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prometeo_metric.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_coeffs.h"
#include "my_array.hpp"
#include "PointDomain_helper.hpp"
#include <math.h>
#ifndef __CUDA_H__
#ifdef __CUDACC__
#define __CUDA_H__ __device__
#else
#define __CUDA_H__
#endif
#endif
#ifndef __UNROLL__
#ifdef __CUDACC__
#define __UNROLL__ #pragma unroll
#else
#define __UNROLL__
#endif
#endif
#ifndef __CUDACC__
using std::min;
using std::max;
#endif
//-----------------------------------------------------------------------------
// Utility to compute powers of 10 at compile time
//-----------------------------------------------------------------------------
inline constexpr double my_10_pow(const int n){
return n > 0 ? 1.0e1 *my_10_pow(n-1) :
n < 0 ? 1.0e-1*my_10_pow(n+1) :
1;
}
//-----------------------------------------------------------------------------
// Stencil offset helper functions
//-----------------------------------------------------------------------------
__CUDA_H__
inline int8_t offM2(const int t) { return Cp[t][0]; };
__CUDA_H__
inline int8_t offM1(const int t) { return Cp[t][1]; };
__CUDA_H__
inline int8_t offP1(const int t) { return Cp[t][2]; };
__CUDA_H__
inline int8_t offP2(const int t) { return Cp[t][3]; };
__CUDA_H__
inline int8_t offP3(const int t) { return Cp[t][4]; };
//-----------------------------------------------------------------------------
// Interpolation operator
//-----------------------------------------------------------------------------
__CUDA_H__
inline double Interp2Staggered(const int t, const double x1, const double x2) { return Interp[t][0]*(x1) + Interp[t][1]*(x2); };
//-----------------------------------------------------------------------------
// Spatial derivative operator
//-----------------------------------------------------------------------------
__CUDA_H__
inline double getDeriv(const int t, const double xm1, const double x, const double xp1, const double m) {
return (Grad[t][0]*(x- xm1) + Grad[t][1]*(xp1 - x))*m;
};
__CUDA_H__
inline double getDerivLeftBC(const int t, const double x, const double xp1, const double m) {
return (Grad[t][1]*(xp1 - x))*m;
};
__CUDA_H__
inline double getDerivRightBC(const int t, const double xm1, const double x, const double m) {
return (Grad[t][0]*(x- xm1))*m;
};
template<direction dir>
__CUDA_H__
inline double getDeriv(const AccessorRO<double, 3> &q,
const Point<3> &p,
const int nType,
const double m,
const Rect<3> &bounds) {
// Compute stencil points
const coord_t dsize = getSize<dir>(bounds);
const Point<3> pM1 = warpPeriodic<dir, Minus>(bounds, p, dsize, offM1(nType));
const Point<3> pP1 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP1(nType));
return getDeriv(nType, q[pM1], q[p], q[pP1], m);
};
template<direction dir, typename T, int SIZE>
__CUDA_H__
inline MyArray<T, SIZE> getDeriv(const AccessorRO<MyArray<T, SIZE>, 3> &q,
const Point<3> &p,
const int nType,
const double m,
const Rect<3> &bounds) {
// Compute stencil points
const coord_t dsize = getSize<dir>(bounds);
const Point<3> pM1 = warpPeriodic<dir, Minus>(bounds, p, dsize, offM1(nType));
const Point<3> pP1 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP1(nType));
MyArray<T, SIZE> d;
__UNROLL__
for (int i=0; i<SIZE; i++)
d[i] = getDeriv(nType, q[pM1][i], q[p][i], q[pP1][i], m);
return d;
};
template<direction dir, typename T, int SIZE>
__CUDA_H__
inline double getDeriv(const AccessorRO<MyArray<T, SIZE>, 3> &q,
const Point<3> &p,
const int i,
const int nType,
const double m,
const Rect<3> &bounds) {
// Compute stencil points
const coord_t dsize = getSize<dir>(bounds);
const Point<3> pM1 = warpPeriodic<dir, Minus>(bounds, p, dsize, offM1(nType));
const Point<3> pP1 = warpPeriodic<dir, Plus >(bounds, p, dsize, offP1(nType));
return getDeriv(nType, q[pM1][i], q[p][i], q[pP1][i], m);
};
