void problem(DomainS *pDomain)
{
GridS *pGrid=(pDomain->Grid);
int i,il,iu,j,jl,ju,k,kl,ku;
int is,ie,js,je,ks,ke,nx1,nx2,nx3;
int shk_dir; /* Shock direction: {1,2,3} -> {x1,x2,x3} */
Real ang_2, ang_3; /* Rotation angles about the y and z' axis */
Real sin_a2, cos_a2, sin_a3, cos_a3;
Real x1,x2,x3;
Prim1DS Wl, Wr;
Cons1DS U1d, Ul, Ur;
Real Bxl=0.0, Bxr=0.0, Bxb=0.0;
/* speeds of shock, contact, head and foot of rarefaction for Sod test */
/* speeds of slow/fast shocks, Alfven wave and contact in RJ2a test */
Real tlim;
int err_test;
Real r,xs,xc,xf,xh,vs,vc,vf,vh;
Real xfp,xrp,xsp,xsm,xrm,xfm,vfp,vrp,vsp,vsm,vrm,vfm;
Real d0,v0,Mx,My,Mz,E0,r0,Bx,By,Bz;
#if (NSCALARS > 0)
int n;
#endif
is = pGrid->is; ie = pGrid->ie;
js = pGrid->js; je = pGrid->je;
ks = pGrid->ks; ke = pGrid->ke;
nx1 = (ie-is)+1 + 2*nghost;
nx2 = (je-js)+1 + 2*nghost;
nx3 = (ke-ks)+1 + 2*nghost;
printf("here1\n");
if (pDomain->Level == 0){
if ((RootSoln = (ConsS***)calloc_3d_array(nx3,nx2,nx1,sizeof(ConsS)))
== NULL) ath_error("[problem]: Error alloc memory for RootSoln\n");
}
/* Parse left state read from input file: dl,pl,ul,vl,wl,bxl,byl,bzl */
Wl.d = par_getd("problem","dl");
#ifdef ADIABATIC
Wl.P = par_getd("problem","pl");
#endif
Wl.Vx = par_getd("problem","v1l");
Wl.Vy = par_getd("problem","v2l");
Wl.Vz = par_getd("problem","v3l");
#ifdef MHD
Bxl = par_getd("problem","b1l");
Wl.By = par_getd("problem","b2l");
Wl.Bz = par_getd("problem","b3l");
#endif
#if (NSCALARS > 0)
Wl.r[0] = par_getd("problem","r0l");
#endif
/* Parse right state read from input file: dr,pr,ur,vr,wr,bxr,byr,bzr */
Wr.d = par_getd("problem","dr");
#ifdef ADIABATIC
Wr.P = par_getd("problem","pr");
#endif
Wr.Vx = par_getd("problem","v1r");
Wr.Vy = par_getd("problem","v2r");
Wr.Vz = par_getd("problem","v3r");
#ifdef MHD
Bxr = par_getd("problem","b1r");
Wr.By = par_getd("problem","b2r");
Wr.Bz = par_getd("problem","b3r");
if (Bxr != Bxl) ath_error(0,"[shkset1d] L/R values of Bx not the same\n");
#endif
#if (NSCALARS > 0)
Wr.r[0] = par_getd("problem","r0r");
#endif
printf("here2\n");
#ifdef SAC_INTEGRATOR
Ul = Prim1D_to_Cons1D(&Wl, &Bxl,&Bxb);
Ur = Prim1D_to_Cons1D(&Wr, &Bxr,&Bxb);
#elif defined SMAUG_INTEGRATOR
Ul = Prim1D_to_Cons1D(&Wl, &Bxl,&Bxb);
Ur = Prim1D_to_Cons1D(&Wr, &Bxr,&Bxb);
#else
Ul = Prim1D_to_Cons1D(&Wl, &Bxl);
Ur = Prim1D_to_Cons1D(&Wr, &Bxr);
#endif
printf("here3\n");
/* Parse shock direction */
shk_dir = par_geti("problem","shk_dir");
if (shk_dir != 1 && shk_dir != 2 && shk_dir != 3) {
ath_error("[problem]: shk_dir = %d must be either 1,2 or 3\n",shk_dir);
}
/* Set up the index bounds for initializing the grid */
iu = pGrid->ie + nghost;
il = pGrid->is - nghost;
if (pGrid->Nx[1] > 1) {
ju = pGrid->je + nghost;
jl = pGrid->js - nghost;
}
else {
ju = pGrid->je;
jl = pGrid->js;
}
if (pGrid->Nx[2] > 1) {
ku = pGrid->ke + nghost;
kl = pGrid->ks - nghost;
}
else {
ku = pGrid->ke;
kl = pGrid->ks;
}
printf("here4\n");
/* Initialize the grid including the ghost cells. Discontinuity is always
* located at x=0, so xmin/xmax in input file must be set appropriately. */
switch(shk_dir) {
/*--- shock in 1-direction ---------------------------------------------------*/
case 1: /* shock in 1-direction */
ang_2 = 0.0;
ang_3 = 0.0;
for (k=kl; k<=ku; k++) {
for (j=jl; j<=ju; j++) {
for (i=il; i<=iu; i++) {
cc_pos(pGrid, i, j, k, &x1, &x2, &x3);
/* set primitive and conserved variables to be L or R state */
if (x1 <= 0.0) {
U1d = Ul;
} else {
U1d = Ur;
}
/* Initialize conserved (and with SR the primitive) variables in Grid */
pGrid->U[k][j][i].d = U1d.d;
pGrid->U[k][j][i].M1 = U1d.Mx;
pGrid->U[k][j][i].M2 = U1d.My;
pGrid->U[k][j][i].M3 = U1d.Mz;
#ifdef MHD
pGrid->B1i[k][j][i] = Bxl;
pGrid->B2i[k][j][i] = U1d.By;
pGrid->B3i[k][j][i] = U1d.Bz;
pGrid->U[k][j][i].B1c = Bxl;
pGrid->U[k][j][i].B2c = U1d.By;
pGrid->U[k][j][i].B3c = U1d.Bz;
#endif
#ifdef ADIABATIC
pGrid->U[k][j][i].E = U1d.E;
#endif
#if (NSCALARS > 0)
pGrid->U[k][j][i].s[0] = U1d.s[0];
#endif
}
}
}
break;
/*--- shock in 2-direction ---------------------------------------------------*/
case 2: /* shock in 2-direction */
ang_2 = 0.0;
ang_3 = PI/2.0;
for (k=kl; k<=ku; k++) {
for (j=jl; j<=ju; j++) {
for (i=il; i<=iu; i++) {
cc_pos(pGrid, i, j, k, &x1, &x2, &x3);
/* set primitive variables to be L or R state */
if (x2 <= 0.0) {
U1d = Ul;
} else {
U1d = Ur;
}
/* Initialize conserved (and with SR the primitive) variables in Grid */
pGrid->U[k][j][i].d = U1d.d;
pGrid->U[k][j][i].M1 = -U1d.My;
pGrid->U[k][j][i].M2 = U1d.Mx;
pGrid->U[k][j][i].M3 = U1d.Mz;
#ifdef MHD
pGrid->B1i[k][j][i] = -U1d.By;
pGrid->B2i[k][j][i] = Bxl;
pGrid->B3i[k][j][i] = U1d.Bz;
pGrid->U[k][j][i].B1c = -U1d.By;
pGrid->U[k][j][i].B2c = Bxl;
pGrid->U[k][j][i].B3c = U1d.Bz;
#endif
#ifdef ADIABATIC
pGrid->U[k][j][i].E = U1d.E;
#endif
#if (NSCALARS > 0)
pGrid->U[k][j][i].s[0] = U1d.s[0];
#endif
}
}
}
break;
/*--- shock in 3-direction ---------------------------------------------------*/
case 3: /* shock in 3-direction */
ang_2 = PI/2.0;
ang_3 = 0.0;
for (k=kl; k<=ku; k++) {
for (j=jl; j<=ju; j++) {
for (i=il; i<=iu; i++) {
cc_pos(pGrid, i, j, k, &x1, &x2, &x3);
/* set primitive variables to be L or R state */
if (x3 <= 0.0) {
U1d = Ul;
} else {
U1d = Ur;
}
/* Initialize conserved (and with SR the primitive) variables in Grid */
pGrid->U[k][j][i].d = U1d.d;
pGrid->U[k][j][i].M1 = -U1d.Mz;
pGrid->U[k][j][i].M2 = U1d.My;
pGrid->U[k][j][i].M3 = U1d.Mx;
#ifdef MHD
pGrid->B1i[k][j][i] = -U1d.Bz;
pGrid->B2i[k][j][i] = U1d.By;
pGrid->B3i[k][j][i] = Bxl;
pGrid->U[k][j][i].B1c = -U1d.Bz;
pGrid->U[k][j][i].B2c = U1d.By;
pGrid->U[k][j][i].B3c = Bxl;
#endif
#ifdef ADIABATIC
pGrid->U[k][j][i].E = U1d.E;
#endif
#if (NSCALARS > 0)
pGrid->U[k][j][i].s[0] = U1d.s[0];
#endif
}
}
}
break;
default:
ath_error("[shkset1d]: invalid shk_dir = %i\n",shk_dir);
}
/* Compute Analytic solution for Sod and RJ4a tests, if required */
tlim = par_getd("time","tlim");
err_test = par_getd_def("problem","error_test",0);
if (err_test == 1) {
sin_a3 = sin(ang_3);
cos_a3 = cos(ang_3);
sin_a2 = sin(ang_2);
cos_a2 = cos(ang_2);
/* wave speeds for Sod test */
#ifdef HYDRO
vs = 1.7522; xs = vs*tlim;
vc = 0.92745; xc = vc*tlim;
vf = -0.07027; xf = vf*tlim;
vh = -1.1832; xh = vh*tlim;
#endif /* HYDRO */
/* wave speeds for RJ2a test */
#ifdef MHD
vfp = 2.2638; xfp = vfp*tlim;
vrp = (0.53432 + 1.0/sqrt(PI*1.309)); xrp = vrp*tlim;
vsp = (0.53432 + 0.48144/1.309); xsp = vsp*tlim;
vc = 0.57538; xc = vc*tlim;
vsm = (0.60588 - 0.51594/1.4903); xsm = vsm*tlim;
vrm = (0.60588 - 1.0/sqrt(PI*1.4903)); xrm = vrm*tlim;
vfm = (1.2 - 2.3305/1.08); xfm = vfm*tlim;
#endif /* MHD */
for (k=ks; k<=ke; k++) {
for (j=js; j<=je; j++) {
for (i=is; i<=ie; i++) {
cc_pos(pGrid,i,j,k,&x1,&x2,&x3);
r = cos_a2*(x1*cos_a3 + x2*sin_a3) + x3*sin_a2;
/* Sod solution */
