void CConvective_Template::ComputeResidual(double *val_residual, double **val_Jacobian_i, double **val_Jacobian_j, CConfig *config) {
Area = 0;
for (iDim = 0; iDim < nDim; iDim++)
/*!< \brief Normal: Normal vector, it norm is the area of the face. */
Area += Normal[iDim]*Normal[iDim];
Area = sqrt(Area); /*! Area of the face*/
for (iDim = 0; iDim < nDim; iDim++)
UnitNormal[iDim] = Normal[iDim]/Area; /* ! Unit Normal*/
/*--- Point i, Needs to recompute SoundSpeed / Pressure / Enthalpy in case of 2nd order reconstruction ---*/
Density_i = U_i[0];
sq_vel = 0;
for (iDim = 0; iDim < nDim; iDim++) {
Velocity_i[iDim] = U_i[iDim+1] / Density_i;
sq_vel += Velocity_i[iDim]*Velocity_i[iDim];
}
Energy_i = U_i[nDim+1] / Density_i;
SoundSpeed_i = sqrt(Gamma*Gamma_Minus_One*(Energy_i-0.5*sq_vel));
Pressure_i = (SoundSpeed_i * SoundSpeed_i * Density_i) / Gamma;
Enthalpy_i = (U_i[nDim+1] + Pressure_i) / Density_i;
/*--- Point j, Needs to recompute SoundSpeed / Pressure / Enthalpy in case of 2nd order reconstruction ---*/
Density_j = U_j[0];
sq_vel = 0;
for (iDim = 0; iDim < nDim; iDim++) {
Velocity_j[iDim] = U_j[iDim+1] / Density_j;
sq_vel += Velocity_j[iDim]*Velocity_j[iDim];
}
Energy_j = U_j[nDim+1] / Density_j;
SoundSpeed_j = sqrt(Gamma*Gamma_Minus_One*(Energy_j-0.5*sq_vel));
Pressure_j = (SoundSpeed_j * SoundSpeed_j * Density_j) / Gamma;
Enthalpy_j = (U_j[nDim+1] + Pressure_j) / Density_j;
/*--- Promediate Roe variables iPoint and jPoint ---*/
R = sqrt(Density_j/Density_i);
RoeDensity = R*Density_i;
sq_vel = 0;
for (iDim = 0; iDim < nDim; iDim++) {
RoeVelocity[iDim] = (R*Velocity_j[iDim]+Velocity_i[iDim])/(R+1);
sq_vel += RoeVelocity[iDim]*RoeVelocity[iDim];
}
RoeEnthalpy = (R*Enthalpy_j+Enthalpy_i)/(R+1);
RoeSoundSpeed = sqrt((Gamma-1)*(RoeEnthalpy-0.5*sq_vel));
/*--- Compute Proj_flux_tensor_i ---*/
GetInviscidProjFlux(&Density_i, Velocity_i, &Pressure_i, &Enthalpy_i, Normal, Proj_flux_tensor_i);
/*--- Compute Proj_flux_tensor_j ---*/
GetInviscidProjFlux(&Density_j, Velocity_j, &Pressure_j, &Enthalpy_j, Normal, Proj_flux_tensor_j);
/*--- Compute P and Lambda (do it with the Normal) ---*/
GetPMatrix(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, P_Tensor);
ProjVelocity = 0.0; ProjVelocity_i = 0.0; ProjVelocity_j = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
ProjVelocity += RoeVelocity[iDim]*UnitNormal[iDim];
ProjVelocity_i += Velocity_i[iDim]*UnitNormal[iDim];
ProjVelocity_j += Velocity_j[iDim]*UnitNormal[iDim];
}
/*--- Flow eigenvalues and Entropy correctors ---*/
for (iDim = 0; iDim < nDim; iDim++) {
Lambda[iDim] = ProjVelocity;
Epsilon[iDim] = 4.0*max(0.0, max(Lambda[iDim]-ProjVelocity_i,ProjVelocity_j-Lambda[iDim]));
}
Lambda[nVar-2] = ProjVelocity + RoeSoundSpeed;
