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viscosity.cu
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/**
* @author Marius Morlock and Christoph Schaefer
*
* @section LICENSE
* Copyright (c) 2019 Christoph Schaefer
*
* This file is part of miluphcuda.
*
* miluphcuda is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* miluphcuda is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with miluphcuda. If not, see <http://www.gnu.org/licenses/>.
*
*/
#include "viscosity.h"
#include "miluph.h"
#include "soundspeed.h"
#include "timeintegration.h"
#include "kernel.h"
#include "parameter.h"
extern __device__ SPH_kernel kernel;
#if NAVIER_STOKES
__global__ void calculate_shear_stress_tensor(int *interactions)
{
int i, inc;
int e, f, g;
int j, k;
inc = blockDim.x * gridDim.x;
//Particle Loop
for (i = threadIdx.x + blockIdx.x * blockDim.x; i < numRealParticles; i += inc) {
double dv[DIM];
double dr[DIM];
double r;
double sml;
double dWdr, W;
double dWdx[DIM];
for (k = 0; k < DIM*DIM; k++) {
p.Tshear[i*DIM*DIM+k] = 0.0;
}
for (k = 0; k < p.noi[i]; k++) {
j = interactions[i * MAX_NUM_INTERACTIONS + k];
dv[0] = p.vx[i] - p.vx[j];
#if DIM > 1
dv[1] = p.vy[i] - p.vy[j];
#if DIM > 2
dv[2] = p.vz[i] - p.vz[j];
#endif
#endif
// relative vector
dr[0] = p.x[i] - p.x[j];
#if DIM > 1
dr[1] = p.y[i] - p.y[j];
#if DIM > 2
dr[2] = p.z[i] - p.z[j];
#endif
#endif
r = 0;
for (e = 0; e < DIM; e++) {
r += dr[e]*dr[e];
dWdx[e] = 0.0;
}
W = 0.0;
dWdr = 0.0;
r = sqrt(r);
sml = p.h[i];
#if (VARIABLE_SML || INTEGRATE_SML || DEAL_WITH_TOO_MANY_INTERACTIONS)
sml = 0.5*(p.h[i] + p.h[j]);
#endif
// get kernel values for this interaction
kernel(&W, dWdx, &dWdr, dr, sml);
#if TENSORIAL_CORRECTION
for (e = 0; e < DIM; e++) {
for (f = 0; f < DIM; f++) {
for (g = 0; g < DIM; g++) {
p.Tshear[i*DIM*DIM+e*DIM+f] += p.m[j]/p.rho[j] * (p_rhs.tensorialCorrectionMatrix[i*DIM*DIM+f*DIM+g] * (-dv[e]) * dr[g] * dWdr/r + p_rhs.tensorialCorrectionMatrix[i*DIM*DIM+e*DIM+g] * (-dv[f]) * dr[g] * dWdr/r);
}
// traceless
if (e == f) {
for (g = 0; g < DIM; g++) {
p.Tshear[i*DIM*DIM+e*DIM+f] -= 2./3 * p.m[j]/p.rho[j] * (p_rhs.tensorialCorrectionMatrix[i*DIM*DIM+e*DIM+g] * (-dv[e]) * dr[g] * dWdr/r);
}
}
}
}
#else
double trace = 0;
for (e = 0; e < DIM; e++) {
# if (SPHEQUATIONS == SPH_VERSION1)
trace += p.m[j]/p.rho[i] * (-dv[e])*dWdx[e] ;
# elif (SPHEQUATIONS == SPH_VERSION2)
trace += p.m[j]/p.rho[j] * (-dv[e])*dWdx[e] ;
#endif
}
for (e = 0; e < DIM; e++) {
for (f = 0; f < DIM; f++) {
# if (SPHEQUATIONS == SPH_VERSION1)
p.Tshear[i*DIM*DIM+e*DIM+f] += p.m[j]/p.rho[i] * (-dv[e]*dWdx[f] - dv[f]*dWdx[e]);
# elif (SPHEQUATIONS == SPH_VERSION2)
p.Tshear[i*DIM*DIM+e*DIM+f] += p.m[j]/p.rho[j] * (-dv[e]*dWdx[f] - dv[f]*dWdx[e]);
#endif
// traceless
if (e == f) {
# if (SPHEQUATIONS == SPH_VERSION1)
p.Tshear[i*DIM*DIM+e*DIM+f] -= 2./3 * trace;
# elif (SPHEQUATIONS == SPH_VERSION2)
p.Tshear[i*DIM*DIM+e*DIM+f] -= 2./3 * trace;
#endif
}
}
}
#endif
}
}
}
#endif
/*normally known as beta viscosity, here we use beta due to naming concerns of other variables in this code and to avoid confusion */
#if INVISCID_SPH
__global__ void betaviscosity(int *interactions)
{
register int d, i, j, k, m, inc, numInteractions;
inc = blockDim.x * gridDim.x;
double dv[DIM], dx[DIM];