#ifdef HYDRO
My = Mz = 0.0;
if (r > xs) {
d0 = 0.125;
Mx = 0.0;
E0 = 0.25;
r0 = 0.0;
} else if (r > xc) {
d0 = 0.26557;
Mx = 0.92745*d0;
E0 = 0.87204;
r0 = 0.0;
} else if (r > xf) {
d0 = 0.42632;
Mx = 0.92745*d0;
E0 = 0.94118;
r0 = 1.0;
} else if (r > xh) {
v0 = 0.92745*(r-xh)/(xf-xh);
d0 = 0.42632*pow((1.0+0.20046*(0.92745-v0)),5);
E0 = (0.30313*pow((1.0+0.20046*(0.92745-v0)),7))/0.4 + 0.5*d0*v0*v0;
r0 = 1.0;
Mx = v0*d0;
} else {
d0 = 1.0;
Mx = 0.0;
E0 = 2.5;
r0 = 1.0;
}
#endif /* HYDRO */
/* RJ2a solution (Dai & Woodward 1994 Tables Ia and Ib) */
#ifdef MHD
Bx = 2.0/sqrt(4.0*PI);
if (r > xfp) {
d0 = 1.0;
Mx = 0.0;
My = 0.0;
Mz = 0.0;
By = 4.0/sqrt(4.0*PI);
Bz = 2.0/sqrt(4.0*PI);
E0 = 1.0/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 0.0;
} else if (r > xrp) {
d0 = 1.3090;
Mx = 0.53432*d0;
My = -0.094572*d0;
Mz = -0.047286*d0;
By = 5.3452/sqrt(4.0*PI);
Bz = 2.6726/sqrt(4.0*PI);
E0 = 1.5844/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 0.0;
} else if (r > xsp) {
d0 = 1.3090;
Mx = 0.53432*d0;
My = -0.18411*d0;
Mz = 0.17554*d0;
By = 5.7083/sqrt(4.0*PI);
Bz = 1.7689/sqrt(4.0*PI);
E0 = 1.5844/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 0.0;
} else if (r > xc) {
d0 = 1.4735;
Mx = 0.57538*d0;
My = 0.047601*d0;
Mz = 0.24734*d0;
By = 5.0074/sqrt(4.0*PI);
Bz = 1.5517/sqrt(4.0*PI);
E0 = 1.9317/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 0.0;
} else if (r > xsm) {
d0 = 1.6343;
Mx = 0.57538*d0;
My = 0.047601*d0;
Mz = 0.24734*d0;
By = 5.0074/sqrt(4.0*PI);
Bz = 1.5517/sqrt(4.0*PI);
E0 = 1.9317/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 1.0;
} else if (r > xrm) {
d0 = 1.4903;
Mx = 0.60588*d0;
My = 0.22157*d0;
Mz = 0.30125*d0;
By = 5.5713/sqrt(4.0*PI);
Bz = 1.7264/sqrt(4.0*PI);
E0 = 1.6558/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 1.0;
} else if (r > xfm) {
d0 = 1.4903;
Mx = 0.60588*d0;
My = 0.11235*d0;
Mz = 0.55686*d0;
By = 5.0987/sqrt(4.0*PI);
Bz = 2.8326/sqrt(4.0*PI);
E0 = 1.6558/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 1.0;
} else {
d0 = 1.08;
Mx = 1.2*d0;
My = 0.01*d0;
Mz = 0.5*d0;
By = 3.6/sqrt(4.0*PI);
Bz = 2.0/sqrt(4.0*PI);
E0 = 0.95/Gamma_1 + 0.5*((Mx*Mx+My*My+Mz*Mz)/d0 + (Bx*Bx+By*By+Bz*Bz));
r0 = 1.0;
}
#endif /* MHD */
RootSoln[k][j][i].d = d0;
RootSoln[k][j][i].M1 = Mx*cos_a2*cos_a3 - My*sin_a3 - Mz*sin_a2*cos_a3;
RootSoln[k][j][i].M2 = Mx*cos_a2*sin_a3 + My*cos_a3 - Mz*sin_a2*sin_a3;
RootSoln[k][j][i].M3 = Mx*sin_a2 + Mz*cos_a2;
#ifdef MHD
RootSoln[k][j][i].B1c = Bx*cos_a2*cos_a3 - By*sin_a3 - Bz*sin_a2*cos_a3;
RootSoln[k][j][i].B2c = Bx*cos_a2*sin_a3 + By*cos_a3 - Bz*sin_a2*sin_a3;
RootSoln[k][j][i].B3c = Bx*sin_a2 + Bz*cos_a2;
#endif /* MHD */
#ifndef ISOTHERMAL
RootSoln[k][j][i].E = E0;
#endif /* ISOTHERMAL */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++) RootSoln[k][j][i].s[n] = r0*d0;
#endif
}
}}
} /* end calculation of analytic (root) solution */
return;
}
void integrate_2d_smaug(DomainS *pD)
{
GridS *pG=(pD->Grid);
Real dtodx1=pG->dt/pG->dx1, dtodx2=pG->dt/pG->dx2, dtodx3=pG->dt/pG->dx3;
Real hdt = 0.5*pG->dt, dx2=pG->dx2;
Real q1 = 0.5*dtodx1, q2 = 0.5*dtodx2, q3 = 0.5*dtodx3;
int dir;
int i,il,iu, is = pG->is, ie = pG->ie;
int j,jl,ju, js = pG->js, je = pG->je;
int k,kl,ku, ks = pG->ks, ke = pG->ke;
Real x1,x2,x3,phicl,phicr,phifc,phil,phir,phic,M1h,M2h,M3h,Bx=0.0,Bxb=0.0;
/*Used for hyperdiffusion computations*/
int ii1, dim, ii, ii0;
int field; /*integers map to following index rho, mom1, mom2, energy, b1, b2,energyb,rhob,b1b,b2b*/
#ifdef MHD
Real MHD_src_By,MHD_src_Bz,mdb1,mdb2,mdb3;
Real db1,db2,db3,l1,l2,l3,B1,B2,B3,V1,V2,V3;
Real B1ch,B2ch,B3ch;
#endif
// #if defined(MHD) || defined(SELF_GRAVITY)
Real dx1i=1.0/pG->dx1, dx2i=1.0/pG->dx2, dx3i=1.0/pG->dx3;
// #endif
#if (NSCALARS > 0)
int n;
#endif
#ifdef SELF_GRAVITY
Real gxl,gxr,gyl,gyr,gzl,gzr,flx_m1l,flx_m1r,flx_m2l,flx_m2r,flx_m3l,flx_m3r;
#endif
#ifdef FEEDBACK
Real dt1 = 1.0/pG->dt;
#endif
#ifdef STATIC_MESH_REFINEMENT
int ncg,npg,dim;
int ii,ics,ice,jj,jcs,jce,kk,kcs,kce,ips,ipe,jps,jpe,kps,kpe;
#endif
Real g,gl,gr;
Real lsf=1.0, rsf=1.0;
/* With particles, one more ghost cell must be updated in predict step */
#ifdef PARTICLES
Real d1;
il = is - 3;
iu = ie + 3;
jl = js - 3;
ju = je + 3;
kl = ks - 3;
ku = ke + 3;
#else
il = is - 2;
iu = ie + 2;
jl = js - 2;
ju = je + 2;
kl = ks - 2;
ku = ke + 2;
#endif
/* Set etah=0 so first calls to flux functions do not use H-correction */
etah = 0.0;
/* Compute predictor feedback from particle drag */
#ifdef FEEDBACK
feedback_predictor(pD);
exchange_gpcouple(pD,1);
#endif
/*=== STEP 1: Compute L/R x1-interface states and 1D x1-Fluxes ===============*/
/*--- Step 1a ------------------------------------------------------------------
* Load 1D vector of conserved variables;
* U1d = (d, M1, M2, M3, E, B2c, B3c, s[n])
*/
for (j=jl; j<=ju; j++) {
for (i=is-nghost; i<=ie+nghost; i++) {
U1d[i].d = pG->U[ks][j][i].d;
U1d[i].Mx = pG->U[ks][j][i].M1;
U1d[i].My = pG->U[ks][j][i].M2;
U1d[i].Mz = pG->U[ks][j][i].M3;
#ifndef BAROTROPIC
U1d[i].E = pG->U[ks][j][i].E;
#endif /* BAROTROPIC */
#ifdef MHD
U1d[i].By = pG->U[ks][j][i].B2c;
U1d[i].Bz = pG->U[ks][j][i].B3c;
Bxc[i] = pG->U[ks][j][i].B1c;
Bxi[i] = pG->B1i[ks][j][i];
B1_x1[j][i] = pG->B1i[ks][j][i];
#endif /* MHD */
#ifdef BKG
U1d[i].db = pG->U[ks][j][i].db;
U1d[i].Byb = pG->U[ks][j][i].B2cb;
U1d[i].Bzb = pG->U[ks][j][i].B3cb;
#endif
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++) U1d[i].s[n] = pG->U[ks][j][i].s[n];
#endif
}
/*--- Step 1b ------------------------------------------------------------------
* Compute L and R states at X1-interfaces, add "MHD source terms" for 0.5*dt
*/
for (i=is-nghost; i<=ie+nghost; i++) {
W[i] = Cons1D_to_Prim1D(&U1d[i],&Bxc[i],&Bxb);
/*--- Step 1c ------------------------------------------------------------------
* Add source terms from static gravitational potential for 0.5*dt to L/R states
*/
/*if (StaticGravPot != NULL){
for (i=il+1; i<=iu; i++) {
cc_pos(pG,i,j,ks,&x1,&x2,&x3);
phicr = (*StaticGravPot)( x1 ,x2,x3);
phicl = (*StaticGravPot)((x1- pG->dx1),x2,x3);
phifc = (*StaticGravPot)((x1-0.5*pG->dx1),x2,x3);
gl = 2.0*(phifc - phicl)*dx1i;
gr = 2.0*(phicr - phifc)*dx1i;
#if defined(CYLINDRICAL) && defined(FARGO)
gl -= r[i-1]*SQR((*OrbitalProfile)(r[i-1]));
gr -= r[i ]*SQR((*OrbitalProfile)(r[i ]));
#endif
W[i].Vx -= hdt*gl;
}
}*/
/*--- Step 1c (cont) -----------------------------------------------------------
* Add the geometric source-terms now using cell-centered primitive
* variables at time t^n
*/
/*--- Step 1d ------------------------------------------------------------------
* Compute 1D fluxes in x1-direction, storing into 3D array
*/
for (i=il+1; i<=iu; i++) {
Uc_x1[j][i] = Prim1D_to_Cons1D(&W[i],&Bxi[i],&Bxb);
#ifdef MHD
Bx = B1_x1[j][i];
Bxb=0.0;//?????????????????????????
