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prometeo_rhs.inl
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// Copyright (c) "2019, by Stanford University
// Developer: Mario Di Renzo
// Affiliation: Center for Turbulence Research, Stanford University
// URL: https://ctr.stanford.edu
// Citation: Di Renzo, M., Lin, F., and Urzay, J. (2020).
// HTR solver: An open-source exascale-oriented task-based
// multi-GPU high-order code for hypersonic aerothermodynamics.
// Computer Physics Communications 255, 107262"
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
// DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY
// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
// ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include "prometeo_metric.inl"
#ifndef __CUDACC__
using std::max;
using std::min;
#endif
//-----------------------------------------------------------------------------
// INLINE FUNCTIONS FOR UpdateUsingEulerFluxUtils
//-----------------------------------------------------------------------------
template<direction dir>
__CUDA_H__
void UpdateUsingEulerFluxUtils<dir>::ComputeKGSums(double * Sums,
const AccessorRO<VecNEq, 3> &Conserved,
const AccessorRO<double, 3> &rho,
const AccessorRO<VecNSp, 3> &MassFracs,
const AccessorRO< Vec3, 3> &velocity,
const AccessorRO<double, 3> &pressure,
const Point<3> &p,
const int nType,
const coord_t dsize,
const Rect<3> &bounds) {
// Index of normal direction
constexpr int iN = normalIndex(dir);
const double H = (Conserved[p][irE] + pressure[p])/rho[p];
for (int l=0; l < KennedyNSum[nType]; l++) {
// offset point
const Point<3> pp = warpPeriodic<dir, Plus>(bounds, p, dsize, l+1);
const int off_l = l*(nEq+1);
// compute the summations
const double rhom = rho[p] + rho[pp];
const double vm = -(velocity[p][iN] + velocity[pp][iN]);
__UNROLL__
for (int i=0; i<nSpec; i++)
Sums[off_l+i] = rhom*vm*(MassFracs[p][i] + MassFracs[pp][i]);
__UNROLL__
for (int i=0; i<3; i++)
Sums[off_l+irU+i] = rhom*vm*(velocity[p][i] + velocity[pp][i]);
Sums[off_l+irE] = rhom*vm*(H + (Conserved[pp][irE] + pressure[pp])/rho[pp]);
Sums[off_l+nEq] = (pressure[p] + pressure[pp]);
}
}
template<direction dir>
__CUDA_H__
void UpdateUsingEulerFluxUtils<dir>::KGFluxReconstruction(VecNEq &Flux,
const double *Sums,
const AccessorRO<VecNEq, 3> &Conserved,
const AccessorRO< Vec3, 3> &velocity,
const AccessorRO<double, 3> &pressure,
const Point<3> &p,
const int nType,
const coord_t dsize,
const Rect<3> &bounds) {
// Index of normal direction
constexpr int iN = normalIndex(dir);
if (nType == L_S_node) {
// This is a staggered node
__UNROLL__
for (int i=0; i<nEq; i++)
Flux[i] = -(Conserved[p][i]*velocity[p][iN]);
Flux[irU+iN] -= pressure[p];
Flux[irE ] -= pressure[p]*velocity[p][iN];
}
else if (nType == Rm1_S_node) {
// This is a staggered node
const Point<3> pp = warpPeriodic<dir, Plus >(bounds, p, dsize, offP1(nType));
__UNROLL__
for (int i=0; i<nEq; i++)
Flux[i] = -(Conserved[pp][i]*velocity[pp][iN]);
Flux[irU+iN] -= pressure[pp];
Flux[irE ] -= pressure[pp]*velocity[pp][iN];
}
else {
double f[nEq+1];
double acc[nEq+1];
const double * Coeff = KennedyCoeff[nType];
__UNROLL__
for (int i=0; i<nEq+1; i++) f[i] = 0.0;
for (int l=0; l<KennedyOrder[nType]; l++) {
__UNROLL__
for (int i = 0; i < nEq+1; i++) acc[i] = 0.0;
for (int m = 0; m < l+1; m++) {
// Sums sums is a vector of 6(nEq+1) elements rappresenting
// a 3*3 triangular matrix whose indices are l and m