Epsilon[nVar-2] = 4.0*max(0.0, max(Lambda[nVar-2]-(ProjVelocity_i+SoundSpeed_i),(ProjVelocity_j+SoundSpeed_j)-Lambda[nVar-2]));
Lambda[nVar-1] = ProjVelocity - RoeSoundSpeed;
Epsilon[nVar-1] = 4.0*max(0.0, max(Lambda[nVar-1]-(ProjVelocity_i-SoundSpeed_i),(ProjVelocity_j-SoundSpeed_j)-Lambda[nVar-1]));
/*--- Entropy correction ---*/
for (iVar = 0; iVar < nVar; iVar++)
if ( fabs(Lambda[iVar]) < Epsilon[iVar] )
Lambda[iVar] = (Lambda[iVar]*Lambda[iVar] + Epsilon[iVar]*Epsilon[iVar])/(2.0*Epsilon[iVar]);
else
Lambda[iVar] = fabs(Lambda[iVar]);
if (!implicit) {
/*--- Compute wave amplitudes (characteristics) ---*/
proj_delta_vel = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
delta_vel[iDim] = Velocity_j[iDim] - Velocity_i[iDim];
proj_delta_vel += delta_vel[iDim]*Normal[iDim];
}
delta_p = Pressure_j - Pressure_i;
delta_rho = Density_j - Density_i;
proj_delta_vel = proj_delta_vel/Area;
if (nDim == 3) {
delta_wave[0] = delta_rho - delta_p/(RoeSoundSpeed*RoeSoundSpeed);
delta_wave[1] = UnitNormal[0]*delta_vel[2]-UnitNormal[2]*delta_vel[0];
delta_wave[2] = UnitNormal[1]*delta_vel[0]-UnitNormal[0]*delta_vel[1];
delta_wave[3] = proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
delta_wave[4] = -proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
}
else {
delta_wave[0] = delta_rho - delta_p/(RoeSoundSpeed*RoeSoundSpeed);
delta_wave[1] = UnitNormal[1]*delta_vel[0]-UnitNormal[0]*delta_vel[1];
delta_wave[2] = proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
delta_wave[3] = -proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
}
/*--- Roe's Flux approximation ---*/
for (iVar = 0; iVar < nVar; iVar++) {
val_residual[iVar] = 0.5*(Proj_flux_tensor_i[iVar]+Proj_flux_tensor_j[iVar]);
for (jVar = 0; jVar < nVar; jVar++)
val_residual[iVar] -= 0.5*Lambda[jVar]*delta_wave[jVar]*P_Tensor[iVar][jVar]*Area;
}
}
else {
/*--- Compute inverse P ---*/
GetPMatrix_inv(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, invP_Tensor);
/*--- Jacobias of the inviscid flux, scale = 0.5 because val_resconv ~ 0.5*(fc_i+fc_j)*Normal ---*/
GetInviscidProjJac(Velocity_i, &Energy_i, Normal, 0.5, val_Jacobian_i);
GetInviscidProjJac(Velocity_j, &Energy_j, Normal, 0.5, val_Jacobian_j);
/*--- Diference variables iPoint and jPoint ---*/
for (iVar = 0; iVar < nVar; iVar++)
Diff_U[iVar] = U_j[iVar]-U_i[iVar];
/*--- Roe's Flux approximation ---*/
for (iVar = 0; iVar < nVar; iVar++) {
val_residual[iVar] = 0.5*(Proj_flux_tensor_i[iVar]+Proj_flux_tensor_j[iVar]);
for (jVar = 0; jVar < nVar; jVar++) {
Proj_ModJac_Tensor_ij = 0.0;
/*--- Compute |Proj_ModJac_Tensor| = P x |Lambda| x inverse P ---*/
for (kVar = 0; kVar < nVar; kVar++)