#endif
fluxes(Uc_x1[j][i],Uc_x1[j][i],W[i],W[i],Bx,Bxb,&x1Flux[j][i]);
}
}
/*=== STEP 2: Compute L/R x2-interface states and 1D x2-Fluxes ===============*/
/*--- Step 2a ------------------------------------------------------------------
* Load 1D vector of conserved variables;
* U1d = (d, M2, M3, M1, E, B3c, B1c, s[n])
*/
for (i=il; i<=iu; i++) {
#ifdef CYLINDRICAL
dx2 = r[i]*pG->dx2;
dx2i = 1.0/dx2;
dtodx2 = pG->dt*dx2i;
hdtodx2 = 0.5*dtodx2;
#endif
for (j=js-nghost; j<=je+nghost; j++) {
U1d[j].d = pG->U[ks][j][i].d;
U1d[j].Mx = pG->U[ks][j][i].M2;
U1d[j].My = pG->U[ks][j][i].M3;
U1d[j].Mz = pG->U[ks][j][i].M1;
#ifndef BAROTROPIC
U1d[j].E = pG->U[ks][j][i].E;
#endif /* BAROTROPIC */
#ifdef MHD
U1d[j].By = pG->U[ks][j][i].B3c;
U1d[j].Bz = pG->U[ks][j][i].B1c;
Bxc[j] = pG->U[ks][j][i].B2c;
Bxi[j] = pG->B2i[ks][j][i];
B2_x2[j][i] = pG->B2i[ks][j][i];
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++) U1d[j].s[n] = pG->U[ks][j][i].s[n];
#endif
}
/*--- Step 2b ------------------------------------------------------------------
* Compute L and R states at X2-interfaces, add "MHD source terms" for 0.5*dt
*/
/*--- Step 2c ------------------------------------------------------------------
* Add source terms from static gravitational potential for 0.5*dt to L/R states
*/
/* if (StaticGravPot != NULL){
for (j=jl+1; j<=ju; j++) {
cc_pos(pG,i,j,ks,&x1,&x2,&x3);
phicr = (*StaticGravPot)(x1, x2 ,x3);
phicl = (*StaticGravPot)(x1,(x2- pG->dx2),x3);
phifc = (*StaticGravPot)(x1,(x2-0.5*pG->dx2),x3);
W[j].Vx -= dtodx2*(phifc - phicl);
}
}*/
/*--- Step 2d ------------------------------------------------------------------
* Compute 1D fluxes in x2-direction, storing into 3D array
*/
for (j=jl+1; j<=ju; j++) {
Uc_x2[j][i] = Prim1D_to_Cons1D(&W[j],&Bxi[j],&Bxb);
#ifdef MHD
Bx = B2_x2[j][i];
Bxb=0.0;//?????????????????????????
#endif
fluxes(Uc_x2[j][i],Uc_x2[j][i],W[j],W[j],Bx,Bxb,&x2Flux[j][i]);
}
}
/*--- Step 3c ------------------------------------------------------------------
* Add source terms from static gravitational potential for 0.5*dt to L/R states
*/
/* if (StaticGravPot != NULL){
for (k=kl+1; k<=ku; k++) {
cc_pos(pG,i,j,ks,&x1,&x2,&x3);
phicr = (*StaticGravPot)(x1,x2, x3 );
phicl = (*StaticGravPot)(x1,x2,(x3- pG->dx3));
phifc = (*StaticGravPot)(x1,x2,(x3-0.5*pG->dx3));
W[k].Vx -= dtodx3*(phifc - phicl);
}
}*/
/*--- Step 3d ------------------------------------------------------------------
* Compute 1D fluxes in x3-direction, storing into 3D array
*/
/*Not needed here for 2d problem*/
/*=== STEP 4: Update face-centered B for 0.5*dt =============================*/
/*--- Step 4a ------------------------------------------------------------------
* Calculate the cell centered value of emf1,2,3 at t^{n} and integrate
* to corner.
*/
/*--- Step 4b ------------------------------------------------------------------
* Update the interface magnetic fields using CT for a half time step.
*/
/*=== STEP 5: Correct x1-interface states with transverse flux gradients =====*/
/*--- Step 5a ------------------------------------------------------------------
* Correct x1-interface states using x2-fluxes computed in Step 2d.
* Since the fluxes come from an x2-sweep, (x,y,z) on RHS -> (z,x,y) on LHS
*/
/*--- Step 5b ------------------------------------------------------------------
* Correct x1-interface states using x3-fluxes computed in Step 3d.
* Since the fluxes come from an x3-sweep, (x,y,z) on RHS -> (y,z,x) on LHS
*/
/*--- Step 5c ------------------------------------------------------------------
* Add the "MHD source terms" from the x2- and x3-flux-gradients to the
* conservative variables on the x1Face. Limiting is used as in GS (2007)
*/
/*--- Step 5d ------------------------------------------------------------------
* Add source terms for a static gravitational potential arising from x2-Flux
* and x3-Flux gradients. To improve conservation of total energy, average
* the energy source term computed at cell faces.
* S_{M} = -(\rho) Grad(Phi); S_{E} = -(\rho v) Grad{Phi}
*/
/* if (StaticGravPot != NULL){
for (k=kl+1; k<=ku-1; k++) {
for (j=jl+1; j<=ju-1; j++) {
for (i=il+1; i<=iu; i++) {
cc_pos(pG,i,j,k,&x1,&x2,&x3);
phic = (*StaticGravPot)(x1, x2 ,x3);
phir = (*StaticGravPot)(x1,(x2+0.5*pG->dx2),x3);
phil = (*StaticGravPot)(x1,(x2-0.5*pG->dx2),x3); ---------*/
/* correct right states; x2 and x3 gradients */
/*-----------------------------
#ifdef CYLINDRICAL
q2 = hdt/(r[i]*pG->dx2);
#endif
Ur_x1Face[k][j][i].My -= q2*(phir-phil)*pG->U[k][j][i].d;
#ifndef BAROTROPIC
Ur_x1Face[k][j][i].E -= q2*(x2Flux[k][j ][i ].d*(phic - phil)
+ x2Flux[k][j+1][i ].d*(phir - phic));
#ifdef ROTATING_FRAME
Ur_x1Face[k][j][i].E += hdt * 0.5*(x2Flux[k][j ][i ].d*sin(x2-0.5*pG->dx2) +
x2Flux[k][j+1][i ].d*sin(x2+0.5*pG->dx2)) *SQR(Omega_0)*Rc;
#endif
#endif
phir = (*StaticGravPot)(x1,x2,(x3+0.5*pG->dx3));
phil = (*StaticGravPot)(x1,x2,(x3-0.5*pG->dx3));
Ur_x1Face[k][j][i].Mz -= q3*(phir-phil)*pG->U[k][j][i].d;
#ifndef BAROTROPIC
Ur_x1Face[k][j][i].E -= q3*(x3Flux[k ][j][i ].d*(phic - phil)
+ x3Flux[k+1][j][i ].d*(phir - phic));
#endif
-----------------------*/
/* correct left states; x2 and x3 gradients */
/*--------------------------------------------
phic = (*StaticGravPot)((x1-pG->dx1), x2 ,x3);
phir = (*StaticGravPot)((x1-pG->dx1),(x2+0.5*pG->dx2),x3);
phil = (*StaticGravPot)((x1-pG->dx1),(x2-0.5*pG->dx2),x3);
#ifdef CYLINDRICAL
q2 = hdt/(r[i-1]*pG->dx2);
#endif
Ul_x1Face[k][j][i].My -= q2*(phir-phil)*pG->U[k][j][i-1].d;
#ifndef BAROTROPIC
Ul_x1Face[k][j][i].E -= q2*(x2Flux[k][j ][i-1].d*(phic - phil)
+ x2Flux[k][j+1][i-1].d*(phir - phic));
#ifdef ROTATING_FRAME
Ul_x1Face[k][j][i].E += hdt * 0.5*(x2Flux[k][j ][i-1].d*sin(x2-0.5*pG->dx2) +
x2Flux[k][j+1][i-1].d*sin(x2+0.5*pG->dx2)) *SQR(Omega_0)*Rc;
#endif
#endif
phir = (*StaticGravPot)((x1-pG->dx1),x2,(x3+0.5*pG->dx3));
phil = (*StaticGravPot)((x1-pG->dx1),x2,(x3-0.5*pG->dx3));
Ul_x1Face[k][j][i].Mz -= q3*(phir-phil)*pG->U[k][j][i-1].d;
#ifndef BAROTROPIC
Ul_x1Face[k][j][i].E -= q3*(x3Flux[k ][j][i-1].d*(phic - phil)
+ x3Flux[k+1][j][i-1].d*(phir - phic));
#endif
}
}
}}*/
/*=== STEP 6: Correct x2-interface states with transverse flux gradients =====*/
/*--- Step 6a ------------------------------------------------------------------
* Correct x2-interface states using x1-fluxes computed in Step 1d.
* Since the fluxes come from an x1-sweep, (x,y,z) on RHS -> (y,z,x) on LHS
*/
/*--- Step 6b ------------------------------------------------------------------
* Correct x2-interface states using x3-fluxes computed in Step 3d.
* Since the fluxes come from an x3-sweep, (x,y,z) on RHS -> (z,x,y) on LHS
*/
/*--- Step 6c ------------------------------------------------------------------
* Add the "MHD source terms" from the x1- and x3-flux-gradients to the
* conservative variables on the x2Face. Limiting is used as in GS (2007)
*/
/*--- Step 6d ------------------------------------------------------------------
* Add source terms for a static gravitational potential arising from x1-Flux
* and x3-Flux gradients. To improve conservation of total energy,
* average the energy source term computed at cell faces.