const int off = (nEq+1)*((5-m)*m/2 + l);
for (int i = 0; i < nEq+1; i++)
acc[i] += Sums[off + i];
}
__UNROLL__
for (int i=0; i<nEq+1; i++) f[i] += Coeff[l]*acc[i];
}
for (int i=0; i<nEq; i++) Flux[i] = 0.25*f[i];
// add pressure contribution to normal momentum equation
Flux[irU+iN] -= f[nEq];
}
}
template<direction dir>
__CUDA_H__
void UpdateUsingEulerFluxUtils<dir>::KGFluxReconstruction(VecNEq &Flux,
const AccessorRO<VecNEq, 3> &Conserved,
const AccessorRO<double, 3> &rho,
const AccessorRO<VecNSp, 3> &MassFracs,
const AccessorRO< Vec3, 3> &velocity,
const AccessorRO<double, 3> &pressure,
const Point<3> &p,
const int nType,
const coord_t dsize,
const Rect<3> &bounds) {
// Index of normal direction
constexpr int iN = normalIndex(dir);
// Compute points of the stencil
const Point<3> pM2 = warpPeriodic<dir, Minus>(bounds, p, dsize, offM2(nType));
const Point<3> pM1 = warpPeriodic<dir, Minus>(bounds, p, dsize, offM1(nType));
const Point<3> pP1 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP1(nType));
const Point<3> pP2 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP2(nType));
const Point<3> pP3 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP3(nType));
// Define common arrays
const double rhov[] = {rho[pM2], rho[pM1], rho[p ],
rho[pP1], rho[pP2], rho[pP3]};
// Put a minus here remembering that flux are on the RHS
const double vNorm[] = {-velocity[pM2][iN], -velocity[pM1][iN], -velocity[p ][iN],
-velocity[pP1][iN], -velocity[pP2][iN], -velocity[pP3][iN]};
// Species fluxes
__UNROLL__
for (int i=0; i<nSpec; i++) {
const double phi[] = {MassFracs[pM2][i], MassFracs[pM1][i], MassFracs[p ][i],
MassFracs[pP1][i], MassFracs[pP2][i], MassFracs[pP3][i]};
Flux[i] = KennedyReconstruct(rhov, vNorm, phi, nType);
}
// Momentum fluxes
__UNROLL__
for (int i=0; i<3; i++) {
const double phi[] = {velocity[pM2][i], velocity[pM1][i], velocity[p ][i],
velocity[pP1][i], velocity[pP2][i], velocity[pP3][i]};
Flux[irU+i] = KennedyReconstruct(rhov, vNorm, phi, nType);
}
{
const double phi[] ={pressure[pM2], pressure[pM1], pressure[p ],
pressure[pP1], pressure[pP2], pressure[pP3]};
Flux[irU+iN] -= KennedyReconstruct(phi, nType);
}
// Energy flux
{
const double phi[] = {(Conserved[pM2][irE] + pressure[pM2])/rho[pM2],
(Conserved[pM1][irE] + pressure[pM1])/rho[pM1],
(Conserved[p ][irE] + pressure[p ])/rho[p ],
(Conserved[pP1][irE] + pressure[pP1])/rho[pP1],
(Conserved[pP2][irE] + pressure[pP2])/rho[pP2],
(Conserved[pP3][irE] + pressure[pP3])/rho[pP3]};
Flux[irE] = KennedyReconstruct(rhov, vNorm, phi, nType);
}
}
template<direction dir>
__CUDA_H__
void UpdateUsingEulerFluxUtils<dir>::ComputeRoeAverages(
RoeAveragesStruct &avgs, const Mix &mix,
const VecNEq &ConservedL, const VecNEq &ConservedR,
const VecNSp &YiL, const VecNSp &YiR,
const double pressureL, const double pressureR,
const Vec3 &velocityL, const Vec3 &velocityR,
const double rhoL, const double rhoR) {
// Compute quantities on the left (L) and right (R) states
const double InternalEnergyL = ConservedL[irE]/rhoL - 0.5*velocityL.mod2();
const double InternalEnergyR = ConservedR[irE]/rhoR - 0.5*velocityR.mod2();
const double TotalEnthalpyL = (ConservedL[irE] + pressureL)/rhoL;
const double TotalEnthalpyR = (ConservedR[irE] + pressureR)/rhoR;
// Compute Roe averaged state...
const double RoeFactorL = sqrt(rhoL)/(sqrt(rhoL) + sqrt(rhoR));
const double RoeFactorR = sqrt(rhoR)/(sqrt(rhoL) + sqrt(rhoR));
// ... density...