Proj_ModJac_Tensor_ij += P_Tensor[iVar][kVar]*Lambda[kVar]*invP_Tensor[kVar][jVar];
val_residual[iVar] -= 0.5*Proj_ModJac_Tensor_ij*Diff_U[jVar]*Area;
val_Jacobian_i[iVar][jVar] += 0.5*Proj_ModJac_Tensor_ij*Area;
val_Jacobian_j[iVar][jVar] -= 0.5*Proj_ModJac_Tensor_ij*Area;
}
}
}
}
void CUpwHLLC_Flow::ComputeResidual(double *val_residual, double **val_Jacobian_i, double **val_Jacobian_j, CConfig *config) {
/*--- Face area (norm or the normal vector) ---*/
Area = 0.0;
for (iDim = 0; iDim < nDim; iDim++)
Area += Normal[iDim]*Normal[iDim];
Area = sqrt(Area);
/*-- Unit Normal ---*/
for (iDim = 0; iDim < nDim; iDim++)
UnitNormal[iDim] = Normal[iDim]/Area;
/*--- Primitive variables at point i ---*/
sq_vel_i = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
Velocity_i[iDim] = V_i[iDim+1];
sq_vel_i += Velocity_i[iDim]*Velocity_i[iDim];
}
Pressure_i = V_i[nDim+1];
Density_i = V_i[nDim+2];
Enthalpy_i = V_i[nDim+3];
Energy_i = Enthalpy_i - Pressure_i/Density_i;
SoundSpeed_i = sqrt(Gamma*Gamma_Minus_One*(Energy_i-0.5*sq_vel_i));
/*--- Primitive variables at point j ---*/
sq_vel_j = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
Velocity_j[iDim] = V_j[iDim+1];
sq_vel_j += Velocity_j[iDim]*Velocity_j[iDim];
}
Pressure_j = V_j[nDim+1];
Density_j = V_j[nDim+2];
Enthalpy_j = V_j[nDim+3];
Energy_j = Enthalpy_j - Pressure_j/Density_j;
SoundSpeed_j = sqrt(Gamma*Gamma_Minus_One*(Energy_j-0.5*sq_vel_j));
/*--- Projected velocities ---*/
ProjVelocity_i = 0.0; ProjVelocity_j = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
ProjVelocity_i += Velocity_i[iDim]*UnitNormal[iDim];
ProjVelocity_j += Velocity_j[iDim]*UnitNormal[iDim];
}
/*--- Roe's averaging ---*/
Rrho = sqrt(Density_j/Density_i);
tmp = 1.0/(1.0+Rrho);
for (iDim = 0; iDim < nDim; iDim++)
velRoe[iDim] = tmp*(Velocity_i[iDim] + Velocity_j[iDim]*Rrho);
uRoe = 0.0;
for (iDim = 0; iDim < nDim; iDim++)
uRoe += velRoe[iDim]*UnitNormal[iDim];
gamPdivRho = tmp*((Gamma*Pressure_i/Density_i+0.5*(Gamma-1.0)*sq_vel_i) + (Gamma*Pressure_j/Density_j+0.5*(Gamma-1.0)*sq_vel_j)*Rrho);
sq_velRoe = 0.0;
for (iDim = 0; iDim < nDim; iDim++)
sq_velRoe += velRoe[iDim]*velRoe[iDim];
cRoe = sqrt(gamPdivRho - ((Gamma+Gamma)*0.5-1.0)*0.5*sq_velRoe);
/*--- Speed of sound at L and R ---*/
sL = min(uRoe-cRoe, ProjVelocity_i-SoundSpeed_i);
sR = max(uRoe+cRoe, ProjVelocity_j+SoundSpeed_j);
/*--- speed of contact surface ---*/
sM = (Pressure_i-Pressure_j
- Density_i*ProjVelocity_i*(sL-ProjVelocity_i)
+ Density_j*ProjVelocity_j*(sR-ProjVelocity_j))
/(Density_j*(sR-ProjVelocity_j)-Density_i*(sL-ProjVelocity_i));
/*--- Pressure at right and left (Pressure_j=Pressure_i) side of contact surface ---*/
pStar = Density_j * (ProjVelocity_j-sR)*(ProjVelocity_j-sM) + Pressure_j;