* S_{M} = -(\rho) Grad(Phi); S_{E} = -(\rho v) Grad{Phi}
*/
/*=== STEP 7: Correct x3-interface states with transverse flux gradients =====*/
/*--- Step 7a ------------------------------------------------------------------
* Correct x3-interface states using x1-fluxes computed in Step 1d.
* Since the fluxes come from an x1-sweep, (x,y,z) on RHS -> (z,x,y) on LHS
*/
/*--- Step 7b ------------------------------------------------------------------
* Correct x3-interface states using x2-fluxes computed in Step 2d.
* Since the fluxes come from an x2-sweep, (x,y,z) on RHS -> (y,z,x) on LHS
*/
/*--- Step 7c ------------------------------------------------------------------
* Add the "MHD source terms" from the x1- and x2-flux-gradients to the
* conservative variables on the x3Face. Limiting is used as in GS07.
*/
/*--- Step 7d ------------------------------------------------------------------
* Add source terms for a static gravitational potential arising from x1-Flux
* and x2-Flux gradients. To improve conservation of total energy,
* average the energy source term computed at cell faces.
* S_{M} = -(\rho) Grad(Phi); S_{E} = -(\rho v) Grad{Phi}
*/
/*--- Step 7e ------------------------------------------------------------------
* Apply density floor
*/
/*=== STEP 8: Compute cell-centered values at n+1/2 ==========================*/
/*=== STEP 9: Compute 3D x1-Flux, x2-Flux, x3-Flux ===========================*/
/*--- Step 9a ------------------------------------------------------------------
* Compute maximum wavespeeds in multidimensions (eta in eq. 10 from Sanders et
* al. (1998)) for H-correction
*/
/*--- Step 9b ------------------------------------------------------------------
* Compute 3D x1-fluxes from corrected L/R states.
*/
/*--- Step 9c ------------------------------------------------------------------
* Compute 3D x2-fluxes from corrected L/R states.
*/
/*--- Step 9d ------------------------------------------------------------------
* Compute 3D x3-fluxes from corrected L/R states.
*/
/*=== STEP 10: Update face-centered B for a full timestep ====================*/
/*--- Step 10a -----------------------------------------------------------------
* Integrate emf*^{n+1/2} to the grid cell corners
*/
/*--- Step 10b -----------------------------------------------------------------
* Update the interface magnetic fields using CT for a full time step.
*/
/*=== STEP 11: Add source terms for a full timestep using n+1/2 states =======*/
/*=== STEP 12: Update cell-centered values for a full timestep ===============*/
/*--- Step 12a -----------------------------------------------------------------
* Update cell-centered variables in pG using 3D x1-Fluxes
*/
for (j=js; j<=je; j++) {
for (i=is; i<=ie; i++) {
#ifdef CYLINDRICAL
rsf = ri[i+1]/r[i]; lsf = ri[i]/r[i];
#endif
pG->U[ks][j][i].d -= dtodx1*(rsf*x1Flux[j][i+1].d - lsf*x1Flux[j][i].d );
pG->U[ks][j][i].M1 -= dtodx1*(rsf*x1Flux[j][i+1].Mx - lsf*x1Flux[j][i].Mx);
pG->U[ks][j][i].M2 -= dtodx1*(SQR(rsf)*x1Flux[j][i+1].My - SQR(lsf)*x1Flux[j][i].My);
pG->U[ks][j][i].M3 -= dtodx1*(rsf*x1Flux[j][i+1].Mz - lsf*x1Flux[j][i].Mz);
#ifndef BAROTROPIC
pG->U[ks][j][i].E -= dtodx1*(rsf*x1Flux[j][i+1].E - lsf*x1Flux[j][i].E );
#endif /* BAROTROPIC */
#ifdef MHD
pG->U[ks][j][i].B2c -= dtodx1*(x1Flux[j][i+1].By - x1Flux[j][i].By);
pG->U[ks][j][i].B3c -= dtodx1*(rsf*x1Flux[j][i+1].Bz - lsf*x1Flux[j][i].Bz);
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->U[ks][j][i].s[n] -= dtodx1*(rsf*x1Flux[j][i+1].s[n]
- lsf*x1Flux[j][i ].s[n]);
#endif
}
}
/*--- Step 12b -----------------------------------------------------------------
* Update cell-centered variables in pG using 3D x2-Fluxes
*/
for (j=js; j<=je; j++) {
for (i=is; i<=ie; i++) {
#ifdef CYLINDRICAL
dtodx2 = pG->dt/(r[i]*pG->dx2);
#endif
pG->U[ks][j][i].d -= dtodx2*(x2Flux[j+1][i].d - x2Flux[j][i].d );
pG->U[ks][j][i].M1 -= dtodx2*(x2Flux[j+1][i].Mz - x2Flux[j][i].Mz);
pG->U[ks][j][i].M2 -= dtodx2*(x2Flux[j+1][i].Mx - x2Flux[j][i].Mx);
pG->U[ks][j][i].M3 -= dtodx2*(x2Flux[j+1][i].My - x2Flux[j][i].My);
#ifndef BAROTROPIC
pG->U[ks][j][i].E -= dtodx2*(x2Flux[j+1][i].E - x2Flux[j][i].E );
#endif /* BAROTROPIC */
#ifdef MHD
pG->U[ks][j][i].B3c -= dtodx2*(x2Flux[j+1][i].By - x2Flux[j][i].By);
pG->U[ks][j][i].B1c -= dtodx2*(x2Flux[j+1][i].Bz - x2Flux[j][i].Bz);
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->U[ks][j][i].s[n] -= dtodx2*(x2Flux[j+1][i].s[n]
- x2Flux[j ][i].s[n]);
#endif
}
}
/*--- Step 12c -----------------------------------------------------------------
* Update cell-centered variables in pG using 3D x3-Fluxes
*/
//hyperdifvisc1r
//hyperdifvisc1l
//computec
//computemaxc
//density contribution
for(dim=0; dim<2; dim++) //each direction
{
//hyperdifvisc1ir
//hyperdifvisc1il
//hyperdifrhosource1
;
}
//energy hyperdiffusion term
for(dim=0; dim<2; dim++) //each direction
{
//hyperdifvisc1ir
//hyperdifvisc1il
//hyperdifesource1
;
}
//momentum hyperdiffusion term
for(dim=0; dim<2; dim++) //each direction
{
//hyperdifvisc1ir
//hyperdifvisc1il
//hyperdifesource1
for(ii1=0;ii1<=1;ii1++)
{
if (ii1 == 0)
{
ii=dim;
ii0=field; //f is field
}
else
{
ii=field;
ii0=dim;
}
if(ii==dim)
;// hyperdifmomsource1(ii,ii0,pG->dt);
else
;// hyperdifmomsourcene1(ii,ii0,pG->dt); //off diagonal
}
}
#ifdef MHD
//b field hyperdiffusion term
for(dim=0; dim<2; dim++) //each direction
{
//hyperdifvisc1ir
//hyperdifvisc1il
for(ii1=0;ii1<=1;ii1++)
{
if (ii1 == 0)
{
ii=dim;
ii0=field; //f is field
}
else
{
ii=field;
ii0=dim;
}
if(ii==dim)
;// hyperdifbsource(ii,ii0,pG->dt,pG);
else
;// hyperdifbsourcene(ii,ii0,pG->dt,pG); //off diagonal
}
}
#endif /*hyperdiffusion source term for bfield*/
/*static mesh refinement part goes here*/
#ifdef STATIC_MESH_REFINEMENT
/*--- Step 12e -----------------------------------------------------------------
* With SMR, store fluxes at boundaries of child and parent grids.