__CUDA_H__
inline Vec3 getGrad(const AccessorRO<double, 3> &q,
const Point<3> &p,
const int nType_x,
const int nType_y,
const int nType_z,
const double m_x,
const double m_y,
const double m_z,
const Rect<3> &bounds) {
Vec3 grad;
grad[0] = getDeriv<Xdir>(q, p, nType_x, m_x, bounds);
grad[1] = getDeriv<Ydir>(q, p, nType_y, m_y, bounds);
grad[2] = getDeriv<Zdir>(q, p, nType_z, m_z, bounds);
return grad;
};
template<typename T, int SIZE>
__CUDA_H__
inline Vec3 getGrad(const AccessorRO<MyArray<T, SIZE>, 3> &q,
const Point<3> &p,
const int i,
const int nType_x,
const int nType_y,
const int nType_z,
const double m_x,
const double m_y,
const double m_z,
const Rect<3> &bounds) {
Vec3 grad;
grad[0] = getDeriv<Xdir>(q, p, i, nType_x, m_x, bounds);
grad[1] = getDeriv<Ydir>(q, p, i, nType_y, m_y, bounds);
grad[2] = getDeriv<Zdir>(q, p, i, nType_z, m_z, bounds);
return grad;
};
//-----------------------------------------------------------------------------
// Linear reconstruction operator
//-----------------------------------------------------------------------------
// TODO: this is extremely ineficient (do not use in the actual calculation)
// Linear reconstruction based on TENO
__CUDA_H__
inline double LinearReconstruct(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
// Load coefficients
const double *Coeffs = Coeffs_Plus[nType];
const double *Recon = Recon_Plus[nType];
if (nType == R_C_node) return 0.0;
else if ((nType == L_C_node) || (nType == Rm1_C_node)) return 0.5*y + 0.5*yp1;
else
return ym2*(Recon[6*Stencil1+0]*Coeffs[Stencil1] + Recon[6*Stencil2+0]*Coeffs[Stencil2] + Recon[6*Stencil3+0]*Coeffs[Stencil3] + Recon[6*Stencil4+0]*Coeffs[Stencil4]) +
ym1*(Recon[6*Stencil1+1]*Coeffs[Stencil1] + Recon[6*Stencil2+1]*Coeffs[Stencil2] + Recon[6*Stencil3+1]*Coeffs[Stencil3] + Recon[6*Stencil4+1]*Coeffs[Stencil4]) +
y *(Recon[6*Stencil1+2]*Coeffs[Stencil1] + Recon[6*Stencil2+2]*Coeffs[Stencil2] + Recon[6*Stencil3+2]*Coeffs[Stencil3] + Recon[6*Stencil4+2]*Coeffs[Stencil4]) +
yp1*(Recon[6*Stencil1+3]*Coeffs[Stencil1] + Recon[6*Stencil2+3]*Coeffs[Stencil2] + Recon[6*Stencil3+3]*Coeffs[Stencil3] + Recon[6*Stencil4+3]*Coeffs[Stencil4]) +
yp2*(Recon[6*Stencil1+4]*Coeffs[Stencil1] + Recon[6*Stencil2+4]*Coeffs[Stencil2] + Recon[6*Stencil3+4]*Coeffs[Stencil3] + Recon[6*Stencil4+4]*Coeffs[Stencil4]) +
yp3*(Recon[6*Stencil1+5]*Coeffs[Stencil1] + Recon[6*Stencil2+5]*Coeffs[Stencil2] + Recon[6*Stencil3+5]*Coeffs[Stencil3] + Recon[6*Stencil4+5]*Coeffs[Stencil4]);
}
//-----------------------------------------------------------------------------
// Kennedy Gruber reconstruction operator
//-----------------------------------------------------------------------------
// See Eq. 16 of Pirozzoli JCP (2010)
__CUDA_H__
inline double KennedyReconstruct(const double *rho, const double *u, const double *phi, const int nType) {
double flux;
if (nType == L_S_node)
// This is a staggered node
flux = rho[2]*u[2]*phi[2];
else if (nType == Rm1_S_node)
// This is a staggered node
flux = rho[3]*u[3]*phi[3];
else {
flux = 0.0;
const double * Coeff = KennedyCoeff[nType];
__UNROLL__
for (int l = 0; l < KennedyOrder[nType]; l++) {
const int lp = l+1;
double acc = 0.0;
__UNROLL__
for (int m = 0; m < lp; m++)
acc += ((rho[2-m] + rho[2-m+lp])*
( u[2-m] + u[2-m+lp])*
(phi[2-m] + phi[2-m+lp]));
flux += Coeff[l]*acc;
}
flux *= 0.25;
}
return flux;
}
__CUDA_H__
inline double KennedyReconstruct(const double *u, const double *phi, const int nType) {
double flux;
if (nType == L_S_node)
// This is a staggered node
flux = u[2]*phi[2];
else if (nType == Rm1_S_node)
// This is a staggered node
flux = u[3]*phi[3];
else {
flux = 0.0;
const double * Coeff = KennedyCoeff[nType];
__UNROLL__
for (int l = 0; l < KennedyOrder[nType]; l++) {
const int lp = l+1;
double acc = 0.0;
__UNROLL__
for (int m = 0; m < lp; m++)
acc += (( u[2-m] + u[2-m+lp])*
(phi[2-m] + phi[2-m+lp]));