if (sM >= 0.0) {
if (sL > 0.0) {
val_residual[0] = Density_i*ProjVelocity_i;
for (iDim = 0; iDim < nDim; iDim++)
val_residual[iDim+1] = Density_i*Velocity_i[iDim]*ProjVelocity_i + Pressure_i*UnitNormal[iDim];
val_residual[nVar-1] = Energy_i*Density_i*ProjVelocity_i + Pressure_i*ProjVelocity_i;
}
else {
invSLmSs = 1.0/(sL-sM);
sLmuL = sL-ProjVelocity_i;
rhoSL = Density_i*sLmuL*invSLmSs;
for (iDim = 0; iDim < nDim; iDim++)
rhouSL[iDim] = (Density_i*Velocity_i[iDim]*sLmuL+(pStar-Pressure_i)*UnitNormal[iDim])*invSLmSs;
eSL = (sLmuL*Energy_i*Density_i-Pressure_i*ProjVelocity_i+pStar*sM)*invSLmSs;
val_residual[0] = rhoSL*sM;
for (iDim = 0; iDim < nDim; iDim++)
val_residual[iDim+1] = rhouSL[iDim]*sM + pStar*UnitNormal[iDim];
val_residual[nVar-1] = (eSL+pStar)*sM;
}
}
else {
if (sR >= 0.0) {
invSRmSs = 1.0/(sR-sM);
sRmuR = sR-ProjVelocity_j;
rhoSR = Density_j*sRmuR*invSRmSs;
for (iDim = 0; iDim < nDim; iDim++)
rhouSR[iDim] = (Density_j*Velocity_j[iDim]*sRmuR+(pStar-Pressure_j)*UnitNormal[iDim])*invSRmSs;
eSR = (sRmuR*Energy_j*Density_j-Pressure_j*ProjVelocity_j+pStar*sM)*invSRmSs;
val_residual[0] = rhoSR*sM;
for (iDim = 0; iDim < nDim; iDim++)
val_residual[iDim+1] = rhouSR[iDim]*sM + pStar*UnitNormal[iDim];
val_residual[nVar-1] = (eSR+pStar)*sM;
}
else {
val_residual[0] = Density_j*ProjVelocity_j;
for (iDim = 0; iDim < nDim; iDim++)
val_residual[iDim+1] = Density_j*Velocity_j[iDim]*ProjVelocity_j + Pressure_j*UnitNormal[iDim];
val_residual[nVar-1] = Energy_j*Density_j*ProjVelocity_j + Pressure_j*ProjVelocity_j;
}
}
for (iVar = 0; iVar < nVar; iVar++)
val_residual[iVar] *= Area;
if (implicit) {
/*--- Average Roe variables iPoint and jPoint ---*/
R = sqrt(Density_j/Density_i);
RoeDensity = R*Density_i;
sq_vel = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
RoeVelocity[iDim] = (R*Velocity_j[iDim]+Velocity_i[iDim])/(R+1);
sq_vel += RoeVelocity[iDim]*RoeVelocity[iDim];
}
RoeEnthalpy = (R*Enthalpy_j+Enthalpy_i)/(R+1);
RoeSoundSpeed = sqrt((Gamma-1)*(RoeEnthalpy-0.5*sq_vel));
/*--- Compute P and Lambda (do it with the Normal) ---*/
GetPMatrix(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, P_Tensor);
ProjVelocity = 0.0; ProjVelocity_i = 0.0; ProjVelocity_j = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
ProjVelocity += RoeVelocity[iDim]*UnitNormal[iDim];
ProjVelocity_i += Velocity_i[iDim]*UnitNormal[iDim];
ProjVelocity_j += Velocity_j[iDim]*UnitNormal[iDim];
}
/*--- Flow eigenvalues and Entropy correctors ---*/
for (iDim = 0; iDim < nDim; iDim++)
Lambda[iDim] = ProjVelocity;
Lambda[nVar-2] = ProjVelocity + RoeSoundSpeed;
Lambda[nVar-1] = ProjVelocity - RoeSoundSpeed;
/*--- Compute inverse P ---*/
GetPMatrix_inv(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, invP_Tensor);