*/
for (ncg=0; ncg<pG->NCGrid; ncg++) {
/* x1-boundaries of child Grids (interior to THIS Grid) */
for (dim=0; dim<2; dim++){
if (pG->CGrid[ncg].myFlx[dim] != NULL) {
if (dim==0) i = pG->CGrid[ncg].ijks[0];
if (dim==1) i = pG->CGrid[ncg].ijke[0] + 1;
jcs = pG->CGrid[ncg].ijks[1];
jce = pG->CGrid[ncg].ijke[1];
for (j=jcs, jj=0; j<=jce; j++, jj++){
pG->CGrid[ncg].myFlx[dim][ks][jj].d = x1Flux[j][i].d;
pG->CGrid[ncg].myFlx[dim][ks][jj].M1 = x1Flux[j][i].Mx;
pG->CGrid[ncg].myFlx[dim][ks][jj].M2 = x1Flux[j][i].My;
pG->CGrid[ncg].myFlx[dim][ks][jj].M3 = x1Flux[j][i].Mz;
#ifndef BAROTROPIC
pG->CGrid[ncg].myFlx[dim][ks][jj].E = x1Flux[j][i].E;
#endif /* BAROTROPIC */
#ifdef MHD
pG->CGrid[ncg].myFlx[dim][ks][jj].B1c = 0.0;
pG->CGrid[ncg].myFlx[dim][ks][jj].B2c = x1Flux[j][i].By;
pG->CGrid[ncg].myFlx[dim][ks][jj].B3c = x1Flux[j][i].Bz;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->CGrid[ncg].myFlx[dim][ks][jj].s[n] = x1Flux[j][i].s[n];
#endif
}
#ifdef MHD
for (j=jcs, jj=0; j<=jce+1; j++, jj++){
pG->CGrid[ncg].myEMF3[dim][ks][jj] = emf3[j][i];
}
#endif /* MHD */
}
}
/* x2-boundaries of child Grids (interior to THIS Grid) */
for (dim=2; dim<4; dim++){
if (pG->CGrid[ncg].myFlx[dim] != NULL) {
ics = pG->CGrid[ncg].ijks[0];
ice = pG->CGrid[ncg].ijke[0];
if (dim==2) j = pG->CGrid[ncg].ijks[1];
if (dim==3) j = pG->CGrid[ncg].ijke[1] + 1;
for (i=ics, ii=0; i<=ice; i++, ii++){
pG->CGrid[ncg].myFlx[dim][ks][ii].d = x2Flux[j][i].d;
pG->CGrid[ncg].myFlx[dim][ks][ii].M1 = x2Flux[j][i].Mz;
pG->CGrid[ncg].myFlx[dim][ks][ii].M2 = x2Flux[j][i].Mx;
pG->CGrid[ncg].myFlx[dim][ks][ii].M3 = x2Flux[j][i].My;
#ifndef BAROTROPIC
pG->CGrid[ncg].myFlx[dim][ks][ii].E = x2Flux[j][i].E;
#endif /* BAROTROPIC */
#ifdef MHD
pG->CGrid[ncg].myFlx[dim][ks][ii].B1c = x2Flux[j][i].Bz;
pG->CGrid[ncg].myFlx[dim][ks][ii].B2c = 0.0;
pG->CGrid[ncg].myFlx[dim][ks][ii].B3c = x2Flux[j][i].By;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->CGrid[ncg].myFlx[dim][ks][ii].s[n] = x2Flux[j][i].s[n];
#endif
}
#ifdef MHD
for (i=ics, ii=0; i<=ice+1; i++, ii++){
pG->CGrid[ncg].myEMF3[dim][ks][ii] = emf3[j][i];
}
#endif /* MHD */
}
}
}
for (npg=0; npg<pG->NPGrid; npg++) {
/* x1-boundaries of parent Grids (at boundaries of THIS Grid) */
for (dim=0; dim<2; dim++){
if (pG->PGrid[npg].myFlx[dim] != NULL) {
if (dim==0) i = pG->PGrid[npg].ijks[0];
if (dim==1) i = pG->PGrid[npg].ijke[0] + 1;
jps = pG->PGrid[npg].ijks[1];
jpe = pG->PGrid[npg].ijke[1];
for (j=jps, jj=0; j<=jpe; j++, jj++){
pG->PGrid[npg].myFlx[dim][ks][jj].d = x1Flux[j][i].d;
pG->PGrid[npg].myFlx[dim][ks][jj].M1 = x1Flux[j][i].Mx;
pG->PGrid[npg].myFlx[dim][ks][jj].M2 = x1Flux[j][i].My;
pG->PGrid[npg].myFlx[dim][ks][jj].M3 = x1Flux[j][i].Mz;
#ifndef BAROTROPIC
pG->PGrid[npg].myFlx[dim][ks][jj].E = x1Flux[j][i].E;
#endif /* BAROTROPIC */
#ifdef MHD
pG->PGrid[npg].myFlx[dim][ks][jj].B1c = 0.0;
pG->PGrid[npg].myFlx[dim][ks][jj].B2c = x1Flux[j][i].By;
pG->PGrid[npg].myFlx[dim][ks][jj].B3c = x1Flux[j][i].Bz;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->PGrid[npg].myFlx[dim][ks][jj].s[n] = x1Flux[j][i].s[n];
#endif
}
#ifdef MHD
for (j=jps, jj=0; j<=jpe+1; j++, jj++){
pG->PGrid[npg].myEMF3[dim][ks][jj] = emf3[j][i];
}
#endif /* MHD */
}
}
/* x2-boundaries of parent Grids (at boundaries of THIS Grid) */
for (dim=2; dim<4; dim++){
if (pG->PGrid[npg].myFlx[dim] != NULL) {
ips = pG->PGrid[npg].ijks[0];
ipe = pG->PGrid[npg].ijke[0];
if (dim==2) j = pG->PGrid[npg].ijks[1];
if (dim==3) j = pG->PGrid[npg].ijke[1] + 1;
for (i=ips, ii=0; i<=ipe; i++, ii++){
pG->PGrid[npg].myFlx[dim][ks][ii].d = x2Flux[j][i].d;
pG->PGrid[npg].myFlx[dim][ks][ii].M1 = x2Flux[j][i].Mz;
pG->PGrid[npg].myFlx[dim][ks][ii].M2 = x2Flux[j][i].Mx;
pG->PGrid[npg].myFlx[dim][ks][ii].M3 = x2Flux[j][i].My;
#ifndef BAROTROPIC
pG->PGrid[npg].myFlx[dim][ks][ii].E = x2Flux[j][i].E;
#endif /* BAROTROPIC */
#ifdef MHD
pG->PGrid[npg].myFlx[dim][ks][ii].B1c = x2Flux[j][i].Bz;
pG->PGrid[npg].myFlx[dim][ks][ii].B2c = 0.0;
pG->PGrid[npg].myFlx[dim][ks][ii].B3c = x2Flux[j][i].By;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->PGrid[npg].myFlx[dim][ks][ii].s[n] = x2Flux[j][i].s[n];
#endif
}
#ifdef MHD
for (i=ips, ii=0; i<=ipe+1; i++, ii++){
pG->PGrid[npg].myEMF3[dim][ks][ii] = emf3[j][i];
}
#endif /* MHD */
}
}
}
#endif /* STATIC_MESH_REFINEMENT */
}
return;
}
void integrate_1d_vl(DomainS *pD)
{
GridS *pG=(pD->Grid);
Real dtodx1=pG->dt/pG->dx1, hdtodx1=0.5*pG->dt/pG->dx1;
int i, is = pG->is, ie = pG->ie;
int js = pG->js;
int ks = pG->ks;
Real x1,x2,x3,phicl,phicr,phifc,phil,phir,phic;
#if (NSCALARS > 0)
int n;
#endif
#ifdef SELF_GRAVITY
Real gxl,gxr,flx_m1l,flx_m1r;
#endif
#ifdef STATIC_MESH_REFINEMENT
int ncg,npg,dim;
#endif
int il=is-(nghost-1), iu=ie+(nghost-1);
for (i=is-nghost; i<=ie+nghost; i++) {
Uhalf[i] = pG->U[ks][js][i];
}
/*=== STEP 1: Compute first-order fluxes at t^{n} in x1-direction ============*/
/* No source terms are needed since there is no temporal evolution */
/*--- Step 1a ------------------------------------------------------------------
* Load 1D vector of conserved variables;
* U1d = (d, M1, M2, M3, E, B2c, B3c, s[n])
*/
for (i=is-nghost; i<=ie+nghost; i++) {
U1d[i].d = pG->U[ks][js][i].d;
U1d[i].Mx = pG->U[ks][js][i].M1;
U1d[i].My = pG->U[ks][js][i].M2;
U1d[i].Mz = pG->U[ks][js][i].M3;
#ifndef BAROTROPIC
U1d[i].E = pG->U[ks][js][i].E;
#endif /* BAROTROPIC */
#ifdef MHD
U1d[i].By = pG->U[ks][js][i].B2c;
U1d[i].Bz = pG->U[ks][js][i].B3c;
Bxc[i] = pG->U[ks][js][i].B1c;
Bxi[i] = pG->B1i[ks][js][i];
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++) U1d[i].s[n] = pG->U[ks][js][i].s[n];
#endif
}
/*--- Step 1b ------------------------------------------------------------------
* Compute first-order L/R states */
for (i=is-nghost; i<=ie+nghost; i++) {
W[i] = Cons1D_to_Prim1D(&U1d[i],&Bxc[i]);
}
for (i=il; i<=ie+nghost; i++) {
Wl[i] = W[i-1];
Wr[i] = W[i ];
Ul[i] = U1d[i-1];
Ur[i] = U1d[i ];
}
/*--- Step 1c ------------------------------------------------------------------
* No source terms needed */
/*--- Step 1d ------------------------------------------------------------------
* Compute flux in x1-direction */
for (i=il; i<=ie+nghost; i++) {
fluxes(Ul[i],Ur[i],Wl[i],Wr[i],Bxi[i],&x1Flux[i]);
}
/*=== STEPS 2-4: Not needed in 1D ===*/
/*=== STEP 5: Update cell-centered variables to half-timestep ================*/
/*--- Step 5a ------------------------------------------------------------------
* Update cell-centered variables (including B2c and B3c) to half-timestep
*/
for (i=il; i<=iu; i++) {
Uhalf[i].d -= hdtodx1*(x1Flux[i+1].d - x1Flux[i].d );
Uhalf[i].M1 -= hdtodx1*(x1Flux[i+1].Mx - x1Flux[i].Mx);
Uhalf[i].M2 -= hdtodx1*(x1Flux[i+1].My - x1Flux[i].My);
Uhalf[i].M3 -= hdtodx1*(x1Flux[i+1].Mz - x1Flux[i].Mz);
#ifndef BAROTROPIC
Uhalf[i].E -= hdtodx1*(x1Flux[i+1].E - x1Flux[i].E );
#endif /* BAROTROPIC */
#ifdef MHD
Uhalf[i].B2c -= hdtodx1*(x1Flux[i+1].By - x1Flux[i].By);
Uhalf[i].B3c -= hdtodx1*(x1Flux[i+1].Bz - x1Flux[i].Bz);
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
Uhalf[i].s[n] -= hdtodx1*(x1Flux[i+1].s[n] - x1Flux[i].s[n]);
#endif
}
/*=== STEP 6: Add source terms to predict values at half-timestep ============*/
/*--- Step 6a ------------------------------------------------------------------
* Add source terms from a static gravitational potential for 0.5*dt to predict
* step. To improve conservation of total energy, we average the energy
* source term computed at cell faces.
* S_{M} = -(\rho) Grad(Phi); S_{E} = -(\rho v) Grad{Phi}
*/
if (StaticGravPot != NULL){
for (i=il; i<=iu; i++) {
cc_pos(pG,i,js,ks,&x1,&x2,&x3);
phic = (*StaticGravPot)((x1 ),x2,x3);
phir = (*StaticGravPot)((x1+0.5*pG->dx1),x2,x3);
phil = (*StaticGravPot)((x1-0.5*pG->dx1),x2,x3);
Uhalf[i].M1 -= hdtodx1*pG->U[ks][js][i].d*(phir-phil);
#ifndef BAROTROPIC
Uhalf[i].E -= hdtodx1*(x1Flux[i ].d*(phic - phil) +
x1Flux[i+1].d*(phir - phic));
#endif
}
}
Real accl, accc1, accr;
if(1) {
accc = pG->AccX[i];
accl = pG->AccX[i-1];
accr = pG->AccX[i+1];
}
/*--- Step 6b ------------------------------------------------------------------
* Add source terms for self gravity for 0.5*dt to predict step.