flux += Coeff[l]*acc;
}
flux *= 0.5;
}
return flux;
}
__CUDA_H__
inline double KennedyReconstruct(const double *phi, const int nType) {
double flux;
if (nType == L_S_node)
// This is a staggered node
flux = phi[2];
else if (nType == Rm1_S_node)
// This is a staggered node
flux = phi[3];
else {
flux = 0.0;
const double * Coeff = KennedyCoeff[nType];
__UNROLL__
for (int l = 0; l < KennedyOrder[nType]; l++) {
const int lp = l+1;
double acc = 0.0;
__UNROLL__
for (int m = 0; m < lp; m++)
acc += (phi[2-m] + phi[2-m+lp]);
flux += Coeff[l]*acc;
}
}
return flux;
}
//-----------------------------------------------------------------------------
// TENO sensors
//-----------------------------------------------------------------------------
class TENOsensor {
public:
__CUDA_H__
static inline bool TENO(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
if ((nType == L_S_node) or (nType == Rm1_S_node))
// Staggered nodes
return true;
else if (nType == L_C_node) {
// Ren sensor
const double var1 = yp1 - y;
const double var2 = yp2 - yp1;
const double eta = (fabs(2.0*var1*var2) + Ren_eps)/(var1*var1 + var2*var2 + Ren_eps);
return ((1.0 - min(1.0, Ren_irc*eta)) < 0.5);
}
else if (nType == Rm1_C_node) {
// Ren sensor
const double var1 = y - ym1;
const double var2 = yp1 - y;
const double eta = (fabs(2.0*var1*var2) + Ren_eps)/(var1*var1 + var2*var2 + Ren_eps);
return ((1.0 - min(1.0, Ren_irc*eta)) < 0.5);
}
else {
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (ym1 - 2*y + yp1); aux2 = ( ym1 - yp1); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (y - 2*yp1 + yp2); aux2 = (3*y - 4*yp1 + yp2); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (ym2 - 2*ym1 + y ); aux2 = (3*y - 4*ym1 + ym2); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*y + 18*yp1 - 9*yp2 + 2*yp3);
aux2 = ( 2*y - 5*yp1 + 4*yp2 - yp3);
aux3 = (- y + 3*yp1 - 3*yp2 + yp3);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
// We can do this as we know that the sensor is applied on density and density is always > 0
double eps = (ym2 + ym1 + y + yp1 + yp2 + yp3)/6;
eps *= eps*1e-4;
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
const double a1 = pow(1 + tau6/(s1 + eps), 6);
const double a2 = pow(1 + tau6/(s2 + eps), 6);
const double a3 = pow(1 + tau6/(s3 + eps), 6);
const double a4 = pow(1 + tau6/(s4 + eps), 6);
const double a = 1.0/(a1 + a2 + a3 + a4);
return ((a1*a > TENO_cut_off) and
(a2*a > TENO_cut_off) and
(a3*a > TENO_cut_off) and
(a4*a > TENO_cut_off));
}
};
__CUDA_H__
static inline bool TENOA(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType, const double Phi) {
if ((nType == L_S_node) or (nType == Rm1_S_node))
// Staggered nodes
return true;
else if (nType == L_C_node) {
// Ren sensor
const double var1 = yp1 - y;
const double var2 = yp2 - yp1;
const double eta = (fabs(2.0*var1*var2) + Ren_eps)/(var1*var1 + var2*var2 + Ren_eps);
return ((1.0 - min(1.0, Ren_irc*eta)) < 0.5);
}
else if (nType == Rm1_C_node) {
// Ren sensor
const double var1 = y - ym1;
const double var2 = yp1 - y;
const double eta = (fabs(2.0*var1*var2) + Ren_eps)/(var1*var1 + var2*var2 + Ren_eps);
return ((1.0 - min(1.0, Ren_irc*eta)) < 0.5);
}
else {
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (ym1 - 2*y + yp1); aux2 = ( ym1 - yp1); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (y - 2*yp1 + yp2); aux2 = (3*y - 4*yp1 + yp2); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (ym2 - 2*ym1 + y ); aux2 = (3*y - 4*ym1 + ym2); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*y + 18*yp1 - 9*yp2 + 2*yp3);
aux2 = ( 2*y - 5*yp1 + 4*yp2 - yp3);
aux3 = (- y + 3*yp1 - 3*yp2 + yp3);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
const double a1 = pow(1 + tau6/(s1 + eps), 6);
const double a2 = pow(1 + tau6/(s2 + eps), 6);
const double a3 = pow(1 + tau6/(s3 + eps), 6);
const double a4 = pow(1 + tau6/(s4 + eps), 6);