/*--- Jacobias of the inviscid flux, scale = 0.5 because val_residual ~ 0.5*(fc_i+fc_j)*Normal ---*/
GetInviscidProjJac(Velocity_i, &Energy_i, Normal, 0.5, val_Jacobian_i);
GetInviscidProjJac(Velocity_j, &Energy_j, Normal, 0.5, val_Jacobian_j);
/*--- Roe's Flux approximation ---*/
for (iVar = 0; iVar < nVar; iVar++) {
for (jVar = 0; jVar < nVar; jVar++) {
Proj_ModJac_Tensor_ij = 0.0;
/*--- Compute |Proj_ModJac_Tensor| = P x |Lambda| x inverse P ---*/
for (kVar = 0; kVar < nVar; kVar++)
Proj_ModJac_Tensor_ij += P_Tensor[iVar][kVar]*fabs(Lambda[kVar])*invP_Tensor[kVar][jVar];
val_Jacobian_i[iVar][jVar] += 0.5*Proj_ModJac_Tensor_ij*Area;
val_Jacobian_j[iVar][jVar] -= 0.5*Proj_ModJac_Tensor_ij*Area;
}
}
}
}
void CUpwRoe_Flow::ComputeResidual(double *val_residual, double **val_Jacobian_i, double **val_Jacobian_j, CConfig *config) {
/*--- Face area (norm or the normal vector) ---*/
Area = 0.0;
for (iDim = 0; iDim < nDim; iDim++)
Area += Normal[iDim]*Normal[iDim];
Area = sqrt(Area);
/*-- Unit Normal ---*/
for (iDim = 0; iDim < nDim; iDim++)
UnitNormal[iDim] = Normal[iDim]/Area;
/*--- Primitive variables at point i ---*/
for (iDim = 0; iDim < nDim; iDim++)
Velocity_i[iDim] = V_i[iDim+1];
Pressure_i = V_i[nDim+1];
Density_i = V_i[nDim+2];
Enthalpy_i = V_i[nDim+3];
Energy_i = Enthalpy_i - Pressure_i/Density_i;
SoundSpeed_i = sqrt(Pressure_i*Gamma/Density_i);
/*--- Primitive variables at point j ---*/
for (iDim = 0; iDim < nDim; iDim++)
Velocity_j[iDim] = V_j[iDim+1];
Pressure_j = V_j[nDim+1];
Density_j = V_j[nDim+2];
Enthalpy_j = V_j[nDim+3];
Energy_j = Enthalpy_j - Pressure_j/Density_j;
SoundSpeed_j = sqrt(Pressure_j*Gamma/Density_j);
/*--- Recompute conservative variables ---*/
double U_i[5], U_j[5];
U_i[0] = Density_i; U_j[0] = Density_j;
for (iDim = 0; iDim < nDim; iDim++) {
U_i[iDim+1] = Density_i*Velocity_i[iDim]; U_j[iDim+1] = Density_j*Velocity_j[iDim];
}
U_i[nDim+1] = Density_i*Energy_i; U_j[nDim+1] = Density_j*Energy_j;
/*--- Roe-averaged variables at interface between i & j ---*/
R = sqrt(fabs(Density_j/Density_i));
RoeDensity = R*Density_i;
sq_vel = 0;
for (iDim = 0; iDim < nDim; iDim++) {
RoeVelocity[iDim] = (R*Velocity_j[iDim]+Velocity_i[iDim])/(R+1);
sq_vel += RoeVelocity[iDim]*RoeVelocity[iDim];
}
RoeEnthalpy = (R*Enthalpy_j+Enthalpy_i)/(R+1);
RoeSoundSpeed = sqrt((Gamma-1)*(RoeEnthalpy-0.5*sq_vel));
/*--- Compute Proj_flux_tensor_i ---*/
GetInviscidProjFlux(&Density_i, Velocity_i, &Pressure_i, &Enthalpy_i, Normal, Proj_flux_tensor_i);
/*--- Compute Proj_flux_tensor_j ---*/
GetInviscidProjFlux(&Density_j, Velocity_j, &Pressure_j, &Enthalpy_j, Normal, Proj_flux_tensor_j);
/*--- Compute P and Lambda (do it with the Normal) ---*/