* S_{M} = -(\rho) Grad(Phi); S_{E} = -(\rho v) Grad{Phi}
*/
#ifdef SELF_GRAVITY
for (i=il; i<=iu; i++) {
phic = pG->Phi[ks][js][i];
phir = 0.5*(pG->Phi[ks][js][i] + pG->Phi[ks][js][i+1]);
phil = 0.5*(pG->Phi[ks][js][i] + pG->Phi[ks][js][i-1]);
Uhalf[i].M1 -= hdtodx1*pG->U[ks][js][i].d*(phir-phil);
#ifndef BAROTROPIC
Uhalf[i].E -= hdtodx1*(x1Flux[i ].d*(phic - phil) +
x1Flux[i+1].d*(phir - phic));
#endif
}
#endif /* SELF_GRAVITY */
/*=== STEP 7: Compute second-order L/R x1-interface states ===================*/
/*--- Step 7a ------------------------------------------------------------------
* Load 1D vector of conserved variables;
* U = (d, M1, M2, M3, E, B2c, B3c, s[n])
*/
for (i=il; i<=iu; i++) {
U1d[i].d = Uhalf[i].d;
U1d[i].Mx = Uhalf[i].M1;
U1d[i].My = Uhalf[i].M2;
U1d[i].Mz = Uhalf[i].M3;
#ifndef BAROTROPIC
U1d[i].E = Uhalf[i].E;
#endif /* BAROTROPIC */
#ifdef MHD
U1d[i].By = Uhalf[i].B2c;
U1d[i].Bz = Uhalf[i].B3c;
Bxc[i] = Uhalf[i].B1c;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++) U1d[i].s[n] = Uhalf[i].s[n];
#endif /* NSCALARS */
}
/*--- Step 7b ------------------------------------------------------------------
* Compute L/R states on x1-interfaces, store into arrays
*/
for (i=il; i<=iu; i++) {
W[i] = Cons1D_to_Prim1D(&U1d[i],&Bxc[i]);
}
lr_states(pG,W,Bxc,pG->dt,pG->dx1,is,ie,Wl,Wr,1);
for (i=is; i<=ie+1; i++) {
Wl_x1Face[i] = Wl[i];
Wr_x1Face[i] = Wr[i];
}
/*=== STEPS 8-9: Not needed in 1D ===*/
/*=== STEP 10: Compute x1-Flux ===============================================*/
/*--- Step 10b -----------------------------------------------------------------
* Compute second-order fluxes in x1-direction
*/
for (i=is; i<=ie+1; i++) {
Ul[i] = Prim1D_to_Cons1D(&Wl_x1Face[i],&Bxi[i]);
Ur[i] = Prim1D_to_Cons1D(&Wr_x1Face[i],&Bxi[i]);
fluxes(Ul[i],Ur[i],Wl_x1Face[i],Wr_x1Face[i],Bxi[i],&x1Flux[i]);
}
/*=== STEP 11: Not needed in 1D ===*/
/*=== STEP 12: Add source terms for a full timestep using n+1/2 states =======*/
/*--- Step 12a -----------------------------------------------------------------
* Add gravitational source terms due to a Static Potential
* To improve conservation of total energy, we average the energy
* source term computed at cell faces.
* S_{M} = -(\rho)^{n+1/2} Grad(Phi); S_{E} = -(\rho v)^{n+1/2} Grad{Phi}
*/
if (StaticGravPot != NULL){
for (i=is; i<=ie; i++) {
cc_pos(pG,i,js,ks,&x1,&x2,&x3);
phic = (*StaticGravPot)((x1 ),x2,x3);
phir = (*StaticGravPot)((x1+0.5*pG->dx1),x2,x3);
phil = (*StaticGravPot)((x1-0.5*pG->dx1),x2,x3);
pG->U[ks][js][i].M1 -= dtodx1*Uhalf[i].d*(phir-phil);
#ifndef BAROTROPIC
pG->U[ks][js][i].E -= dtodx1*(x1Flux[i ].d*(phic - phil) +
x1Flux[i+1].d*(phir - phic));
#endif
}
}
/*--- Step 12b -----------------------------------------------------------------
* Add gravitational source terms for self-gravity.
* A flux correction using Phi^{n+1} in the main loop is required to make
* the source terms 2nd order: see selfg_flux_correction().
*/
#ifdef SELF_GRAVITY
/* Add fluxes and source terms due to (d/dx1) terms */
for (i=is; i<=ie; i++){
phic = pG->Phi[ks][js][i];
phil = 0.5*(pG->Phi[ks][js][i-1] + pG->Phi[ks][js][i ]);
phir = 0.5*(pG->Phi[ks][js][i ] + pG->Phi[ks][js][i+1]);
/* gx, gy and gz centered at L and R x1-faces */
gxl = (pG->Phi[ks][js][i-1] - pG->Phi[ks][js][i ])/(pG->dx1);
gxr = (pG->Phi[ks][js][i ] - pG->Phi[ks][js][i+1])/(pG->dx1);
/* momentum fluxes in x1. 2nd term is needed only if Jean's swindle used */
flx_m1l = 0.5*(gxl*gxl)/four_pi_G + grav_mean_rho*phil;
flx_m1r = 0.5*(gxr*gxr)/four_pi_G + grav_mean_rho*phir;
/* Update momenta and energy with d/dx1 terms */
pG->U[ks][js][i].M1 -= dtodx1*(flx_m1r - flx_m1l);
#ifndef BAROTROPIC
pG->U[ks][js][i].E -= dtodx1*(x1Flux[i ].d*(phic - phil) +
x1Flux[i+1].d*(phir - phic));
#endif /* BAROTROPIC */
}
/* Save mass fluxes in Grid structure for source term correction in main loop */
for (i=is; i<=ie+1; i++) {
pG->x1MassFlux[ks][js][i] = x1Flux[i].d;
}
#endif /* SELF_GRAVITY */
/*=== STEP 13: Update cell-centered values for a full timestep ===============*/
/*--- Step 13a -----------------------------------------------------------------
* Update cell-centered variables in pG (including B2c and B3c) using x1-Fluxes
*/
for (i=is; i<=ie; i++) {
pG->U[ks][js][i].d -= dtodx1*(x1Flux[i+1].d - x1Flux[i].d );
pG->U[ks][js][i].M1 -= dtodx1*(x1Flux[i+1].Mx - x1Flux[i].Mx);
pG->U[ks][js][i].M2 -= dtodx1*(x1Flux[i+1].My - x1Flux[i].My);
pG->U[ks][js][i].M3 -= dtodx1*(x1Flux[i+1].Mz - x1Flux[i].Mz);
#ifndef BAROTROPIC
pG->U[ks][js][i].E -= dtodx1*(x1Flux[i+1].E - x1Flux[i].E );
#endif /* BAROTROPIC */
#ifdef MHD
pG->U[ks][js][i].B2c -= dtodx1*(x1Flux[i+1].By - x1Flux[i].By);
pG->U[ks][js][i].B3c -= dtodx1*(x1Flux[i+1].Bz - x1Flux[i].Bz);
/* For consistency, set B2i and B3i to cell-centered values. */
pG->B2i[ks][js][i] = pG->U[ks][js][i].B2c;
pG->B3i[ks][js][i] = pG->U[ks][js][i].B3c;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->U[ks][js][i].s[n] -= dtodx1*(x1Flux[i+1].s[n] - x1Flux[i].s[n]);
#endif
}
#ifdef STATIC_MESH_REFINEMENT
/*--- Step 13d -----------------------------------------------------------------
* With SMR, store fluxes at boundaries of child and parent grids.
*/
/* x1-boundaries of child Grids (interior to THIS Grid) */
for (ncg=0; ncg<pG->NCGrid; ncg++) {
for (dim=0; dim<2; dim++){
if (pG->CGrid[ncg].myFlx[dim] != NULL) {
if (dim==0) i = pG->CGrid[ncg].ijks[0];
if (dim==1) i = pG->CGrid[ncg].ijke[0] + 1;
pG->CGrid[ncg].myFlx[dim][ks][js].d = x1Flux[i].d;
pG->CGrid[ncg].myFlx[dim][ks][js].M1 = x1Flux[i].Mx;
pG->CGrid[ncg].myFlx[dim][ks][js].M2 = x1Flux[i].My;
pG->CGrid[ncg].myFlx[dim][ks][js].M3 = x1Flux[i].Mz;
#ifndef BAROTROPIC
pG->CGrid[ncg].myFlx[dim][ks][js].E = x1Flux[i].E;
#endif /* BAROTROPIC */
#ifdef MHD
pG->CGrid[ncg].myFlx[dim][ks][js].B1c = 0.0;
pG->CGrid[ncg].myFlx[dim][ks][js].B2c = x1Flux[i].By;
pG->CGrid[ncg].myFlx[dim][ks][js].B3c = x1Flux[i].Bz;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->CGrid[ncg].myFlx[dim][ks][js].s[n] = x1Flux[i].s[n];
#endif
}
}
}
/* x1-boundaries of parent Grids (at boundaries of THIS Grid) */
for (npg=0; npg<pG->NPGrid; npg++) {
for (dim=0; dim<2; dim++){
if (pG->PGrid[npg].myFlx[dim] != NULL) {
if (dim==0) i = pG->PGrid[npg].ijks[0];
if (dim==1) i = pG->PGrid[npg].ijke[0] + 1;
pG->PGrid[npg].myFlx[dim][ks][js].d = x1Flux[i].d;
pG->PGrid[npg].myFlx[dim][ks][js].M1 = x1Flux[i].Mx;
pG->PGrid[npg].myFlx[dim][ks][js].M2 = x1Flux[i].My;
pG->PGrid[npg].myFlx[dim][ks][js].M3 = x1Flux[i].Mz;
#ifndef BAROTROPIC
pG->PGrid[npg].myFlx[dim][ks][js].E = x1Flux[i].E;
#endif /* BAROTROPIC */
#ifdef MHD
pG->PGrid[npg].myFlx[dim][ks][js].B1c = 0.0;
pG->PGrid[npg].myFlx[dim][ks][js].B2c = x1Flux[i].By;
pG->PGrid[npg].myFlx[dim][ks][js].B3c = x1Flux[i].Bz;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->PGrid[npg].myFlx[dim][ks][js].s[n] = x1Flux[i].s[n];
#endif
}
}
}
#endif /* STATIC_MESH_REFINEMENT */
return;
}
void problem(DomainS *pDomain)
{
GridS *pGrid=(pDomain->Grid);
int i,il,iu,j,jl,ju,k,kl,ku;
int shk_dir; /* Shock direction: {1,2,3} -> {x1,x2,x3} */
Real x1,x2,x3;
Prim1DS Wl, Wr;
Cons1DS U1d, Ul, Ur;
Real Bxl=0.0, Bxr=0.0;
/* Parse left state read from input file: dl,pl,ul,vl,wl,bxl,byl,bzl */
Wl.d = par_getd("problem","dl");
#ifdef ADIABATIC
Wl.P = par_getd("problem","pl");
#endif
Wl.Vx = par_getd("problem","v1l");
Wl.Vy = par_getd("problem","v2l");
Wl.Vz = par_getd("problem","v3l");
#ifdef MHD
Bxl = par_getd("problem","b1l");
Wl.By = par_getd("problem","b2l");
Wl.Bz = par_getd("problem","b3l");
