void fdprep(const double omega,
const float eps,
const int n1, const int n2,
const float d1, const float d2,
float **v,
const int npml,
const int pad1, const int pad2,
SuiteSparse_long n, SuiteSparse_long nz,
SuiteSparse_long *Ti, SuiteSparse_long *Tj,
double* Tx, double *Tz)
/*< 5-point finite-difference scheme >*/
{
int i, j, index;
double eta1, eta2, mvel, c1, c2;
double *g1, *g2, **pad;
double complex *s1, *s2, neib, cent;
SuiteSparse_long count;
/* prepare PML */
eta1 = (double) npml*d1;
eta2 = (double) npml*d2;
mvel = maxvel(n1*n2,v[0]);
c1 = -3.*log((double) eps)*mvel/(eta1*omega);
c2 = -3.*log((double) eps)*mvel/(eta2*omega);
g1 = (double*) sf_alloc(pad1,sizeof(double));
for (i=0; i < pad1; i++) {
if (i < npml) {
g1[i] = pow(c1*((npml-i)*d1/eta1),2.);
} else if (i >= pad1-npml) {
g1[i] = pow(c1*((i-(pad1-npml-1))*d1/eta1),2.);
} else {
g1[i] = 0.;
}
}
s1 = (double complex*) sf_alloc(pad1,sizeof(double complex));
for (i=0; i < pad1; i++) {
s1[i] = 1./(1.+I*g1[i]);
}
g2 = (double*) sf_alloc(pad2,sizeof(double));
for (j=0; j < pad2; j++) {
if (j < npml) {
g2[j] = pow(c2*((npml-j)*d2/eta2),2.);
} else if (j >= pad2-npml) {
g2[j] = pow(c2*((j-(pad2-npml-1))*d2/eta2),2.);
} else {
g2[j] = 0.;
}
}
s2 = (double complex*) sf_alloc(pad2,sizeof(double complex));
for (j=0; j < pad2; j++) {
s2[j] = 1./(1.+I*g2[j]);
}
/* extend model */
pad = (double**) sf_alloc(pad2,sizeof(double*));
pad[0] = (double*) sf_alloc(pad1*pad2,sizeof(double));
for (j=1; j < pad2; j++) {
pad[j] = pad[0]+j*pad1;
}
for (j=0; j < npml; j++) {
for (i=0; i < npml; i++) {
pad[j][i] = v[0][0];
}
for (i=npml; i < pad1-npml; i++) {
pad[j][i] = v[0][i-npml];
}
for (i=pad1-npml; i < pad1; i++) {
pad[j][i] = v[0][n1-1];
}
}
for (j=npml; j < pad2-npml; j++) {
for (i=0; i < npml; i++) {
pad[j][i] = v[j-npml][0];
}
for (i=npml; i < pad1-npml; i++) {
pad[j][i] = v[j-npml][i-npml];
}
for (i=pad1-npml; i < pad1; i++) {
pad[j][i] = v[j-npml][n1-1];
}
}
for (j=pad2-npml; j < pad2; j++) {
for (i=0; i < npml; i++) {
pad[j][i] = v[n2-1][0];
}
for (i=npml; i < pad1-npml; i++) {
pad[j][i] = v[n2-1][i-npml];
}
for (i=pad1-npml; i < pad1; i++) {
pad[j][i] = v[n2-1][n1-1];
}
}
/* assemble matrix in triplet form */
count = 0;
for (j=1; j < pad2-1; j++) {
for (i=1; i < pad1-1; i++) {
index = (j-1)*(pad1-2)+(i-1);
cent = 0.+I*0.;
/* left */
neib = (s1[i]/s2[j]+s1[i-1]/s2[j])/(2.*d1*d1);
cent += -neib;
if (i != 1) {
Ti[count] = index;
Tj[count] = index-1;
Tx[count] = creal(neib);
Tz[count] = cimag(neib);
count++;
}
/* right */
neib = (s1[i]/s2[j]+s1[i+1]/s2[j])/(2.*d1*d1);
cent += -neib;
if (i != pad1-2) {
Ti[count] = index;
Tj[count] = index+1;
Tx[count] = creal(neib);
Tz[count] = cimag(neib);
count++;
}
/* down */
neib = (s2[j]/s1[i]+s2[j-1]/s1[i])/(2.*d2*d2);