avgs.rho = sqrt(rhoL*rhoR);
// ... mass fractions...
__UNROLL__
for (int i=0; i<nSpec; i++)
avgs.Yi[i] = YiL[i]*RoeFactorL + YiR[i]*RoeFactorR;
// .. velocity ...
__UNROLL__
for (int i=0; i<3; i++)
avgs.velocity[i] = velocityL[i]*RoeFactorL + velocityR[i]*RoeFactorR;
// Total enthalpy
avgs.H = TotalEnthalpyL*RoeFactorL + TotalEnthalpyR*RoeFactorR;
// Internal energy
avgs.e = InternalEnergyL*RoeFactorL + InternalEnergyR*RoeFactorR;
// Compute pressure derivatives based on the averaged state
const double PovRhoRoe = avgs.H - avgs.e - 0.5*avgs.velocity.mod2();
const double MixWRoe = mix.GetMolarWeightFromYi(avgs.Yi);
const double TRoe_eos = mix.GetTFromRhoAndP(avgs.rho, MixWRoe, PovRhoRoe*avgs.rho);
const double TRoe = mix.GetTFromInternalEnergy(avgs.e, TRoe_eos, avgs.Yi);
const double gammaRoe = mix.GetGamma(TRoe, MixWRoe, avgs.Yi);
avgs.dpde = mix.Getdpde(avgs.rho, gammaRoe);
mix.Getdpdrhoi(avgs.dpdrhoi, gammaRoe, TRoe, avgs.Yi);
// correct the pressure derivatives in order to satisfy the pressure jump condition
// using the procedure in Shuen, Liou and Leer (1990)
const double dp = pressureR - pressureL;
const double de = InternalEnergyR - InternalEnergyL;
VecNSp drhoi;
__UNROLL__
for (int i=0; i<nSpec; i++)
drhoi[i] = rhoR*YiR[i] - rhoL*YiL[i];
// find the error in the pressure jump due to Roe averages
double dpError = dp - de*avgs.dpde;
double fact = de*avgs.dpde; fact *= fact;
__UNROLL__
for (int i=0; i<nSpec; i++) {
const double dpi = drhoi[i]*avgs.dpdrhoi[i];
dpError -= dpi;
fact += dpi*dpi;
}
// correct pressure derivatives
// this threshold should not be affect the solution since fact is zero when all the jumps are zero
fact = dpError/max(fact, 1e-6);
__UNROLL__
for (int i=0; i<nSpec; i++)
avgs.dpdrhoi[i] = avgs.dpdrhoi[i]*(1.0 + avgs.dpdrhoi[i]*drhoi[i]*fact);
avgs.dpde = avgs.dpde*(1.0 + avgs.dpde*de*fact);
// compute the Roe averaged speed of sound
avgs.a2 = PovRhoRoe/avgs.rho*avgs.dpde;
__UNROLL__
for (int i=0; i<nSpec; i++)
avgs.a2 += avgs.Yi[i]*avgs.dpdrhoi[i];
avgs.a = sqrt(avgs.a2);
}
template<direction dir>
__CUDA_H__
inline void UpdateUsingEulerFluxUtils<dir>::computeLeftEigenvectors(MyMatrix<double, nEq, nEq> &L, const RoeAveragesStruct &avgs) {
constexpr int iN = normalIndex(dir);
constexpr int iT1 = tangential1Index(dir);
constexpr int iT2 = tangential2Index(dir);
// initialize L
L.init(0);
// Compute constants
const double iaRoe = 1.0/avgs.a;
const double iaRoe2 = 1.0/avgs.a2;
const double Coeff = (avgs.e - 0.5*avgs.velocity.mod2())*avgs.dpde/avgs.rho;
double b[nSpec];
__UNROLL__
for (int i=0; i<nSpec; i++)
b[i] = (Coeff - avgs.dpdrhoi[i])*iaRoe2;
const double d = avgs.dpde/(avgs.rho*avgs.a2);
const Vec3 c(avgs.velocity*d);
// First row
{
__UNROLL__
for (int j=0; j<nSpec; j++)
L(0, j) = -0.5*(b[j] - avgs.velocity[iN]*iaRoe);
__UNROLL__
for (int j=0; j<3; j++)
L(0, nSpec+j ) = -0.5*c[j];
L(0, nSpec+iN) -= 0.5*iaRoe;
L(0, nSpec+3 ) = 0.5*d;
}
// From 1 to nSpec
__UNROLL__
for (int i=1; i<nSpec+1; i++) {
__UNROLL__
for (int j=0; j<nSpec; j++)
L(i, j) = avgs.Yi[i-1]*b[j];
L(i, i-1) += 1.0;
__UNROLL__
for (int j=0; j<3; j++)
L(i, nSpec+j) = avgs.Yi[i-1]*c[j];
L(i, nSpec+3) = -avgs.Yi[i-1]*d;
}
// nSpec + 1
{
const int row = (nSpec+1);
__UNROLL__
for (int j=0; j<nSpec; j++)
L(row, j) = - avgs.velocity[iT1];
// L(row, nSpec+iN) = 0.0;
L(row, nSpec+iT1) = 1.0;
//L(row, nSpec+iT2) = 0.0;
//L(row, nSpec+ 3) = 0.0;
}
// nSpec + 2
{
const int row = (nSpec+2);
