2i(i, j);
glVertex2i(i+1, j);
glVertex2i(i+1, j+1);
glVertex2i(i, j+1);
}
}
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glEnd ();
}
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void draw_wave_highres_palette(int size, double *phi[NX], double *psi[NX], double *total_energy[NX], double *total_flux, short int *xy_in[NX], double scale, int time, int plot, int palette, int fade, double fade_value)
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/* same as draw_wave_highres, but with color scheme option */
{
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int i, j, k, iplus, iminus, jplus, jminus;
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double rgb[3], xy[2], x1, y1, x2, y2, velocity, energy, gradientx2, gradienty2, arg, mod, flux_factor, gx, gy, mgx, mgy;
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static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
glBegin(GL_QUADS);
// printf("dtinverse = %.5lg\n", dtinverse);
for (i=0; i<NX; i+=size)
for (j=0; j<NY; j+=size)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
switch (plot) {
case (P_AMPLITUDE):
{
// /* make wave luminosity larger inside obstacles */
// if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, phi[i][j], scale, time, 0.7, rgb);
// else
color_scheme_palette(COLOR_SCHEME, palette, phi[i][j], scale, time, rgb);
break;
}
case (P_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
/* adjust energy to color palette */
if (COLOR_PALETTE >= COL_TURBO) color_scheme_asym_palette(COLOR_SCHEME, palette, energy, scale, time, rgb);
else color_scheme_palette(COLOR_SCHEME, palette, energy, scale, time, rgb);
break;
}
case (P_MIXED):
{
if (j > NY/2) color_scheme_palette(COLOR_SCHEME, palette, phi[i][j], scale, time, rgb);
else color_scheme_palette(COLOR_SCHEME, palette, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
total_energy[i][j] += energy;
if (COLOR_PALETTE >= COL_TURBO)
color_scheme_asym_palette(COLOR_SCHEME, palette, total_energy[i][j]/(double)(time+1), scale, time, rgb);
else color_scheme_palette(COLOR_SCHEME, palette, total_energy[i][j]/(double)(time+1), scale, time, rgb);
break;
}
case (P_LOG_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
// energy = LOG_SHIFT + LOG_SCALE*log(energy);
// if (energy < 0.0) energy = 0.0;
color_scheme_palette(COLOR_SCHEME, palette, LOG_SHIFT + LOG_SCALE*log(energy), scale, time, rgb);
break;
}
case (P_LOG_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
if (energy == 0.0) energy = 1.0e-20;
total_energy[i][j] += energy;
color_scheme_palette(COLOR_SCHEME, palette, LOG_SHIFT + LOG_SCALE*log(total_energy[i][j]/(double)(time+1)), scale, time, rgb);
break;
}
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case (P_ENERGY_FLUX):
{
compute_energy_flux(phi, psi, xy_in, i, j, &gx, &gy, &arg, &mod);
color_scheme_palette(C_ONEDIM_LINEAR, palette, arg/DPI, 1.0, 1, rgb);
flux_factor = tanh(mod*E_SCALE);
for (k=0; k<3; k++) rgb[k] *= flux_factor;
break;
}
case (P_TOTAL_ENERGY_FLUX):
{
compute_energy_flux(phi, psi, xy_in, i, j, &gx, &gy, &arg, &mod);
total_flux[2*j*NX + 2*i] *= 0.99;
total_flux[2*j*NX + 2*i + 1] *= 0.99;
total_flux[2*j*NX + 2*i] += gx;
total_flux[2*j*NX + 2*i + 1] += gy;
// mgx = total_flux[2*j*NX + 2*i]/(double)(time+1);
// mgy = total_flux[2*j*NX + 2*i + 1]/(double)(time+1);
mgx = total_flux[2*j*NX + 2*i];
mgy = total_flux[2*j*NX + 2*i + 1];
// mgx = total_flux[2*j*NX + 2*i]/log((double)(time+2));
// mgy = total_flux[2*j*NX + 2*i + 1]/log((double)(time+2));
mod = module2(mgx, mgy);
arg = argument(mgx, mgy);
if (arg < 0.0) arg += DPI;
color_scheme_palette(C_ONEDIM_LINEAR, palette, arg/DPI, 1.0, 1, rgb);
flux_factor = tanh(mod*E_SCALE);
for (k=0; k<3; k++) rgb[k] *= flux_factor;
break;
}
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}
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if (fade) for (k=0; k<3; k++) rgb[k] *= fade_value;
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glVertex2i(i, j);
glVertex2i(i+size, j);
glVertex2i(i+size, j+size);
glVertex2i(i, j+size);
}
}
glEnd ();
}
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/* modified function for "flattened" wave tables */
void init_circular_wave_mod(double x, double y, double phi[NX*NY], double psi[NX*NY], short int xy_in[NX*NY])
/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
printf("Initializing wave\n");
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// #pragma omp parallel for private(i,j,xy,dist2)
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for (i=0; i<NX; i++)
{