const double a = 1.0/(a1 + a2 + a3 + a4);
// Use TENO-A cutoff adaptation
const double decay = pow((1 - Phi), 12) * (1 + 12*Phi);
const int power = min(max(int(floor(Smooth_pow - Diff_pow*(1 - decay))), 0), 13);
const float cut_off = p10[power];
return ((a1*a > cut_off) and
(a2*a > cut_off) and
(a3*a > cut_off) and
(a4*a > cut_off));
}
};
private:
// Ren sensor coefficients
static constexpr double Ren_r_c = 0.2;
static constexpr double Ren_eps = 0.9*Ren_r_c*1e-6/(1.0 - 0.9*Ren_r_c);
static constexpr double Ren_irc = 1.0/Ren_r_c;
// Constants for TENO cut-off
static constexpr double TENO_cut_off = 1e-6;
static constexpr double Smooth_pow = 12.5;
static constexpr double Shock_pow = 1.0;
static constexpr double Diff_pow = Smooth_pow - Shock_pow;
// Small number
static constexpr double eps = 1e-8;
// JS coefficients
static constexpr double C13 = 13.0/12.0;
static constexpr double C23 = 3.0/12.0;
static constexpr double C14 = 1.0/36.0;
static constexpr double C24 = 13.0/12.0;
static constexpr double C34 = 781.0/720.0;
};
//-----------------------------------------------------------------------------
// TENO reconstruction operators
//-----------------------------------------------------------------------------
template<int exp = -10>
class TENO_Op {
public:
__CUDA_H__
static inline double reconstructPlus(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
// Load coefficients
const double *Coeffs = Coeffs_Plus[nType];
const double *Recon = Recon_Plus[nType];
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (ym1 - 2*y + yp1); aux2 = ( ym1 - yp1); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (y - 2*yp1 + yp2); aux2 = (3*y - 4*yp1 + yp2); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (ym2 - 2*ym1 + y ); aux2 = (3*y - 4*ym1 + ym2); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*y + 18*yp1 - 9*yp2 + 2*yp3);
aux2 = ( 2*y - 5*yp1 + 4*yp2 - yp3);
aux3 = (- y + 3*yp1 - 3*yp2 + yp3);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
// not recommend to rescale the small number
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
double a1 = pow(1 + tau6/(s1 + eps), 6);
double a2 = pow(1 + tau6/(s2 + eps), 6);
double a3 = pow(1 + tau6/(s3 + eps), 6);
double a4 = pow(1 + tau6/(s4 + eps), 6);
if (Coeffs[Stencil1] < 1e-10) a1 = 0.0;
if (Coeffs[Stencil2] < 1e-10) a2 = 0.0;
if (Coeffs[Stencil3] < 1e-10) a3 = 0.0;
if (Coeffs[Stencil4] < 1e-10) a4 = 0.0;
double a = 1.0/(a1 + a2 + a3 + a4);
const int b1 = (a1*a < cut_off) ? 0 : 1;
const int b2 = (a2*a < cut_off) ? 0 : 1;
const int b3 = (a3*a < cut_off) ? 0 : 1;
const int b4 = (a4*a < cut_off) ? 0 : 1;
const double Variation1 = ym2*Recon[6*Stencil1+0] +
ym1*Recon[6*Stencil1+1] +
y *Recon[6*Stencil1+2] +
yp1*Recon[6*Stencil1+3] +
yp2*Recon[6*Stencil1+4] +
yp3*Recon[6*Stencil1+5] - y;
const double Variation2 = ym2*Recon[6*Stencil2+0] +
ym1*Recon[6*Stencil2+1] +
y *Recon[6*Stencil2+2] +
yp1*Recon[6*Stencil2+3] +
yp2*Recon[6*Stencil2+4] +
yp3*Recon[6*Stencil2+5] - y;
const double Variation3 = ym2*Recon[6*Stencil3+0] +
ym1*Recon[6*Stencil3+1] +
y *Recon[6*Stencil3+2] +
yp1*Recon[6*Stencil3+3] +
yp2*Recon[6*Stencil3+4] +
yp3*Recon[6*Stencil3+5] - y;
const double Variation4 = ym2*Recon[6*Stencil4+0] +
ym1*Recon[6*Stencil4+1] +
y *Recon[6*Stencil4+2] +
yp1*Recon[6*Stencil4+3] +
yp2*Recon[6*Stencil4+4] +
yp3*Recon[6*Stencil4+5] - y;
// Assemble the operator
a1 = Coeffs[Stencil1]*b1;
a2 = Coeffs[Stencil2]*b2;
a3 = Coeffs[Stencil3]*b3;
a4 = Coeffs[Stencil4]*b4;
a = 1.0/(a1 + a2 + a3 + a4);
const double w1 = a1*a;
const double w2 = a2*a;
const double w3 = a3*a;
const double w4 = a4*a;
return y + w1*Variation1 + w2*Variation2 + w3*Variation3 + w4*Variation4;
}
__CUDA_H__
static inline double reconstructMinus(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
// Load coefficients
const double *Coeffs = Coeffs_Minus[nType];
const double *Recon = Recon_Minus[nType];