double vi[DIM], vj[DIM];
double mj, rhoi;
double W, dWdx[DIM], dWdr;
double divv[DIM], divV, divvdt;
double tau, sml, csound;
double Ai, Ri, Xii;
double curlj[DIM][DIM] = {0};
double transpose[DIM][DIM] = {0};
double limiterMatrix[DIM][DIM] = {0};
double traceLimiter = 0;
double beta_loc;
double beta_max = 4;
//Particle Loop
for (i = threadIdx.x + blockIdx.x * blockDim.x; i < numRealParticles; i += inc) {
numInteractions = p.noi[i];
sml = p.h[i];
csound = p.cs[i];
rhoi = p.rho[i];
W = 0.0;
dWdr = 0.0;
Ai = 0;
Ri = 0;
Xii = 0;
//Interaction Partner Loop
for(k = 0; k < numInteractions; k++) {
j = interactions[i * MAX_NUM_INTERACTIONS + k];
dx[0] = p.x[i] - p.x[j];
dv[0] = p.vx[i] - p.vx[j];
#if DIM > 1
dx[1] = p.y[i] - p.y[j];
dv[1] = p.vy[i] - p.vy[j];
#if DIM > 2
dx[2] = p.z[i] - p.z[j];
dv[2] = p.vz[i] - p.vz[j];
#endif
#endif
vi[0] = p.vx[i];
vj[0] = p.vx[j];
#if DIM > 1
vi[1] = p.vy[i];
vj[1] = p.vy[j];
#if DIM > 2
vi[2] = p.vz[i];
vj[2] = p.vz[j];
#endif
#endif
kernel(&W, dWdx, &dWdr, dx, sml);
mj = p.m[j];
/* divv */
for (d = 0; d < DIM; d++) {
divv[d] = mj/rhoi * (vj[d] - vi[d]) * dWdx[d];
/* Limiter Matrix */
for (m = 0; m < DIM; m++) {
curlj[d][m] = 0;
}
}
for (d = 0; d < DIM; d++) {
curlj[d][d] = -1.0/DIM * divv[d];
for (m = 0; m < DIM; m++) {
curlj[d][m] += (mj/rhoi) *(dv[d]*dWdx[d]/(dx[m]*dWdx[m]) + dv[m]*dWdx[m]/(dx[d]*dWdx[d]))/2;
transpose[m][d] = curlj[d][m];
}
}
multiply(curlj, transpose, limiterMatrix);
for (d = 0; d < DIM; d++) {
traceLimiter += limiterMatrix[d][d];
Ri += 1.0/rhoi * sign(dv[d]) * mj * dWdx[d];
}
} /* Ending Interaction Partner Loop */
/* Calculating d/dt(divv) */
divV = p_rhs.divv[i];
divvdt = divV - p.divv_old[i];
/* decay time */
tau = sml / (2.0 * 0.05 * csound);
/* Limiter for strong shear forces */
Xii = pow(fabs(2 * pow((1.0 - Ri),4) * divV),2) / (pow(fabs(2 * pow((1.0 - Ri),4) * divV),2) + pow(1.0+fabs(traceLimiter),2));
//fprintf(stdout, "Ri: %e\n", Ri);
//fprintf(stdout, "vvnablaW: %e\n", vvnablaW);
//fprintf(stdout, "traceLimiter: %e\n", traceLimiter);
//fprintf(stdout, "Xii: %e\n", Xii);
/* Calc shock indicator */
if ((-1.0*divvdt) > 0) {
Ai = Xii * -1.0 * divvdt;
}
else {
Ai = 0;
}
//fprintf(stdout, "p[%d].divvdt: %e\n", i, p[i].divvdt);
beta_loc = beta_max * pow(sml, 2) * Ai / (pow(csound, 2) + pow(sml, 2) * Ai);
//fprintf(stdout, "p[%d].cs: %e\n", i, p[i].cs);
//fprintf(stdout, "p[%d].sml: %e\n", i, p[i].sml);
//fprintf(stdout, "Ai: %e\n", Ai);
//fprintf(stdout, "beta_max: %e\n", beta_max);
//fprintf(stdout, "beta_loc: %e\n", beta_loc);
if (beta_loc > p.beta_old[i]) {
p.beta[i] = beta_loc;
p.dbetadt[i] = 0;
} else
{
p.beta[i] = p.beta_old[i];
p.dbetadt[i] = (p.beta_old[i] - beta_loc) / tau;
}
/* getting ready for the next timestep by giving the "new" old values the current ones */
p.beta_old[i] = p.beta[i];
p.divv_old[i] = divV;
} // Ending Particle Loop
}
#endif
__device__ int sign(double x)
{
if (x < 0) {
return -1;
} else if (x > 0) {
return 1;
} else {
return 0;
}
}
/* function for multiplying two matrices */
__device__ void multiply(double mat1[][DIM], double mat2[][DIM], double res[][DIM])
{
int i, j, k;
for (i = 0; i < DIM; i++) {
for (j = 0; j < DIM; j++) {
for (k = 0; k < DIM; k++) {
res[i][j] += mat1[i][k]*mat2[k][j];
}
}
}
}