GetPMatrix(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, P_Tensor);
ProjVelocity = 0.0; ProjVelocity_i = 0.0; ProjVelocity_j = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
ProjVelocity += RoeVelocity[iDim]*UnitNormal[iDim];
ProjVelocity_i += Velocity_i[iDim]*UnitNormal[iDim];
ProjVelocity_j += Velocity_j[iDim]*UnitNormal[iDim];
}
/*--- Flow eigenvalues and entropy correctors ---*/
for (iDim = 0; iDim < nDim; iDim++)
Lambda[iDim] = ProjVelocity;
Lambda[nVar-2] = ProjVelocity + RoeSoundSpeed;
Lambda[nVar-1] = ProjVelocity - RoeSoundSpeed;
// /*--- Harten and Hyman (1983) entropy correction ---*/
// for (iDim = 0; iDim < nDim; iDim++)
// Epsilon[iDim] = 4.0*max(0.0, max(Lambda[iDim]-ProjVelocity_i,ProjVelocity_j-Lambda[iDim]));
//
// Epsilon[nVar-2] = 4.0*max(0.0, max(Lambda[nVar-2]-(ProjVelocity_i+SoundSpeed_i),(ProjVelocity_j+SoundSpeed_j)-Lambda[nVar-2]));
// Epsilon[nVar-1] = 4.0*max(0.0, max(Lambda[nVar-1]-(ProjVelocity_i-SoundSpeed_i),(ProjVelocity_j-SoundSpeed_j)-Lambda[nVar-1]));
//
// for (iVar = 0; iVar < nVar; iVar++)
// if ( fabs(Lambda[iVar]) < Epsilon[iVar] )
// Lambda[iVar] = (Lambda[iVar]*Lambda[iVar] + Epsilon[iVar]*Epsilon[iVar])/(2.0*Epsilon[iVar]);
// else
// Lambda[iVar] = fabs(Lambda[iVar]);
for (iVar = 0; iVar < nVar; iVar++)
Lambda[iVar] = fabs(Lambda[iVar]);
if (!implicit) {
/*--- Compute wave amplitudes (characteristics) ---*/
proj_delta_vel = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
delta_vel[iDim] = Velocity_j[iDim] - Velocity_i[iDim];
proj_delta_vel += delta_vel[iDim]*Normal[iDim];
}
delta_p = Pressure_j - Pressure_i;
delta_rho = Density_j - Density_i;
proj_delta_vel = proj_delta_vel/Area;
if (nDim == 2) {
delta_wave[0] = delta_rho - delta_p/(RoeSoundSpeed*RoeSoundSpeed);
delta_wave[1] = UnitNormal[1]*delta_vel[0]-UnitNormal[0]*delta_vel[1];
delta_wave[2] = proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
delta_wave[3] = -proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
} else {
delta_wave[0] = delta_rho - delta_p/(RoeSoundSpeed*RoeSoundSpeed);
delta_wave[1] = UnitNormal[0]*delta_vel[2]-UnitNormal[2]*delta_vel[0];
delta_wave[2] = UnitNormal[1]*delta_vel[0]-UnitNormal[0]*delta_vel[1];
delta_wave[3] = proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
delta_wave[4] = -proj_delta_vel + delta_p/(RoeDensity*RoeSoundSpeed);
}
/*--- Roe's Flux approximation ---*/
for (iVar = 0; iVar < nVar; iVar++) {
val_residual[iVar] = 0.5*(Proj_flux_tensor_i[iVar]+Proj_flux_tensor_j[iVar]);
for (jVar = 0; jVar < nVar; jVar++)
val_residual[iVar] -= 0.5*Lambda[jVar]*delta_wave[jVar]*P_Tensor[iVar][jVar]*Area;
}
}
else {
/*--- Compute inverse P ---*/
GetPMatrix_inv(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, invP_Tensor);