__UNROLL__
for (int j=0; j<nSpec; j++)
L(row, j) = - avgs.velocity[iT2];
//L(row, nSpec+iN ) = 0.0;
//L(row, nSpec+iT1) = 0.0;
L(row, nSpec+iT2) = 1.0;
//L(row, nSpec+ 3) = 0.0;
}
// nSpec+3
{
const int row = (nSpec+3);
__UNROLL__
for (int j=0; j<nSpec; j++)
// (nEq-1)*nEq + j
L(row, j) = -0.5*(b[j] + avgs.velocity[iN]*iaRoe);
__UNROLL__
for (int j=0; j<3; j++)
L(row, nSpec+j) = -0.5*c[j];
L(row, nSpec+iN) += 0.5*iaRoe;
L(row, nSpec+3 ) = 0.5*d;
}
}
template<direction dir>
__CUDA_H__
inline void UpdateUsingEulerFluxUtils<dir>::computeRightEigenvectors(MyMatrix<double, nEq, nEq> &K, const RoeAveragesStruct &avgs) {
constexpr int iN = normalIndex(dir);
constexpr int iT1 = tangential1Index(dir);
constexpr int iT2 = tangential2Index(dir);
// initialize K
K.init(0);
// fill K
__UNROLL__
for (int i = 0; i<nSpec; i++) {
K(i, 0) = avgs.Yi[i];
K(i, i+1) = 1.0;
K(i, nSpec+3) = avgs.Yi[i];
}
{
const int row = (nSpec+iN);
K(row, 0) = avgs.velocity[iN] - avgs.a;
__UNROLL__
for (int i = 0; i<nSpec; i++)
K(row, i+1) = avgs.velocity[iN];
//K(row, nSpec+1) = 0.0;
//K(row, nSpec+2) = 0.0;
K(row, nSpec+3) = avgs.velocity[iN] + avgs.a;
}
{
const int row = (nSpec+iT1);
K(row, 0) = avgs.velocity[iT1];
__UNROLL__
for (int i = 0; i<nSpec; i++)
K(row, i+1) = avgs.velocity[iT1];
K(row, nSpec+1) = 1.0;
//K(row, nSpec+2) = 0.0;
K(row, nSpec+3) = avgs.velocity[iT1];
}
{
const int row = (nSpec+iT2);
K(row, 0) = avgs.velocity[iT2];
__UNROLL__
for (int i = 0; i<nSpec; i++)
K(row, i+1) = avgs.velocity[iT2];
//K(row, nSpec+1) = 0.0;
K(row, nSpec+2) = 1.0;
K(row, nSpec+3) = avgs.velocity[iT2];
}
{
const int row = (nSpec+3);
K(row, 0) = avgs.H - avgs.velocity[iN]*avgs.a;
const double dedp = 1.0/avgs.dpde;
const double ERoe = avgs.e + 0.5*avgs.velocity.mod2();
__UNROLL__
for (int i = 0; i<nSpec; i++)
K(row, i+1) = ERoe - avgs.rho*avgs.dpdrhoi[i]*dedp;
K(row, nSpec+1) = avgs.velocity[iT1];
K(row, nSpec+2) = avgs.velocity[iT2];
K(row, nSpec+3) = avgs.H + avgs.velocity[iN]*avgs.a;
}
}
// Projects the state vector q in the characteristic space from the physiscal space
template<direction dir>
__CUDA_H__
inline void UpdateUsingEulerFluxUtils<dir>::projectToCharacteristicSpace(VecNEq &r, const VecNEq &q, const RoeAveragesStruct &avgs) {
constexpr int iN = normalIndex(dir);
constexpr int iT1 = tangential1Index(dir);
constexpr int iT2 = tangential2Index(dir);
// Compute constants
const double iaRoe = 1.0/avgs.a;
const double iaRoe2 = 1.0/avgs.a2;
const double Coeff = (avgs.e - 0.5*avgs.velocity.mod2())*avgs.dpde/avgs.rho;
double sum1 = 0.0;
__UNROLL__
for (int i=0; i<nSpec; i++)
sum1 += (Coeff - avgs.dpdrhoi[i])*iaRoe2*q[i];
double sumQsp = 0.0;
__UNROLL__
for (int i=0; i<nSpec; i++)
sumQsp += q[i];
const double d = avgs.dpde/(avgs.rho*avgs.a2);
const Vec3 c(avgs.velocity*d);
// First row
{
r[0] = sumQsp*avgs.velocity[iN]*iaRoe - sum1;
r[0] -= (c[iN] + iaRoe)*q[nSpec+iN];
r[0] -= c[iT1]*q[nSpec+iT1];
r[0] -= c[iT2]*q[nSpec+iT2];
r[0] += d*q[nSpec+3];
r[0] *= 0.5;
}
// From 1 to nSpec
__UNROLL__
for (int i=1; i<nSpec+1; i++) {
r[i] = avgs.Yi[i-1]*sum1;
r[i] += q[i-1];
__UNROLL__
for (int j=0; j<3; j++)
r[i] += avgs.Yi[i-1]*c[j]*q[nSpec+j];
r[i] += -avgs.Yi[i-1]*d*q[nSpec+3];
}
// nSpec + 1
{
r[nSpec+1] = -avgs.velocity[iT1]*sumQsp;
//r[nSpec+1] += 0.0*q[nSpec+iN];
r[nSpec+1] += q[nSpec+iT1];
//r[nSpec+1] += 0.0*q[nSpec+iT2];
//r[nSpec+1] += 0.0*q[nSpec+3 ];
}
// nSpec + 2
{
r[nSpec+2] = -avgs.velocity[iT2]*sumQsp;