if (i%100 == 0) printf("Initializing column %i of %i\n", i, NX);
for (j=0; j<NY; j++)
{
// printf("i*NY+j = %i\n", i*NY+j);
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
if ((xy_in[i*NY+j])||(TWOSPEEDS))
phi[i*NY+j] = INITIAL_AMP*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
else phi[i*NY+j] = 0.0;
psi[i*NY+j] = 0.0;
}
}
}
void add_circular_wave_mod(double factor, double x, double y, double phi[NX*NY], double psi[NX*NY], short int xy_in[NX*NY])
/* add drop at (x,y) to the field with given prefactor */
{
int i, j;
double xy[2], dist2;
#pragma omp parallel for private(i,j,xy,dist2)
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
if ((xy_in[i*NY+j])||(TWOSPEEDS))
phi[i*NY+j] += INITIAL_AMP*factor*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
}
}
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void init_wave_flat_mod(double phi[NX*NY], double psi[NX*NY], short int xy_in[NX*NY])
/* initialise flat field - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2];
#pragma omp parallel for private(i,j,xy)
for (i=0; i<NX; i++) {
if (i%100 == 0) printf("Wave and table xy_in - Initialising column %i of %i\n", i, NX);
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i*NY+j] = xy_in_billiard(xy[0],xy[1]);
phi[i*NY+j] = 0.0;
psi[i*NY+j] = 0.0;
}
}
}
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double compute_variance_mod(double phi[NX*NY], double psi[NX*NY], short int xy_in[NX*NY])
/* compute the variance of the field, to adjust color scheme */
{
int i, j, n = 0;
double variance = 0.0;
#pragma omp parallel for private(i,j,variance)
for (i=1; i<NX; i++)
for (j=1; j<NY; j++)
{
if (xy_in[i*NY+j])
{
n++;
variance += phi[i*NY+j]*phi[i*NY+j];
}
}
if (n==0) n=1;
return(variance/(double)n);
}
double compute_energy_mod(double phi[NX*NY], double psi[NX*NY], short int xy_in[NX*NY], int i, int j)
{
double velocity, energy, gradientx2, gradienty2;
int iplus, iminus, jplus, jminus;
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static int i1, j1, i2, j2, i3, j3, ij[2];
static int first = 1;
if (first)
{
xy_to_ij(-LAMBDA, -1.0, ij);
i1 = ij[0] + 1; j1 = ij[1] + 1;
xy_to_ij(0.0, 0.0, ij);
i2 = ij[0] - 1; j2 = ij[1] - 1;
xy_to_ij(LAMBDA, 1.0, ij);
i3 = ij[0] - 1; j3 = ij[1] - 1;
first = 0;
}
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velocity = (phi[i*NY+j] - psi[i*NY+j]);
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/* avoid computing gradient across boundary of compared regions */
if (COMPARISON)
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1; else if (jplus == NY/2) jplus = NY/2-1;
jminus = (j-1); if (jminus == -1) jminus = 0; else if (jminus == NY/2-1) jminus = NY/2;
}
else
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
}
// else
// {
// iplus = i+1;
// if ((j<j2)&&(iplus>i3-1)) iplus = i1;
// else if ((j>=j2)&&(iplus>i2-1)) iplus = i1;
//
// iminus = i-1;
// if ((j<j2)&&(iminus<i1)) iminus = i3-1;
// else if ((j>=j2)&&(iminus<i1)) iminus = i2-1;
//
// jplus = j+1;
// if ((i<i2)&&(jplus>j3-1)) jplus = j1;
// else if ((i>=i2)&&(jplus>j2-1)) jplus = j1;
//
// jminus = j-1;
// if ((i<i2)&&(jminus<j1)) jminus = j3-1;
// else if ((i>=i2)&&(jminus<j1)) jminus = j2-1;
//
// jminus = j-1;
// }
if (B_COND == BC_LSHAPE)
{
if ((i<=i1)||(j<=j1)) return(0.0);
if ((i>=i2-1)&&(j>=j2-1)) return(0.0);
if ((i>=i3-1)||(j>=j3-1)) return(0.0);
}
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gradientx2 = (phi[iplus*NY+j]-phi[i*NY+j])*(phi[iplus*NY+j]-phi[i*NY+j])
+ (phi[i*NY+j] - phi[iminus*NY+j])*(phi[i*NY+j] - phi[iminus*NY+j]);
gradienty2 = (phi[i*NY+jplus]-phi[i*NY+j])*(phi[i*NY+jplus]-phi[i*NY+j])
+ (phi[i*NY+j] - phi[i*NY+jminus])*(phi[i*NY+j] - phi[i*NY+jminus]);
if (xy_in[i*NY+j]) return(E_SCALE*E_SCALE*(velocity*velocity + 0.5*COURANT*COURANT*(gradientx2+gradienty2)));
else if (TWOSPEEDS) return(E_SCALE*E_SCALE*(velocity*velocity + 0.5*COURANTB*COURANTB*(gradientx2+gradienty2)));
else return(0.0);
}
double compute_phase(double phi[NX*NY], double psi[NX*NY], short int xy_in[NX*NY], int i, int j)
{
double velocity, angle;
velocity = (phi[i*NY+j] - psi[i*NY+j]);
if (module2(phi[i*NY+j], velocity) < 1.0e-10) return(0.0);
else if (xy_in[i*NY+j])
{
angle = argument(phi[i*NY+j], PHASE_FACTOR*velocity/COURANT);
if (angle < 0.0) angle += DPI;
if ((i==NY/2)&&(j==NY/2)) printf("Phase = %.3lg Pi\n", angle/PI);
return(angle);
}
else if (TWOSPEEDS)
{
angle = argument(phi[i*NY+j], PHASE_FACTOR*velocity/COURANTB);
if (angle < 0.0) angle += DPI;
return(angle);
}
else return(0.0);
}
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