/*--- Jacobians of the inviscid flux, scaled by
0.5 because val_resconv ~ 0.5*(fc_i+fc_j)*Normal ---*/
GetInviscidProjJac(Velocity_i, &Energy_i, Normal, 0.5, val_Jacobian_i);
GetInviscidProjJac(Velocity_j, &Energy_j, Normal, 0.5, val_Jacobian_j);
/*--- Diference variables iPoint and jPoint ---*/
for (iVar = 0; iVar < nVar; iVar++)
Diff_U[iVar] = U_j[iVar]-U_i[iVar];
/*--- Roe's Flux approximation ---*/
for (iVar = 0; iVar < nVar; iVar++) {
val_residual[iVar] = 0.5*(Proj_flux_tensor_i[iVar]+Proj_flux_tensor_j[iVar]);
for (jVar = 0; jVar < nVar; jVar++) {
Proj_ModJac_Tensor_ij = 0.0;
/*--- Compute |Proj_ModJac_Tensor| = P x |Lambda| x inverse P ---*/
for (kVar = 0; kVar < nVar; kVar++)
Proj_ModJac_Tensor_ij += P_Tensor[iVar][kVar]*Lambda[kVar]*invP_Tensor[kVar][jVar];
val_residual[iVar] -= 0.5*Proj_ModJac_Tensor_ij*Diff_U[jVar]*Area;
val_Jacobian_i[iVar][jVar] += 0.5*Proj_ModJac_Tensor_ij*Area;
val_Jacobian_j[iVar][jVar] -= 0.5*Proj_ModJac_Tensor_ij*Area;
}
}
}
}
void CUpwAUSM_Flow::ComputeResidual(double *val_residual, double **val_Jacobian_i, double **val_Jacobian_j, CConfig *config) {
/*--- Face area (norm or the normal vector) ---*/
Area = 0.0;
for (iDim = 0; iDim < nDim; iDim++)
Area += Normal[iDim]*Normal[iDim];
Area = sqrt(Area);
/*-- Unit Normal ---*/
for (iDim = 0; iDim < nDim; iDim++)
UnitNormal[iDim] = Normal[iDim]/Area;
/*--- Primitive variables at point i ---*/
sq_vel = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
Velocity_i[iDim] = V_i[iDim+1];
sq_vel += Velocity_i[iDim]*Velocity_i[iDim];
}
Pressure_i = V_i[nDim+1];
Density_i = V_i[nDim+2];
Enthalpy_i = V_i[nDim+3];
Energy_i = Enthalpy_i - Pressure_i/Density_i;
SoundSpeed_i = sqrt(Gamma*Gamma_Minus_One*(Energy_i-0.5*sq_vel));
/*--- Primitive variables at point j ---*/
sq_vel = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
Velocity_j[iDim] = V_j[iDim+1];
sq_vel += Velocity_j[iDim]*Velocity_j[iDim];
}
Pressure_j = V_j[nDim+1];
Density_j = V_j[nDim+2];
Enthalpy_j = V_j[nDim+3];
Energy_j = Enthalpy_j - Pressure_j/Density_j;
SoundSpeed_j = sqrt(Gamma*Gamma_Minus_One*(Energy_j-0.5*sq_vel));
/*--- Projected velocities ---*/
ProjVelocity_i = 0.0; ProjVelocity_j = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
ProjVelocity_i += Velocity_i[iDim]*UnitNormal[iDim];
ProjVelocity_j += Velocity_j[iDim]*UnitNormal[iDim];
}
mL = ProjVelocity_i/SoundSpeed_i;
mR = ProjVelocity_j/SoundSpeed_j;
if (fabs(mL) <= 1.0) mLP = 0.25*(mL+1.0)*(mL+1.0);
else mLP = 0.5*(mL+fabs(mL));
if (fabs(mR) <= 1.0) mRM = -0.25*(mR-1.0)*(mR-1.0);
else mRM = 0.5*(mR-fabs(mR));
mF = mLP + mRM;
if (fabs(mL) <= 1.0) pLP = 0.25*Pressure_i*(mL+1.0)*(mL+1.0)*(2.0-mL);
else pLP = 0.5*Pressure_i*(mL+fabs(mL))/mL;