//r[nSpec+2] += 0.0*q[nSpec+iN ];
//r[nSpec+2] += 0.0*q[nSpec+iT1];
r[nSpec+2] += q[nSpec+iT2];
//r[nSpec+2] += 0.0*q[nSpec+3 ];
}
// nSpec + 3
{
r[nSpec+3] = -sumQsp*avgs.velocity[iN]*iaRoe - sum1;
r[nSpec+3] -= (c[iN] - iaRoe)*q[nSpec+iN];
r[nSpec+3] -= c[iT1]*q[nSpec+iT1];
r[nSpec+3] -= c[iT2]*q[nSpec+iT2];
r[nSpec+3] += d*q[nSpec+3 ];
r[nSpec+3] *= 0.5;
}
}
// Projects the state vector q from the characteristic space to the physiscal space
template<direction dir>
__CUDA_H__
inline void UpdateUsingEulerFluxUtils<dir>::projectFromCharacteristicSpace(VecNEq &r, const VecNEq &q, const RoeAveragesStruct &avgs) {
constexpr int iN = normalIndex(dir);
constexpr int iT1 = tangential1Index(dir);
constexpr int iT2 = tangential2Index(dir);
// initialize r
r.init(0);
// Compute constants
double sumQsp = 0.0;
__UNROLL__
for (int i=0; i<nSpec; i++)
sumQsp += q[i+1];
// First nSpec rows
__UNROLL__
for (int i = 0; i<nSpec; i++) {
r[i] += avgs.Yi[i]*q[0];
r[i] += q[i+1];
r[i] += avgs.Yi[i]*q[nSpec+3];
}
// nSpec+iN row
{
r[nSpec+iN] += (avgs.velocity[iN] - avgs.a)*q[0];
r[nSpec+iN] += avgs.velocity[iN]*sumQsp;
//r[nSpec+iN] += 0.0*q[nSpec+1];
//r[nSpec+iN] += 0.0*q[nSpec+2];
r[nSpec+iN] += (avgs.velocity[iN] + avgs.a)*q[nSpec+3];
}
// nSpec+iT1 row
{
r[nSpec+iT1] += avgs.velocity[iT1]*q[0];
r[nSpec+iT1] += avgs.velocity[iT1]*sumQsp;
r[nSpec+iT1] += q[nSpec+1];
//r[nSpec+iT1] += 0.0*q[nSpec+2];
r[nSpec+iT1] += avgs.velocity[iT1]*q[nSpec+3];
}
// nSpec+iT2 row
{
r[nSpec+iT2] += avgs.velocity[iT2]*q[0];
r[nSpec+iT2] += avgs.velocity[iT2]*sumQsp;
//r[nSpec+iT2] += 0.0*q[nSpec+1];
r[nSpec+iT2] += q[nSpec+2];
r[nSpec+iT2] += avgs.velocity[iT2]*q[nSpec+3];
}
// nSpec+3 row
{
r[nSpec+3] += (avgs.H - avgs.velocity[iN]*avgs.a)*q[0];
const double dedp = 1.0/avgs.dpde;
const double ERoe = avgs.e + 0.5*avgs.velocity.mod2();
__UNROLL__
for (int i = 0; i<nSpec; i++)
r[nSpec+3] += (ERoe - avgs.rho*avgs.dpdrhoi[i]*dedp)*q[i+1];
r[nSpec+3] += avgs.velocity[iT1]*q[nSpec+1];
r[nSpec+3] += avgs.velocity[iT2]*q[nSpec+2];
r[nSpec+3] += (avgs.H + avgs.velocity[iN]*avgs.a)*q[nSpec+3];
}
}
// Projects the state vector q from the characteristic space to the physiscal space for one species
template<direction dir>
__CUDA_H__
inline double UpdateUsingEulerFluxUtils<dir>::projectFromCharacteristicSpace(const int i, const VecNEq &q, const RoeAveragesStruct &avgs) {
double r = avgs.Yi[i]*q[0];
r += q[i+1];
r += avgs.Yi[i]*q[nSpec+3];
return r;
}
template<direction dir>
__CUDA_H__
void UpdateUsingEulerFluxUtils<dir>::getPlusMinusFlux(VecNEq &FluxP, VecNEq &FluxM,
const RoeAveragesStruct &avgs,
const VecNEq &Conserved,
const double velocity,
const double pressure,
const double Lam1,
const double Lam,
const double LamN) {
constexpr int iN = normalIndex(dir);
// Compute the Euler fluxes
VecNEq Flux;
__UNROLL__
for (int i=0; i<nEq; i++)
Flux[i] = Conserved[i]*velocity;
Flux[irU+iN] += pressure;
Flux[irE ] += pressure*velocity;
// Project in the characteristic space
VecNEq Q; projectToCharacteristicSpace(Q, Conserved, avgs);
VecNEq F; projectToCharacteristicSpace(F, Flux, avgs);
// Plus fluxes
FluxP[ 0] = F[ 0] + Lam1*Q[ 0];
__UNROLL__
for (int i=1; i < nEq-1; i++) FluxP[i] = F[i] + Lam*Q[i];
FluxP[nEq-1] = F[nEq-1] + LamN*Q[nEq-1];
// Minus fluxes
FluxM[ 0] = F[ 0] - Lam1*Q[ 0];
__UNROLL__
for (int i=1; i < nEq-1; i++) FluxM[i] = F[i] - Lam*Q[i];
FluxM[nEq-1] = F[nEq-1] - LamN*Q[nEq-1];
}
template<direction dir>