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (yp2 - 2*yp1 + y ); aux2 = ( yp2 - y ); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (yp1 - 2*y + ym1); aux2 = (3*yp1 - 4*y + ym1); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (yp3 - 2*yp2 + yp1); aux2 = (3*yp1 - 4*yp2 + yp3); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*yp1 + 18*y - 9*ym1 + 2*ym2);
aux2 = ( 2*yp1 - 5*y + 4*ym1 - ym2);
aux3 = (- yp1 + 3*y - 3*ym1 + ym2);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
// not recommend to rescale the small number
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
double a1 = pow(1 + tau6/(s1 + eps), 6);
double a2 = pow(1 + tau6/(s2 + eps), 6);
double a3 = pow(1 + tau6/(s3 + eps), 6);
double a4 = pow(1 + tau6/(s4 + eps), 6);
if (Coeffs[Stencil1] < 1e-10) a1 = 0.0;
if (Coeffs[Stencil2] < 1e-10) a2 = 0.0;
if (Coeffs[Stencil3] < 1e-10) a3 = 0.0;
if (Coeffs[Stencil4] < 1e-10) a4 = 0.0;
double a = 1.0/(a1 + a2 + a3 + a4);
const int b1 = (a1*a < cut_off) ? 0 : 1;
const int b2 = (a2*a < cut_off) ? 0 : 1;
const int b3 = (a3*a < cut_off) ? 0 : 1;
const int b4 = (a4*a < cut_off) ? 0 : 1;
const double Variation1 = ym2*Recon[6*Stencil1+0] +
ym1*Recon[6*Stencil1+1] +
y *Recon[6*Stencil1+2] +
yp1*Recon[6*Stencil1+3] +
yp2*Recon[6*Stencil1+4] +
yp3*Recon[6*Stencil1+5] - yp1;
const double Variation2 = ym2*Recon[6*Stencil2+0] +
ym1*Recon[6*Stencil2+1] +
y *Recon[6*Stencil2+2] +
yp1*Recon[6*Stencil2+3] +
yp2*Recon[6*Stencil2+4] +
yp3*Recon[6*Stencil2+5] - yp1;
const double Variation3 = ym2*Recon[6*Stencil3+0] +
ym1*Recon[6*Stencil3+1] +
y *Recon[6*Stencil3+2] +
yp1*Recon[6*Stencil3+3] +
yp2*Recon[6*Stencil3+4] +
yp3*Recon[6*Stencil3+5] - yp1;
const double Variation4 = ym2*Recon[6*Stencil4+0] +
ym1*Recon[6*Stencil4+1] +
y *Recon[6*Stencil4+2] +
yp1*Recon[6*Stencil4+3] +
yp2*Recon[6*Stencil4+4] +
yp3*Recon[6*Stencil4+5] - yp1;
// Assemble the operator
a1 = Coeffs[Stencil1]*b1;
a2 = Coeffs[Stencil2]*b2;
a3 = Coeffs[Stencil3]*b3;
a4 = Coeffs[Stencil4]*b4;
a = 1.0/(a1 + a2 + a3 + a4);
const double w1 = a1*a;
const double w2 = a2*a;
const double w3 = a3*a;
const double w4 = a4*a;
return yp1 + w1*Variation1 + w2*Variation2 + w3*Variation3 + w4*Variation4;
}
private:
// Constant TENO cut-off
static constexpr double cut_off = 1e-6;
// Small number
static constexpr double eps = my_10_pow(exp);
// JS coefficients
static constexpr double C13 = 13.0/12.0;
static constexpr double C23 = 3.0/12.0;
static constexpr double C14 = 1.0/36.0;
static constexpr double C24 = 13.0/12.0;
static constexpr double C34 = 781.0/720.0;
};
//-----------------------------------------------------------------------------
// TENO-A reconstruction operators
//-----------------------------------------------------------------------------
template<int exp = -8>
class TENOA_Op {
public:
__CUDA_H__
static inline double reconstructPlus(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
// Load coefficients
const double *Coeffs = Coeffs_Plus[nType];
const double *Recon = Recon_Plus[nType];
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (ym1 - 2*y + yp1); aux2 = ( ym1 - yp1); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (y - 2*yp1 + yp2); aux2 = (3*y - 4*yp1 + yp2); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (ym2 - 2*ym1 + y ); aux2 = (3*y - 4*ym1 + ym2); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*y + 18*yp1 - 9*yp2 + 2*yp3);
aux2 = ( 2*y - 5*yp1 + 4*yp2 - yp3);
aux3 = (- y + 3*yp1 - 3*yp2 + yp3);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
// not recommend to rescale the small number
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
double a1 = pow(1 + tau6/(s1 + eps), 6);
double a2 = pow(1 + tau6/(s2 + eps), 6);
double a3 = pow(1 + tau6/(s3 + eps), 6);
double a4 = pow(1 + tau6/(s4 + eps), 6);
float cut_off;
if (nType == Std_node) {
// Adapt cut_off based on Ren sensor