#endif
#if (NSCALARS > 0)
Wl.r[0] = par_getd("problem","r[0]l");
#endif
/* Parse right state read from input file: dr,pr,ur,vr,wr,bxr,byr,bzr */
Wr.d = par_getd("problem","dr");
#ifdef ADIABATIC
Wr.P = par_getd("problem","pr");
#endif
Wr.Vx = par_getd("problem","v1r");
Wr.Vy = par_getd("problem","v2r");
Wr.Vz = par_getd("problem","v3r");
#ifdef MHD
Bxr = par_getd("problem","b1r");
Wr.By = par_getd("problem","b2r");
Wr.Bz = par_getd("problem","b3r");
if (Bxr != Bxl) ath_error(0,"[shkset1d] L/R values of Bx not the same\n");
#endif
#if (NSCALARS > 0)
Wr.r[0] = par_getd("problem","r[0]r");
#endif
Ul = Prim1D_to_Cons1D(&Wl, &Bxl);
Ur = Prim1D_to_Cons1D(&Wr, &Bxr);
/* Parse shock direction */
shk_dir = par_geti("problem","shk_dir");
if (shk_dir != 1 && shk_dir != 2 && shk_dir != 3) {
ath_error("[problem]: shk_dir = %d must be either 1,2 or 3\n",shk_dir);
}
/* Set up the index bounds for initializing the grid */
iu = pGrid->ie + nghost;
il = pGrid->is - nghost;
if (pGrid->Nx[1] > 1) {
ju = pGrid->je + nghost;
jl = pGrid->js - nghost;
}
else {
ju = pGrid->je;
jl = pGrid->js;
}
if (pGrid->Nx[2] > 1) {
ku = pGrid->ke + nghost;
kl = pGrid->ks - nghost;
}
else {
ku = pGrid->ke;
kl = pGrid->ks;
}
/* Initialize the grid including the ghost cells. Discontinuity is always
* located at x=0, so xmin/xmax in input file must be set appropriately. */
switch(shk_dir) {
/*--- shock in 1-direction ---------------------------------------------------*/
case 1: /* shock in 1-direction */
for (k=kl; k<=ku; k++) {
for (j=jl; j<=ju; j++) {
for (i=il; i<=iu; i++) {
cc_pos(pGrid, i, j, k, &x1, &x2, &x3);
/* set primitive and conserved variables to be L or R state */
if (x1 <= 0.0) {
U1d = Ul;
} else {
U1d = Ur;
}
/* Initialize conserved (and with SR the primitive) variables in Grid */
pGrid->U[k][j][i].d = U1d.d;
pGrid->U[k][j][i].M1 = U1d.Mx;
pGrid->U[k][j][i].M2 = U1d.My;
pGrid->U[k][j][i].M3 = U1d.Mz;
#ifdef MHD
pGrid->B1i[k][j][i] = Bxl;
pGrid->B2i[k][j][i] = U1d.By;
pGrid->B3i[k][j][i] = U1d.Bz;
pGrid->U[k][j][i].B1c = Bxl;
pGrid->U[k][j][i].B2c = U1d.By;
pGrid->U[k][j][i].B3c = U1d.Bz;
#endif
#ifdef ADIABATIC
pGrid->U[k][j][i].E = U1d.E;
#endif
#if (NSCALARS > 0)
pGrid->U[k][j][i].s[0] = U1d.s[0];
#endif
}
}
}
break;
/*--- shock in 2-direction ---------------------------------------------------*/
case 2: /* shock in 2-direction */
for (k=kl; k<=ku; k++) {
for (j=jl; j<=ju; j++) {
for (i=il; i<=iu; i++) {
cc_pos(pGrid, i, j, k, &x1, &x2, &x3);
/* set primitive variables to be L or R state */
if (x2 <= 0.0) {
U1d = Ul;
} else {
U1d = Ur;
}
/* Initialize conserved (and with SR the primitive) variables in Grid */
pGrid->U[k][j][i].d = U1d.d;
pGrid->U[k][j][i].M1 = U1d.Mz;
pGrid->U[k][j][i].M2 = U1d.Mx;
pGrid->U[k][j][i].M3 = U1d.My;
#ifdef MHD
pGrid->B1i[k][j][i] = U1d.Bz;
pGrid->B2i[k][j][i] = Bxl;
pGrid->B3i[k][j][i] = U1d.By;
pGrid->U[k][j][i].B1c = U1d.Bz;
pGrid->U[k][j][i].B2c = Bxl;
pGrid->U[k][j][i].B3c = U1d.By;
#endif
#ifdef ADIABATIC
pGrid->U[k][j][i].E = U1d.E;
#endif
#if (NSCALARS > 0)
pGrid->U[k][j][i].s[0] = U1d.s[0];
#endif
}
}
}
break;
/*--- shock in 3-direction ---------------------------------------------------*/
case 3: /* shock in 3-direction */
for (k=kl; k<=ku; k++) {
for (j=jl; j<=ju; j++) {
for (i=il; i<=iu; i++) {
cc_pos(pGrid, i, j, k, &x1, &x2, &x3);
/* set primitive variables to be L or R state */
if (x3 <= 0.0) {
U1d = Ul;
} else {
U1d = Ur;
}
/* Initialize conserved (and with SR the primitive) variables in Grid */
pGrid->U[k][j][i].d = U1d.d;
pGrid->U[k][j][i].M1 = U1d.My;
pGrid->U[k][j][i].M2 = U1d.Mz;
pGrid->U[k][j][i].M3 = U1d.Mx;
#ifdef MHD
pGrid->B1i[k][j][i] = U1d.By;
pGrid->B2i[k][j][i] = U1d.Bz;
pGrid->B3i[k][j][i] = Bxl;
pGrid->U[k][j][i].B1c = U1d.By;
pGrid->U[k][j][i].B2c = U1d.Bz;
pGrid->U[k][j][i].B3c = Bxl;
#endif
#ifdef ADIABATIC
pGrid->U[k][j][i].E = U1d.E;
#endif
#if (NSCALARS > 0)
pGrid->U[k][j][i].s[0] = U1d.s[0];
#endif
}
}
}
break;
default:
ath_error("[shkset1d]: invalid shk_dir = %i\n",shk_dir);
}
return;
}
/*! \fn void integrate_1d_vl(DomainS *pD)
* \brief 1D version of van Leer unsplit integrator for MHD.
*
* The numbering of steps follows the numbering in the 3D version.
* NOT ALL STEPS ARE NEEDED IN 1D.
*/
void integrate_1d_vl(DomainS *pD)
{
GridS *pG=(pD->Grid);
ConsS U;
Real dtodx1=pG->dt/pG->dx1, hdtodx1=0.5*pG->dt/pG->dx1;
int i, is = pG->is, ie = pG->ie;
int js = pG->js;
int ks = pG->ks;
int cart_x1 = 1, cart_x2 = 2, cart_x3 = 3;
Real x1,x2,x3,phicl,phicr,phifc,phil,phir,phic;
#if (NSCALARS > 0)
int n;
#endif
#ifdef SELF_GRAVITY
Real gxl,gxr,flx_m1l,flx_m1r;
#endif
#ifdef STATIC_MESH_REFINEMENT
int ncg,npg,dim;
#endif
#ifdef FIRST_ORDER_FLUX_CORRECTION
int flag_cell=0,negd=0,negP=0,superl=0,NaNFlux=0;
int fail=0,final=0;
Real Vsq,Bx;
PrimS Wcheck;
Int3Vect BadCell;
#endif
int il=is-(nghost-1), iu=ie+(nghost-1);
for (i=is-nghost; i<=ie+nghost; i++) {
Uhalf[i] = pG->U[ks][js][i];
W[i] = Cons_to_Prim(&(pG->U[ks][js][i]));
}
/*=== STEP 1: Compute first-order fluxes at t^{n} in x1-direction ============*/
/* No source terms are needed since there is no temporal evolution */
/*--- Step 1a ------------------------------------------------------------------
* Load 1D vector of primitive variables;
* W1d = (d, V1, V2, V3, P, B2c, B3c, s[n])
*/
for (i=is-nghost; i<=ie+nghost; i++) {
W1d[i].d = W[i].d;
W1d[i].Vx = W[i].V1;
W1d[i].Vy = W[i].V2;
W1d[i].Vz = W[i].V3;
W1d[i].P = W[i].P;
#ifdef MHD
W1d[i].By = W[i].B2c;
W1d[i].Bz = W[i].B3c;
Bxc[i] = W[i].B1c;
Bxi[i] = pG->B1i[ks][js][i];
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++) W1d[i].s[n] = W[i].s[n];
#endif
}
/*--- Step 1b ------------------------------------------------------------------
* Compute first-order L/R states */
/* Ensure that W & U are consistent */
for (i=is-nghost; i<=ie+nghost; i++) {
U1d[i] = Prim1D_to_Cons1D(&W1d[i],&Bxc[i]);
}
for (i=il; i<=ie+nghost; i++) {
Wl[i] = W1d[i-1];
Wr[i] = W1d[i ];
Ul[i] = U1d[i-1];
Ur[i] = U1d[i ];
}
/*--- Step 1c ------------------------------------------------------------------
* No source terms needed */
/*--- Step 1d ------------------------------------------------------------------
* Compute flux in x1-direction */
for (i=il; i<=ie+nghost; i++) {
fluxes(Ul[i],Ur[i],Wl[i],Wr[i],Bxi[i],&x1Flux[i]);
}
/*=== STEPS 2-4: Not needed in 1D ===*/
/*=== STEP 5: Update cell-centered variables to half-timestep ================*/
/*--- Step 5a ------------------------------------------------------------------
* Update cell-centered variables (including B2c and B3c) to half-timestep
*/
for (i=il; i<=iu; i++) {
Uhalf[i].d -= hdtodx1*(x1Flux[i+1].d - x1Flux[i].d );
Uhalf[i].M1 -= hdtodx1*(x1Flux[i+1].Mx - x1Flux[i].Mx);
Uhalf[i].M2 -= hdtodx1*(x1Flux[i+1].My - x1Flux[i].My);
Uhalf[i].M3 -= hdtodx1*(x1Flux[i+1].Mz - x1Flux[i].Mz);
Uhalf[i].E -= hdtodx1*(x1Flux[i+1].E - x1Flux[i].E );
#ifdef MHD
Uhalf[i].B2c -= hdtodx1*(x1Flux[i+1].By - x1Flux[i].By);
Uhalf[i].B3c -= hdtodx1*(x1Flux[i+1].Bz - x1Flux[i].Bz);
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
Uhalf[i].s[n] -= hdtodx1*(x1Flux[i+1].s[n] - x1Flux[i].s[n]);
#endif
#ifdef FIRST_ORDER_FLUX_CORRECTION
x1FluxP[i] = x1Flux[i];
#endif
}
/*=== STEP 6: Add source terms to predict values at half-timestep ============*/
/*--- Step 6a ------------------------------------------------------------------
* Add source terms from a static gravitational potential for 0.5*dt to predict
* step. To improve conservation of total energy, we average the energy
* source term computed at cell faces.