template<class Op>
__CUDA_H__
void UpdateUsingEulerFluxUtils<dir>::FluxReconstruction(VecNEq &Flux,
const AccessorRO<VecNEq, 3> &Conserved,
#if (nSpec > 1)
const AccessorRO<VecNEq, 3> &Conserved_old,
#endif
const AccessorRO<double, 3> &SoS,
const AccessorRO<double, 3> &rho,
const AccessorRO< Vec3, 3> &velocity,
const AccessorRO<double, 3> &pressure,
const AccessorRO<VecNSp, 3> &MassFracs,
const Point<3> &p,
const int nType,
#if (nSpec > 1)
const double RK_coeffs0,
const double RK_coeffs1,
const double lim_f,
#endif
const Mix &mix,
const coord_t dsize,
const Rect<3> &bounds) {
constexpr int iN = normalIndex(dir);
// Compute points of the stencil
const Point<3> pM2 = warpPeriodic<dir, Minus>(bounds, p, dsize, offM2(nType));
const Point<3> pM1 = warpPeriodic<dir, Minus>(bounds, p, dsize, offM1(nType));
const Point<3> pP1 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP1(nType));
const Point<3> pP2 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP2(nType));
const Point<3> pP3 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP3(nType));
// Compute maximum eigenvalues
const double Lam1 = max(max(max(max(max(
fabs(velocity[pM2][iN] - SoS[pM2]),
fabs(velocity[pM1][iN] - SoS[pM1])),
fabs(velocity[p ][iN] - SoS[p ])),
fabs(velocity[pP1][iN] - SoS[pP1])),
fabs(velocity[pP2][iN] - SoS[pP2])),
fabs(velocity[pP3][iN] - SoS[pP3]));
const double Lam = max(max(max(max(max(
fabs(velocity[pM2][iN]),
fabs(velocity[pM1][iN])),
fabs(velocity[p ][iN])),
fabs(velocity[pP1][iN])),
fabs(velocity[pP2][iN])),
fabs(velocity[pP3][iN]));
const double LamN = max(max(max(max(max(
fabs(velocity[pM2][iN] + SoS[pM2]),
fabs(velocity[pM1][iN] + SoS[pM1])),
fabs(velocity[p ][iN] + SoS[p ])),
fabs(velocity[pP1][iN] + SoS[pP1])),
fabs(velocity[pP2][iN] + SoS[pP2])),
fabs(velocity[pP3][iN] + SoS[pP3]));
// Compute the RoeAverages
RoeAveragesStruct RoeAvgs;
ComputeRoeAverages(RoeAvgs, mix,
Conserved[p], Conserved[pP1],
MassFracs[p], MassFracs[pP1],
pressure[p], pressure[pP1],
velocity[p], velocity[pP1],
rho[p], rho[pP1]);
// Compute +/- fluxes
VecNEq FluxPM2; VecNEq FluxMM2; getPlusMinusFlux(FluxPM2, FluxMM2, RoeAvgs, Conserved[pM2], velocity[pM2][iN], pressure[pM2], Lam1, Lam, LamN);
VecNEq FluxPM1; VecNEq FluxMM1; getPlusMinusFlux(FluxPM1, FluxMM1, RoeAvgs, Conserved[pM1], velocity[pM1][iN], pressure[pM1], Lam1, Lam, LamN);
VecNEq FluxP ; VecNEq FluxM ; getPlusMinusFlux(FluxP , FluxM , RoeAvgs, Conserved[p ], velocity[p ][iN], pressure[p ], Lam1, Lam, LamN);
VecNEq FluxPP1; VecNEq FluxMP1; getPlusMinusFlux(FluxPP1, FluxMP1, RoeAvgs, Conserved[pP1], velocity[pP1][iN], pressure[pP1], Lam1, Lam, LamN);
VecNEq FluxPP2; VecNEq FluxMP2; getPlusMinusFlux(FluxPP2, FluxMP2, RoeAvgs, Conserved[pP2], velocity[pP2][iN], pressure[pP2], Lam1, Lam, LamN);
VecNEq FluxPP3; VecNEq FluxMP3; getPlusMinusFlux(FluxPP3, FluxMP3, RoeAvgs, Conserved[pP3], velocity[pP3][iN], pressure[pP3], Lam1, Lam, LamN);
// Reconstruct Fluxes
VecNEq F;
for (int i=0; i<nEq; i++) {
const double FPlus = Op::reconstructPlus(FluxPM2[i], FluxPM1[i], FluxP [i],
FluxPP1[i], FluxPP2[i], FluxPP3[i], nType);
const double FMinus = Op::reconstructMinus(FluxMM2[i], FluxMM1[i], FluxM [i],
FluxMP1[i], FluxMP2[i], FluxMP3[i], nType);
F[i] = -0.5*(FPlus + FMinus);
}
// Go back to the physical space
projectFromCharacteristicSpace(Flux, F, RoeAvgs);
#if (nSpec > 1)
// Flux limiter (blend high order flux with first order)
// Do we need the limiter?