const double var2 = fabs(ym1 - ym2);
const double var3 = fabs(y - ym1);
const double var4 = fabs(yp1 - y );
const double var5 = fabs(yp2 - yp1);
const double var6 = fabs(yp3 - yp2);
double eta = min((2*var2*var3 + Ren_eps) / (var2*var2 + var3*var3 + Ren_eps),
(2*var3*var4 + Ren_eps) / (var3*var3 + var4*var4 + Ren_eps));
eta = min(eta, (2*var4*var5 + Ren_eps) / (var4*var4 + var5*var5 + Ren_eps));
eta = min(eta, (2*var5*var6 + Ren_eps) / (var5*var5 + var6*var6 + Ren_eps));
const double delta = 1 - min(eta*Ren_irc, 1.0);
const double decay = pow((1 - delta), 4) * (1 + 4*delta);
const int power = min(max(int(floor(Smooth_pow - Diff_pow*(1 - decay))), 0), 13);
cut_off = p10[power];
} else {
if (Coeffs[Stencil1] < 1e-10) a1 = 0.0;
if (Coeffs[Stencil2] < 1e-10) a2 = 0.0;
if (Coeffs[Stencil3] < 1e-10) a3 = 0.0;
if (Coeffs[Stencil4] < 1e-10) a4 = 0.0;
cut_off = p10[BC_pow];
}
// Select stencils
double a = 1.0/(a1 + a2 + a3 + a4);
const int b1 = (a1*a < cut_off) ? 0 : 1;
const int b2 = (a2*a < cut_off) ? 0 : 1;
const int b3 = (a3*a < cut_off) ? 0 : 1;
const int b4 = (a4*a < cut_off) ? 0 : 1;
const double Variation1 = ym2*Recon[6*Stencil1+0] +
ym1*Recon[6*Stencil1+1] +
y *Recon[6*Stencil1+2] +
yp1*Recon[6*Stencil1+3] +
yp2*Recon[6*Stencil1+4] +
yp3*Recon[6*Stencil1+5] - y;
const double Variation2 = ym2*Recon[6*Stencil2+0] +
ym1*Recon[6*Stencil2+1] +
y *Recon[6*Stencil2+2] +
yp1*Recon[6*Stencil2+3] +
yp2*Recon[6*Stencil2+4] +
yp3*Recon[6*Stencil2+5] - y;
const double Variation3 = ym2*Recon[6*Stencil3+0] +
ym1*Recon[6*Stencil3+1] +
y *Recon[6*Stencil3+2] +
yp1*Recon[6*Stencil3+3] +
yp2*Recon[6*Stencil3+4] +
yp3*Recon[6*Stencil3+5] - y;
const double Variation4 = ym2*Recon[6*Stencil4+0] +
ym1*Recon[6*Stencil4+1] +
y *Recon[6*Stencil4+2] +
yp1*Recon[6*Stencil4+3] +
yp2*Recon[6*Stencil4+4] +
yp3*Recon[6*Stencil4+5] - y;
// Assemble the operator
a1 = Coeffs[Stencil1]*b1;
a2 = Coeffs[Stencil2]*b2;
a3 = Coeffs[Stencil3]*b3;
a4 = Coeffs[Stencil4]*b4;
a = 1.0/(a1 + a2 + a3 + a4);
const double w1 = a1*a;
const double w2 = a2*a;
const double w3 = a3*a;
const double w4 = a4*a;
return y + w1*Variation1 + w2*Variation2 + w3*Variation3 + w4*Variation4;
}
__CUDA_H__
static inline double reconstructMinus(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
// Load coefficients
const double *Coeffs = Coeffs_Minus[nType];
const double *Recon = Recon_Minus[nType];
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (yp2 - 2*yp1 + y ); aux2 = ( yp2 - y ); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (yp1 - 2*y + ym1); aux2 = (3*yp1 - 4*y + ym1); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (yp3 - 2*yp2 + yp1); aux2 = (3*yp1 - 4*yp2 + yp3); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*yp1 + 18*y - 9*ym1 + 2*ym2);
aux2 = ( 2*yp1 - 5*y + 4*ym1 - ym2);
aux3 = (- yp1 + 3*y - 3*ym1 + ym2);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
// not recommend to rescale the small number
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
double a1 = pow(1 + tau6/(s1 + eps), 6);
double a2 = pow(1 + tau6/(s2 + eps), 6);
double a3 = pow(1 + tau6/(s3 + eps), 6);
double a4 = pow(1 + tau6/(s4 + eps), 6);
float cut_off;
if (nType == Std_node) {
// Adapt cut_off based on Ren sensor
const double var2 = fabs(ym1 - ym2);
const double var3 = fabs(y - ym1);
const double var4 = fabs(yp1 - y );
const double var5 = fabs(yp2 - yp1);
const double var6 = fabs(yp3 - yp2);
double eta = min((2*var2*var3 + Ren_eps) / (var2*var2 + var3*var3 + Ren_eps),
(2*var3*var4 + Ren_eps) / (var3*var3 + var4*var4 + Ren_eps));
eta = min(eta, (2*var4*var5 + Ren_eps) / (var4*var4 + var5*var5 + Ren_eps));
eta = min(eta, (2*var5*var6 + Ren_eps) / (var5*var5 + var6*var6 + Ren_eps));
const double delta = 1 - min(eta*Ren_irc, 1.0);
const double decay = pow((1 - delta), 4) * (1 + 4*delta);
const int power = min(max(int(floor(Smooth_pow - Diff_pow*(1 - decay))), 0), 13);