* S_{M} = -(\rho) Grad(Phi); S_{E} = -(\rho v) Grad{Phi}
*/
if (StaticGravPot != NULL) {
for (i=il; i<=iu; i++) {
cc_pos(pG,i,js,ks,&x1,&x2,&x3);
phic = (*StaticGravPot)((x1 ),x2,x3);
phir = (*StaticGravPot)((x1+0.5*pG->dx1),x2,x3);
phil = (*StaticGravPot)((x1-0.5*pG->dx1),x2,x3);
Uhalf[i].M1 -= hdtodx1*pG->U[ks][js][i].d*(phir-phil);
Uhalf[i].E -= hdtodx1*(x1Flux[i ].d*(phic - phil) +
x1Flux[i+1].d*(phir - phic));
}
}
/*=== STEP 7: Conserved->Primitive variable inversion at t^{n+1/2} ===========*/
/* Invert conserved variables at t^{n+1/2} to primitive variables. With FOFC,
* if cell-centered d < 0, P< 0, or v^2 > 1, correct by switching back to
* values at beginning of step, rendering update first order in time for that
* cell.
*/
#ifdef FIRST_ORDER_FLUX_CORRECTION
negd = 0;
negP = 0;
superl = 0;
flag_cell = 0;
#endif
for (i=il; i<=iu; i++) {
Whalf[i] = Cons_to_Prim(&Uhalf[i]);
#ifdef FIRST_ORDER_FLUX_CORRECTION
if (Whalf[i].d < 0.0) {
flag_cell = 1;
negd++;
}
if (Whalf[i].P < 0.0) {
flag_cell = 1;
negP++;
}
Vsq = SQR(Whalf[i].V1) + SQR(Whalf[i].V2) + SQR(Whalf[i].V3);
if (Vsq > 1.0) {
flag_cell = 1;
superl++;
}
if (flag_cell != 0) {
Whalf[i].d = W[i].d;
Whalf[i].V1 = W[i].V1;
Whalf[i].V2 = W[i].V2;
Whalf[i].V3 = W[i].V3;
Whalf[i].P = W[i].P;
flag_cell=0;
}
#endif
}
#ifdef FIRST_ORDER_FLUX_CORRECTION
if (negd > 0 || negP > 0 || superl > 0)
printf("[Step7]: %i cells had d<0; %i cells had P<0; %i cells had v>1\n"
,negd,negP,superl);
#endif
/*=== STEP 8: Compute second-order L/R x1-interface states ===================*/
/*--- Step 8a ------------------------------------------------------------------
* Load 1D vector of primitive variables;
* W = (d, V1, V2, V3, P, B2c, B3c, s[n])
*/
for (i=il; i<=iu; i++) {
W1d[i].d = Whalf[i].d;
W1d[i].Vx = Whalf[i].V1;
W1d[i].Vy = Whalf[i].V2;
W1d[i].Vz = Whalf[i].V3;
W1d[i].P = Whalf[i].P;
#ifdef MHD
W1d[i].By = Whalf[i].B2c;
W1d[i].Bz = Whalf[i].B3c;
Bxc[i] = Whalf[i].B1c;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++) W1d[i].s[n] = Whalf[i].s[n];
#endif /* NSCALARS */
}
/*--- Step 8b ------------------------------------------------------------------
* Compute L/R states on x1-interfaces, store into arrays
*/
lr_states(pG,W1d,Bxc,pG->dt,pG->dx1,is,ie,Wl,Wr,cart_x1);
#ifdef FIRST_ORDER_FLUX_CORRECTION
for (i=il; i<=iu; i++) {
Vsq = SQR(Wl[i].Vx) + SQR(Wl[i].Vy) + SQR(Wl[i].Vz);
if (Vsq > 1.0) {
Wl[i] = W1d[i];
Wr[i] = W1d[i];
}
Vsq = SQR(Wr[i].Vx) + SQR(Wr[i].Vy) + SQR(Wr[i].Vz);
if (Vsq > 1.0) {
Wl[i] = W1d[i];
Wr[i] = W1d[i];
}
}
#endif
for (i=is; i<=ie+1; i++) {
Wl_x1Face[i] = Wl[i];
Wr_x1Face[i] = Wr[i];
}
/*=== STEPS 9-10: Not needed in 1D ===*/
/*=== STEP 11: Compute x1-Flux ===============================================*/
/*--- Step 11b -----------------------------------------------------------------
* Compute second-order fluxes in x1-direction
*/
for (i=is; i<=ie+1; i++) {
Ul[i] = Prim1D_to_Cons1D(&Wl_x1Face[i],&Bxi[i]);
Ur[i] = Prim1D_to_Cons1D(&Wr_x1Face[i],&Bxi[i]);
fluxes(Ul[i],Ur[i],Wl_x1Face[i],Wr_x1Face[i],Bxi[i],&x1Flux[i]);
}
/*=== STEP 12: Not needed in 1D ===*/
/*=== STEP 13: Add source terms for a full timestep using n+1/2 states =======*/
/*--- Step 13a -----------------------------------------------------------------
* Add gravitational source terms due to a Static Potential
* To improve conservation of total energy, we average the energy
* source term computed at cell faces.
* S_{M} = -(\rho)^{n+1/2} Grad(Phi); S_{E} = -(\rho v)^{n+1/2} Grad{Phi}
*/
if (StaticGravPot != NULL) {
for (i=is; i<=ie; i++) {
cc_pos(pG,i,js,ks,&x1,&x2,&x3);
phic = (*StaticGravPot)((x1 ),x2,x3);
phir = (*StaticGravPot)((x1+0.5*pG->dx1),x2,x3);
phil = (*StaticGravPot)((x1-0.5*pG->dx1),x2,x3);
pG->U[ks][js][i].M1 -= dtodx1*Uhalf[i].d*(phir-phil);
#ifndef BAROTROPIC
pG->U[ks][js][i].E -= dtodx1*(x1Flux[i ].d*(phic - phil) +
x1Flux[i+1].d*(phir - phic));
#endif
}
}
/*=== STEP 14: Update cell-centered values for a full timestep ===============*/
/*--- Step 14a -----------------------------------------------------------------
* Update cell-centered variables in pG (including B2c and B3c) using x1-Fluxes
*/
for (i=is; i<=ie; i++) {
pG->U[ks][js][i].d -= dtodx1*(x1Flux[i+1].d - x1Flux[i].d );
pG->U[ks][js][i].M1 -= dtodx1*(x1Flux[i+1].Mx - x1Flux[i].Mx);
pG->U[ks][js][i].M2 -= dtodx1*(x1Flux[i+1].My - x1Flux[i].My);
pG->U[ks][js][i].M3 -= dtodx1*(x1Flux[i+1].Mz - x1Flux[i].Mz);
#ifndef BAROTROPIC
pG->U[ks][js][i].E -= dtodx1*(x1Flux[i+1].E - x1Flux[i].E );
#endif /* BAROTROPIC */
#ifdef MHD
pG->U[ks][js][i].B2c -= dtodx1*(x1Flux[i+1].By - x1Flux[i].By);
pG->U[ks][js][i].B3c -= dtodx1*(x1Flux[i+1].Bz - x1Flux[i].Bz);
/* For consistency, set B2i and B3i to cell-centered values. */
pG->B2i[ks][js][i] = pG->U[ks][js][i].B2c;
pG->B3i[ks][js][i] = pG->U[ks][js][i].B3c;
#endif /* MHD */
#if (NSCALARS > 0)
for (n=0; n<NSCALARS; n++)
pG->U[ks][js][i].s[n] -= dtodx1*(x1Flux[i+1].s[n] - x1Flux[i].s[n]);
#endif
}
#ifdef FIRST_ORDER_FLUX_CORRECTION
/*=== STEP 15: First-order flux correction ===================================*/
/*--- Step 15a -----------------------------------------------------------------
* If cell-centered d or P have gone negative, or if v^2 > 1, correct
* by using 1st order predictor fluxes */
for (i=is; i<=ie; i++) {
Wcheck = check_Prim(&(pG->U[ks][js][i]));
if (Wcheck.d < 0.0) {
flag_cell = 1;
BadCell.i = i;
BadCell.j = js;
BadCell.k = ks;
negd++;
}
if (Wcheck.P < 0.0) {
flag_cell = 1;
BadCell.i = i;
BadCell.j = js;
BadCell.k = ks;
negP++;
}
Vsq = SQR(Wcheck.V1) + SQR(Wcheck.V2) + SQR(Wcheck.V3);
if (Vsq > 1.0) {
flag_cell = 1;
BadCell.i = i;
BadCell.j = js;
BadCell.k = ks;
superl++;
}
if (flag_cell != 0) {
FixCell(pG, BadCell);
flag_cell=0;
}
}
if (negd > 0 || negP > 0 || superl > 0) {
printf("[Step15a]: %i cells had d<0; %i cells had P<0;\n",negd,negP);
printf("[Step15a]: %i cells had v>1 at 1st correction\n",superl);
}
/*--- Step 15b -----------------------------------------------------------------
* In SR the first-order flux correction can fail to fix an unphysical state.
* We must fix these cells in order to avoid NaN's at the next timestep,
* particuarly if v^2 > 1. We have 2 approaches; firstly, we use the entropy
* equation (which we have not applied a 1st order flux correction to) to
* calculate the pressure and the Lorentz factor of the gas. If this produces
* and unphysical state, then we floor the pressure and iterate on v^2 until
* v^2 < 1. Possibly could improved by averaging density and pressure from
* adjacent cells and then calculating pressure.
*/
#ifdef MHD
fail = 0;
negd = 0;
negP = 0;
final = 0;