// lets allow slightly negative values before activating the limiter
constexpr double eps_l = -1e-8; // threshold for rho
bool limit = false;
for (int i=0; i<nSpec; i++) {
const double dRhoi = lim_f*Flux[i];
if (((RK_coeffs0*Conserved_old[p ][i] + RK_coeffs1*Conserved[p ][i] + dRhoi) < eps_l) or
((RK_coeffs0*Conserved_old[pP1][i] + RK_coeffs1*Conserved[pP1][i] - dRhoi) < eps_l))
limit = true;
}
if (limit) {
constexpr double eps = 1e-60; // threshold for rho
// We need the limiter
// Initialize the blending parameter to 1.0
double theta = 1.0;
// First-order flux in the characteristic space
F = -0.5*(FluxP + FluxMP1);
// Let's use FluxP to store the first-order reconstructed flux in physical space
projectFromCharacteristicSpace(FluxP, F, RoeAvgs);
for (int i=0; i<nSpec; i++) {
// These are the predicted increments
const double dRhoi = lim_f*Flux[i];
const double dRhoi_lo = lim_f*FluxP[i];
// Check p side
double theta_p = 1.0;
const double rhoi_p = RK_coeffs0*Conserved_old[p][i] + RK_coeffs1*Conserved[p][i];
const double rhoHO_p = rhoi_p + dRhoi;
if (rhoHO_p < eps) {
const double rhoLO = rhoi_p + dRhoi_lo;
theta_p = (fabs(rhoHO_p - rhoLO) > eps) ? max(0.0, (eps - rhoLO)/(rhoHO_p - rhoLO)) : 1.0;
}
// Check pP1 side
double theta_pp1 = 1.0;
const double rhoi_pp1 = RK_coeffs0*Conserved_old[pP1][i] + RK_coeffs1*Conserved[pP1][i];
const double rhoHO_pp1 = rhoi_pp1 - dRhoi;
if (rhoHO_pp1 < eps) {
const double rhoLO = rhoi_pp1 - dRhoi_lo;
theta_pp1 = (fabs(rhoHO_pp1 - rhoLO) > eps) ? max(0.0, (eps - rhoLO)/(rhoHO_pp1 - rhoLO)) : 1.0;
}
// Take the minimum blending parameter
theta = min(min(theta_p, theta_pp1), theta);
}
// Apply the limiter
Flux = Flux*theta + (1-theta)*FluxP;
}
#endif
}
//-----------------------------------------------------------------------------
// INLINE FUNCTIONS FOR UpdateUsingHybridEulerFluxTask
//-----------------------------------------------------------------------------
template<direction dir>
__CUDA_H__
void UpdateUsingHybridEulerFluxTask<dir>::updateRHSSpan(
double *KGSum,
const AccessorRW<VecNEq, 3> &Conserved_t,
const AccessorRO<double, 3> &m_e,
const AccessorRO< int, 3> &nType,
const AccessorRO< bool, 3> &shockSensor,
const AccessorRO<VecNEq, 3> &Conserved,
#if (nSpec > 1)
const AccessorRO<VecNEq, 3> &Conserved_old,
#endif
const AccessorRO<double, 3> &rho,
const AccessorRO<double, 3> &SoS,
const AccessorRO<VecNSp, 3> &MassFracs,
const AccessorRO< Vec3, 3> &velocity,
const AccessorRO<double, 3> &pressure,
#if (nSpec > 1)
const double RK_coeffs0,
const double RK_coeffs1,
const double deltaTime,
#endif
const coord_t firstIndex,
const coord_t lastIndex,
const int x,
const int y,
const int z,
const Rect<3> &Flux_bounds,
const Rect<3> &Fluid_bounds,
const Mix &mix) {
VecNEq FluxM; VecNEq FluxP;
const coord_t size = getSize<dir>(Fluid_bounds);
// Compute flux of first minus inter-cell location
{
const Point<3> p0 = GetPointInSpan<dir>(Flux_bounds, firstIndex, x, y, z);
const Point<3> p = warpPeriodic<dir, Minus>(Fluid_bounds, p0, size, offM1(nType[p0]));
const Point<3> pP1 = p0;
const Point<3> pM1 = warpPeriodic<dir, Minus>(Fluid_bounds, p, size, offM1(nType[p]));
const Point<3> pM2 = warpPeriodic<dir, Minus>(Fluid_bounds, p, size, offM2(nType[p]));
// Compute KG summations (... the order is fundamental)
UpdateUsingEulerFluxUtils<dir>::ComputeKGSums(&KGSum[3*(nEq+1)],
Conserved, rho, MassFracs,
velocity, pressure,
pM2, nType[p], size, Fluid_bounds);
UpdateUsingEulerFluxUtils<dir>::ComputeKGSums(&KGSum[2*(nEq+1)],
Conserved, rho, MassFracs,
velocity, pressure,
pM1, nType[p], size, Fluid_bounds);
UpdateUsingEulerFluxUtils<dir>::ComputeKGSums(&KGSum[0],
Conserved, rho, MassFracs,
velocity, pressure,
p, nType[p], size, Fluid_bounds);
if (shockSensor[pM1] &&
shockSensor[p ] &&
shockSensor[pP1])
// KG reconstruction
UpdateUsingEulerFluxUtils<dir>::KGFluxReconstruction(FluxM, KGSum,
Conserved, velocity, pressure,
p, nType[p], size, Fluid_bounds);
else
// TENO reconstruction
UpdateUsingEulerFluxUtils<dir>::template FluxReconstruction<TENO_Op<>>(
FluxM,
Conserved,
#if (nSpec > 1)
Conserved_old,
#endif
SoS, rho,
velocity, pressure, MassFracs,
p, nType[p],
#if (nSpec > 1)
RK_coeffs0, RK_coeffs1,
deltaTime*(m_e[p]+m_e[pP1]),
#endif
mix, size, Fluid_bounds);
}
// Loop across my section of the span
for (coord_t i = firstIndex; i < lastIndex; i++) {
const Point<3> p = GetPointInSpan<dir>(Flux_bounds, i, x, y, z);