cut_off = p10[power];
} else {
if (Coeffs[Stencil1] < 1e-10) a1 = 0.0;
if (Coeffs[Stencil2] < 1e-10) a2 = 0.0;
if (Coeffs[Stencil3] < 1e-10) a3 = 0.0;
if (Coeffs[Stencil4] < 1e-10) a4 = 0.0;
cut_off = p10[BC_pow];
}
// Select stencils
double a = 1.0/(a1 + a2 + a3 + a4);
const int b1 = (a1*a < cut_off) ? 0 : 1;
const int b2 = (a2*a < cut_off) ? 0 : 1;
const int b3 = (a3*a < cut_off) ? 0 : 1;
const int b4 = (a4*a < cut_off) ? 0 : 1;
const double Variation1 = ym2*Recon[6*Stencil1+0] +
ym1*Recon[6*Stencil1+1] +
y *Recon[6*Stencil1+2] +
yp1*Recon[6*Stencil1+3] +
yp2*Recon[6*Stencil1+4] +
yp3*Recon[6*Stencil1+5] - yp1;
const double Variation2 = ym2*Recon[6*Stencil2+0] +
ym1*Recon[6*Stencil2+1] +
y *Recon[6*Stencil2+2] +
yp1*Recon[6*Stencil2+3] +
yp2*Recon[6*Stencil2+4] +
yp3*Recon[6*Stencil2+5] - yp1;
const double Variation3 = ym2*Recon[6*Stencil3+0] +
ym1*Recon[6*Stencil3+1] +
y *Recon[6*Stencil3+2] +
yp1*Recon[6*Stencil3+3] +
yp2*Recon[6*Stencil3+4] +
yp3*Recon[6*Stencil3+5] - yp1;
const double Variation4 = ym2*Recon[6*Stencil4+0] +
ym1*Recon[6*Stencil4+1] +
y *Recon[6*Stencil4+2] +
yp1*Recon[6*Stencil4+3] +
yp2*Recon[6*Stencil4+4] +
yp3*Recon[6*Stencil4+5] - yp1;
// Assemble the operator
a1 = Coeffs[Stencil1]*b1;
a2 = Coeffs[Stencil2]*b2;
a3 = Coeffs[Stencil3]*b3;
a4 = Coeffs[Stencil4]*b4;
a = 1.0/(a1 + a2 + a3 + a4);
const double w1 = a1*a;
const double w2 = a2*a;
const double w3 = a3*a;
const double w4 = a4*a;
return yp1 + w1*Variation1 + w2*Variation2 + w3*Variation3 + w4*Variation4;
}
private:
// Ren sensor coefficients
static constexpr double Ren_r_c = 0.2;
static constexpr double Ren_eps = 0.9*Ren_r_c*1e-16/(1.0 - 0.9*Ren_r_c);
static constexpr double Ren_irc = 1.0/Ren_r_c;
// Constants for TENO cut-off adaptation
static constexpr double Smooth_pow = 9.5;
static constexpr double Shock_pow = 6.0;
static constexpr int BC_pow = 4;
static constexpr double Diff_pow = Smooth_pow - Shock_pow;
// Small number
static constexpr double eps = my_10_pow(exp);
// JS coefficients
static constexpr double C13 = 13.0/12.0;
static constexpr double C23 = 3.0/12.0;
static constexpr double C14 = 1.0/36.0;
static constexpr double C24 = 13.0/12.0;
static constexpr double C34 = 781.0/720.0;
};
//-----------------------------------------------------------------------------
// TENO-LAD reconstruction operators
// See Peng et al. Journal of Computational Physics 425, 2021
//-----------------------------------------------------------------------------
template<int exp = -16>
class TENOLAD_Op {
public:
__CUDA_H__
static inline double reconstructPlus(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
// Load coefficients
const double *Coeffs = Coeffs_Plus[nType];
const double *Recon = Recon_Plus[nType];
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (ym1 - 2*y + yp1); aux2 = ( ym1 - yp1); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (y - 2*yp1 + yp2); aux2 = (3*y - 4*yp1 + yp2); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (ym2 - 2*ym1 + y ); aux2 = (3*y - 4*ym1 + ym2); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*y + 18*yp1 - 9*yp2 + 2*yp3);
aux2 = ( 2*y - 5*yp1 + 4*yp2 - yp3);
aux3 = (- y + 3*yp1 - 3*yp2 + yp3);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
// not recommend to rescale the small number
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
const double chi1 = tau6/(s1 + eps);
const double chi2 = tau6/(s2 + eps);
const double chi3 = tau6/(s3 + eps);
const double chi4 = tau6/(s4 + eps);
double a1 = pow(1 + chi1, 6);
double a2 = pow(1 + chi2, 6);
double a3 = pow(1 + chi3, 6);
double a4 = pow(1 + chi4, 6);
if (Coeffs[Stencil1] < 1e-10) a1 = 0.0;
if (Coeffs[Stencil2] < 1e-10) a2 = 0.0;
if (Coeffs[Stencil3] < 1e-10) a3 = 0.0;
if (Coeffs[Stencil4] < 1e-10) a4 = 0.0;
// Adapt cut_off
const double chiMax = max(chi1, max(chi2,
max(chi3, chi4)));