if (fabs(mR) <= 1.0) pRM = 0.25*Pressure_j*(mR-1.0)*(mR-1.0)*(2.0+mR);
else pRM = 0.5*Pressure_j*(mR-fabs(mR))/mR;
pF = pLP + pRM;
Phi = fabs(mF);
val_residual[0] = 0.5*(mF*((Density_i*SoundSpeed_i)+(Density_j*SoundSpeed_j))-Phi*((Density_j*SoundSpeed_j)-(Density_i*SoundSpeed_i)));
for (iDim = 0; iDim < nDim; iDim++)
val_residual[iDim+1] = 0.5*(mF*((Density_i*SoundSpeed_i*Velocity_i[iDim])+(Density_j*SoundSpeed_j*Velocity_j[iDim]))
-Phi*((Density_j*SoundSpeed_j*Velocity_j[iDim])-(Density_i*SoundSpeed_i*Velocity_i[iDim])))+UnitNormal[iDim]*pF;
val_residual[nVar-1] = 0.5*(mF*((Density_i*SoundSpeed_i*Enthalpy_i)+(Density_j*SoundSpeed_j*Enthalpy_j))-Phi*((Density_j*SoundSpeed_j*Enthalpy_j)-(Density_i*SoundSpeed_i*Enthalpy_i)));
for (iVar = 0; iVar < nVar; iVar++)
val_residual[iVar] *= Area;
/*--- Roe's Jacobian for AUSM (this must be fixed) ---*/
if (implicit) {
/*--- Promediate Roe variables iPoint and jPoint ---*/
R = sqrt(Density_j/Density_i);
RoeDensity = R*Density_i;
sq_vel = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
RoeVelocity[iDim] = (R*Velocity_j[iDim]+Velocity_i[iDim])/(R+1);
sq_vel += RoeVelocity[iDim]*RoeVelocity[iDim];
}
RoeEnthalpy = (R*Enthalpy_j+Enthalpy_i)/(R+1);
RoeSoundSpeed = sqrt((Gamma-1)*(RoeEnthalpy-0.5*sq_vel));
/*--- Compute P and Lambda (do it with the Normal) ---*/
GetPMatrix(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, P_Tensor);
ProjVelocity = 0.0; ProjVelocity_i = 0.0; ProjVelocity_j = 0.0;
for (iDim = 0; iDim < nDim; iDim++) {
ProjVelocity += RoeVelocity[iDim]*UnitNormal[iDim];
ProjVelocity_i += Velocity_i[iDim]*UnitNormal[iDim];
ProjVelocity_j += Velocity_j[iDim]*UnitNormal[iDim];
}
/*--- Flow eigenvalues and Entropy correctors ---*/
for (iDim = 0; iDim < nDim; iDim++)
Lambda[iDim] = ProjVelocity;
Lambda[nVar-2] = ProjVelocity + RoeSoundSpeed;
Lambda[nVar-1] = ProjVelocity - RoeSoundSpeed;
/*--- Compute inverse P ---*/
GetPMatrix_inv(&RoeDensity, RoeVelocity, &RoeSoundSpeed, UnitNormal, invP_Tensor);
/*--- Jacobias of the inviscid flux, scale = 0.5 because val_residual ~ 0.5*(fc_i+fc_j)*Normal ---*/
GetInviscidProjJac(Velocity_i, &Energy_i, Normal, 0.5, val_Jacobian_i);
GetInviscidProjJac(Velocity_j, &Energy_j, Normal, 0.5, val_Jacobian_j);
/*--- Roe's Flux approximation ---*/
for (iVar = 0; iVar < nVar; iVar++) {
for (jVar = 0; jVar < nVar; jVar++) {
Proj_ModJac_Tensor_ij = 0.0;
/*--- Compute |Proj_ModJac_Tensor| = P x |Lambda| x inverse P ---*/
for (kVar = 0; kVar < nVar; kVar++)
Proj_ModJac_Tensor_ij += P_Tensor[iVar][kVar]*fabs(Lambda[kVar])*invP_Tensor[kVar][jVar];
val_Jacobian_i[iVar][jVar] += 0.5*Proj_ModJac_Tensor_ij*Area;
val_Jacobian_j[iVar][jVar] -= 0.5*Proj_ModJac_Tensor_ij*Area;
}
}
}
}