const Point<3> pM1 = warpPeriodic<dir, Minus>(Fluid_bounds, p, size, offM1(nType[p]));
const Point<3> pP1 = warpPeriodic<dir, Plus >(Fluid_bounds, p, size, offP1(nType[p]));
// Shift and update KG summations
__UNROLL__
for (int l=0; l<nEq+1; l++) KGSum[5*(nEq+1) + l] = KGSum[4*(nEq+1) + l];
__UNROLL__
for (int l=0; l<nEq+1; l++) KGSum[4*(nEq+1) + l] = KGSum[2*(nEq+1) + l];
__UNROLL__
for (int l=0; l<nEq+1; l++) KGSum[3*(nEq+1) + l] = KGSum[1*(nEq+1) + l];
UpdateUsingEulerFluxUtils<dir>::ComputeKGSums(&KGSum[0],
Conserved, rho, MassFracs,
velocity, pressure,
p, nType[p], size, Fluid_bounds);
if (shockSensor[pM1] &&
shockSensor[p ] &&
shockSensor[pP1])
// KG reconstruction
UpdateUsingEulerFluxUtils<dir>::KGFluxReconstruction(FluxP, KGSum,
Conserved, velocity, pressure,
p, nType[p], size, Fluid_bounds);
else
// TENO reconstruction
UpdateUsingEulerFluxUtils<dir>::template FluxReconstruction<TENO_Op<>>(
FluxP,
Conserved,
#if (nSpec > 1)
Conserved_old,
#endif
SoS, rho,
velocity, pressure, MassFracs,
p, nType[p],
#if (nSpec > 1)
RK_coeffs0, RK_coeffs1,
deltaTime*(m_e[p]+m_e[pP1]),
#endif
mix, size, Fluid_bounds);
// Update time derivative
Conserved_t[p] += m_e[p]*(FluxP - FluxM);
// Store plus flux for next point
FluxM = FluxP;
}
}
//-----------------------------------------------------------------------------
// INLINE FUNCTIONS FOR UpdateUsingTENOEulerFluxTask
//-----------------------------------------------------------------------------
template<direction dir, class Op>
__CUDA_H__
void UpdateUsingTENOEulerFluxTask<dir, Op>::updateRHSSpan(
const AccessorRW<VecNEq, 3> &Conserved_t,
const AccessorRO<double, 3> &m_e,
const AccessorRO< int, 3> &nType,
const AccessorRO<VecNEq, 3> &Conserved,
#if (nSpec > 1)
const AccessorRO<VecNEq, 3> &Conserved_old,
#endif
const AccessorRO<double, 3> &rho,
const AccessorRO<double, 3> &SoS,
const AccessorRO<VecNSp, 3> &MassFracs,
const AccessorRO< Vec3, 3> &velocity,
const AccessorRO<double, 3> &pressure,
#if (nSpec > 1)
const double RK_coeffs0,
const double RK_coeffs1,
const double deltaTime,
#endif
const coord_t firstIndex,
const coord_t lastIndex,
const int x,
const int y,
const int z,
const Rect<3> &Flux_bounds,
const Rect<3> &Fluid_bounds,
const Mix &mix) {
VecNEq FluxM; VecNEq FluxP;
const coord_t size = getSize<dir>(Fluid_bounds);
// Compute flux of first minus inter-cell location
{
const Point<3> p = GetPointInSpan<dir>(Flux_bounds, firstIndex, x, y, z);
const Point<3> pm1 = warpPeriodic<dir, Minus>(Fluid_bounds, p, size, offM1(nType[p]));
UpdateUsingEulerFluxUtils<dir>::template FluxReconstruction<Op>(
FluxM,
Conserved,
#if (nSpec > 1)
Conserved_old,
#endif
SoS, rho,
velocity, pressure, MassFracs,
pm1, nType[pm1],
#if (nSpec > 1)
RK_coeffs0, RK_coeffs1,
deltaTime*(m_e[pm1]+m_e[p]),
#endif
mix, size, Fluid_bounds);
}
// Loop across my section of the span
for (coord_t i = firstIndex; i < lastIndex; i++) {
const Point<3> p = GetPointInSpan<dir>(Flux_bounds, i, x, y, z);
#if (nSpec > 1)
const Point<3> pP1 = warpPeriodic<dir, Plus >(Fluid_bounds, p, size, offP1(nType[p]));
#endif
// Update plus flux
UpdateUsingEulerFluxUtils<dir>::template FluxReconstruction<Op>(
FluxP,
Conserved,
#if (nSpec > 1)
Conserved_old,
#endif
SoS, rho,
velocity, pressure, MassFracs,
p, nType[p],
#if (nSpec > 1)
RK_coeffs0, RK_coeffs1,
deltaTime*(m_e[p]+m_e[pP1]),
#endif
mix, size, Fluid_bounds);
// Update time derivative
Conserved_t[p] += m_e[p]*(FluxP - FluxM);
// Store plus flux for next point
FluxM = FluxP;
}
};
//-----------------------------------------------------------------------------
// INLINE FUNCTIONS FOR UpdateUsingSkewSymmetricEulerFluxTask
//-----------------------------------------------------------------------------
template<direction dir>
__CUDA_H__
void UpdateUsingSkewSymmetricEulerFluxTask<dir>::updateRHSSpan(
double *KGSum,
const AccessorRW<VecNEq, 3> &Conserved_t,
const AccessorRO<double, 3> &m_e,
const AccessorRO< int, 3> &nType,
const AccessorRO<VecNEq, 3> &Conserved,
const AccessorRO<double, 3> &rho,
const AccessorRO<VecNSp, 3> &MassFracs,
const AccessorRO< Vec3, 3> &velocity,
const AccessorRO<double, 3> &pressure,
const coord_t firstIndex,
const coord_t lastIndex,
const int x,
const int y,
const int z,
const Rect<3> &Flux_bounds,
const Rect<3> &Fluid_bounds) {
VecNEq FluxM; VecNEq FluxP;
const coord_t size = getSize<dir>(Fluid_bounds);