const double theta = 1.0/(1 + chiMax*iH);
const int power = min(max(int(floor(Shock_pow + Diff_pow*theta)), 0), 13);
const float cut_off = p10[power];
// Select stencils
double a = 1.0/(a1 + a2 + a3 + a4);
const int b1 = (a1*a < cut_off) ? 0 : 1;
const int b2 = (a2*a < cut_off) ? 0 : 1;
const int b3 = (a3*a < cut_off) ? 0 : 1;
const int b4 = (a4*a < cut_off) ? 0 : 1;
const double Variation1 = ym2*Recon[6*Stencil1+0] +
ym1*Recon[6*Stencil1+1] +
y *Recon[6*Stencil1+2] +
yp1*Recon[6*Stencil1+3] +
yp2*Recon[6*Stencil1+4] +
yp3*Recon[6*Stencil1+5] - y;
const double Variation2 = ym2*Recon[6*Stencil2+0] +
ym1*Recon[6*Stencil2+1] +
y *Recon[6*Stencil2+2] +
yp1*Recon[6*Stencil2+3] +
yp2*Recon[6*Stencil2+4] +
yp3*Recon[6*Stencil2+5] - y;
const double Variation3 = ym2*Recon[6*Stencil3+0] +
ym1*Recon[6*Stencil3+1] +
y *Recon[6*Stencil3+2] +
yp1*Recon[6*Stencil3+3] +
yp2*Recon[6*Stencil3+4] +
yp3*Recon[6*Stencil3+5] - y;
const double Variation4 = ym2*Recon[6*Stencil4+0] +
ym1*Recon[6*Stencil4+1] +
y *Recon[6*Stencil4+2] +
yp1*Recon[6*Stencil4+3] +
yp2*Recon[6*Stencil4+4] +
yp3*Recon[6*Stencil4+5] - y;
// Assemble the operator
a1 = Coeffs[Stencil1]*b1;
a2 = Coeffs[Stencil2]*b2;
a3 = Coeffs[Stencil3]*b3;
a4 = Coeffs[Stencil4]*b4;
a = 1.0/(a1 + a2 + a3 + a4);
const double w1 = a1*a;
const double w2 = a2*a;
const double w3 = a3*a;
const double w4 = a4*a;
return y + w1*Variation1 + w2*Variation2 + w3*Variation3 + w4*Variation4;
};
__CUDA_H__
static inline double reconstructMinus(const double ym2, const double ym1, const double y, const double yp1, const double yp2, const double yp3, const int nType) {
// Load coefficients
const double *Coeffs = Coeffs_Minus[nType];
const double *Recon = Recon_Minus[nType];
// Compute smoothness factors
double aux1; double aux2; double aux3;
aux1 = (yp2 - 2*yp1 + y ); aux2 = ( yp2 - y ); const double s1 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (yp1 - 2*y + ym1); aux2 = (3*yp1 - 4*y + ym1); const double s2 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (yp3 - 2*yp2 + yp1); aux2 = (3*yp1 - 4*yp2 + yp3); const double s3 = C13*aux1*aux1 + C23*aux2*aux2;
aux1 = (-11*yp1 + 18*y - 9*ym1 + 2*ym2);
aux2 = ( 2*yp1 - 5*y + 4*ym1 - ym2);
aux3 = (- yp1 + 3*y - 3*ym1 + ym2);
const double s4 = C14*aux1*aux1 + C24*aux2*aux2 + C34*aux3*aux3;
// not recommend to rescale the small number
const double tau6 = fabs(s4 - (s3 + s2 + 4*s1)/6);
const double chi1 = tau6/(s1 + eps);
const double chi2 = tau6/(s2 + eps);
const double chi3 = tau6/(s3 + eps);
const double chi4 = tau6/(s4 + eps);
double a1 = pow(1 + chi1, 6);
double a2 = pow(1 + chi2, 6);
double a3 = pow(1 + chi3, 6);
double a4 = pow(1 + chi4, 6);
if (Coeffs[Stencil1] < 1e-10) a1 = 0.0;
if (Coeffs[Stencil2] < 1e-10) a2 = 0.0;
if (Coeffs[Stencil3] < 1e-10) a3 = 0.0;
if (Coeffs[Stencil4] < 1e-10) a4 = 0.0;
// Adapt cut_off
const double chiMax = max(chi1, max(chi2,
max(chi3, chi4)));
const double theta = 1.0/(1 + chiMax*iH);
const int power = min(max(int(floor(Shock_pow + Diff_pow*theta)), 0), 13);
const float cut_off = p10[power];
// Select stencils
double a = 1.0/(a1 + a2 + a3 + a4);
const int b1 = (a1*a < cut_off) ? 0 : 1;
const int b2 = (a2*a < cut_off) ? 0 : 1;
const int b3 = (a3*a < cut_off) ? 0 : 1;
const int b4 = (a4*a < cut_off) ? 0 : 1;
const double Variation1 = ym2*Recon[6*Stencil1+0] +
ym1*Recon[6*Stencil1+1] +
y *Recon[6*Stencil1+2] +
yp1*Recon[6*Stencil1+3] +
yp2*Recon[6*Stencil1+4] +
yp3*Recon[6*Stencil1+5] - yp1;
const double Variation2 = ym2*Recon[6*Stencil2+0] +
ym1*Recon[6*Stencil2+1] +
y *Recon[6*Stencil2+2] +
yp1*Recon[6*Stencil2+3] +
yp2*Recon[6*Stencil2+4] +
yp3*Recon[6*Stencil2+5] - yp1;
const double Variation3 = ym2*Recon[6*Stencil3+0] +
ym1*Recon[6*Stencil3+1] +
y *Recon[6*Stencil3+2] +
yp1*Recon[6*Stencil3+3] +
yp2*Recon[6*Stencil3+4] +
yp3*Recon[6*Stencil3+5] - yp1;
const double Variation4 = ym2*Recon[6*Stencil4+0] +