cent += -neib;
if (j != 1) {
Ti[count] = index;
Tj[count] = index-(pad1-2);
Tx[count] = creal(neib);
Tz[count] = cimag(neib);
count++;
}
/* up */
neib = (s2[j]/s1[i]+s2[j+1]/s1[i])/(2.*d2*d2);
cent += -neib;
if (j != pad2-2) {
Ti[count] = index;
Tj[count] = index+(pad1-2);
Tx[count] = creal(neib);
Tz[count] = cimag(neib);
count++;
}
/* center */
cent += pow(omega/pad[j][i],2.)/(s1[i]*s2[j]);
Ti[count] = index;
Tj[count] = index;
Tx[count] = creal(cent);
Tz[count] = cimag(cent);
count++;
}
}
}
double cell_mindt( struct Cell *** theCells, struct Sim * theSim, struct GravMass * theGravMasses ){
int i_m,j_m,k_m;
double dt_m = 1.e100;//HUGE_VAL;
double a_m,r_m,dx_m;
double mag_vel_m;
int i,j,k;
for( k=sim_Nghost_min(theSim,Z_DIR) ; k<sim_N(theSim,Z_DIR)-sim_Nghost_max(theSim,Z_DIR) ; ++k ){
double zm = sim_FacePos(theSim,k-1,Z_DIR);
double zp = sim_FacePos(theSim,k,Z_DIR);
double dz = zp-zm;
for( i=sim_Nghost_min(theSim,R_DIR) ; i<sim_N(theSim,R_DIR)-sim_Nghost_max(theSim,R_DIR) ; ++i ){
double rm = sim_FacePos(theSim,i-1,R_DIR);
double rp = sim_FacePos(theSim,i,R_DIR);
double dr = rp-rm;
double r = .5*(rp+rm);
for( j=0 ; j<sim_N_p(theSim,i) ; ++j ){
int jm = j-1;
if( j==0 ) jm = sim_N_p(theSim,i)-1;
double w = .5*(theCells[k][i][j].wiph+theCells[k][i][jm].wiph);
double dx = dr;
double rdphi = .5*(rp+rm)*theCells[k][i][j].dphi;
if( rdphi<dr ) {
dx = rdphi;
}
if( dx>dz ) {
dx = dz;
}
double a = maxvel( theCells[k][i][j].prim , w , r ,theSim);
double rho = theCells[k][i][j].prim[RHO];
double Pp = theCells[k][i][j].prim[PPP];
double dt = sim_CFL(theSim)*dx/a;
if( sim_EXPLICIT_VISCOSITY(theSim)>0.0 ){
double nu;
if (sim_VISC_CONST(theSim)==1){
nu = sim_EXPLICIT_VISCOSITY(theSim);
} else{
double tiph = theCells[k][i][j].tiph - 0.5*theCells[k][i][j].dphi;
if (sim_InitialDataType(theSim)==SHEAR){
double HoR = 0.1;
//nu = sim_EXPLICIT_VISCOSITY(theSim)*HoR*HoR*pow(fabs((r*cos(tiph))),1.5);
nu = sim_EXPLICIT_VISCOSITY(theSim)*sim_GAMMALAW(theSim)*Pp/rho*pow(fabs(r*cos(tiph)),2.0);
if (r*cos(tiph)>20.) nu=0.000000001;
} else{
double M0 = gravMass_M(theGravMasses,0);
double M1 = gravMass_M(theGravMasses,1);
double dist_bh0 = gravMass_dist(theGravMasses,0,r,tiph,0.);
double dist_bh1 = gravMass_dist(theGravMasses,1,r,tiph,0.);
double alpha = sim_EXPLICIT_VISCOSITY(theSim);
double eps = sim_G_EPS(theSim);
//nu = sim_EXPLICIT_VISCOSITY(theSim)*sim_GAMMALAW(theSim)*Pp/rho*pow(r,1.5);
nu = alpha*Pp/rho/sqrt(pow(dist_bh0*dist_bh0+eps*eps,-1.5)*M0+pow(dist_bh1*dist_bh1+eps*eps,-1.5)*M1);
}
}
double dt_visc = .25*dx*dx/nu;
dt = dt/( 1. + dt/dt_visc );
}
if( dt_m > dt ) {
dt_m = dt;
}
}
}
}
double dt2;
MPI_Allreduce( &dt_m , &dt2 , 1 , MPI_DOUBLE , MPI_MIN , sim_comm );
return( dt2 );
}
