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Copy pathblue_phase_beris_edwards.c
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blue_phase_beris_edwards.c
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/*****************************************************************************
*
* blue_phase_beris_edwards.c
*
* Time evolution for the blue phase tensor order parameter via the
* Beris-Edwards equation with fluctuations.
*
* We have
*
* d_t Q_ab + div . (u Q_ab) + S(W, Q) = -Gamma H_ab + xi_ab
*
* where S(W, Q) allows for the rotation of rod-like molecules.
* W_ab is the velocity gradient tensor. H_ab is the molecular
* field.
*
* S(W, Q) = (xi D_ab + Omega_ab)(Q_ab + (1/3) d_ab)
* + (Q_ab + (1/3) d_ab)(xiD_ab - Omega_ab)
* - 2xi(Q_ab + (1/3) d_ab) Tr (QW)
*
* D_ab = (1/2) (W_ab + W_ba) and Omega_ab = (1/2) (W_ab - W_ba);
* the final term renders the whole thing traceless.
* xi is defined with the free energy.
*
* The noise term xi_ab is treated following Bhattacharjee et al.
* J. Chem. Phys. 133 044112 (2010). We need to define five constant
* matrices T_ab; these are used in association with five random
* variates at each lattice site to generate consistent noise. The
* variance is 2 kT Gamma from fluctuation dissipation.
*
*
* Edinburgh Soft Matter and Statistical Physics Group and
* Edinburgh Parallel Computing Centre
*
* (c) 2009-2024 The University of Edinburgh
*
* Contributing authors:
* Kevin Stratford ([email protected])
* Alan Gray ([email protected])
* Davide Marenduzzo supplied the inspiration.
*
*****************************************************************************/
#include <assert.h>
#include <limits.h>
#include <stdlib.h>
#include <math.h>
#include "pe.h"
#include "util.h"
#include "coords.h"
#include "physics.h"
#include "leesedwards.h"
#include "advection_bcs.h"
#include "blue_phase.h"
#include "blue_phase_beris_edwards.h"
#include "advection_s.h"
#include "colloids.h"
#include "timer.h"
__host__ int beris_edw_update_driver(beris_edw_t * be, field_t * fq,
field_grad_t * fq_grad,
hydro_t * hydro,
map_t * map, noise_t * noise);
__host__ int beris_edw_fix_swd(beris_edw_t * be, colloids_info_t * cinfo,
hydro_t * hydro, map_t * map);
__host__ int beris_edw_update_host(beris_edw_t * be, fe_t * fe, field_t * fq,
hydro_t * hydro, advflux_t * flux,
map_t * map, noise_t * noise);
__host__ int beris_edw_h_driver(beris_edw_t * be, fe_t * fe);
__global__ void beris_edw_h_kernel_v(kernel_3d_v_t k3v, beris_edw_t * be,
fe_t * fe);
__global__ void beris_edw_kernel_v(kernel_3d_v_t k3v, beris_edw_t * be,
field_t * fq, field_grad_t * fqgrad,
hydro_t * hydro, advflux_t * flux,
map_t * map, noise_t * noise);
__global__ void beris_edw_fix_swd_kernel(kernel_3d_t k3d,
colloids_info_t * cinfo,
hydro_t * hydro, map_t * map,
int noffsetx,
int noffsety, int noffsetz);
struct beris_edw_s {
beris_edw_param_t * param; /* Parameters */
cs_t * cs; /* Coordinate object */
lees_edw_t * le; /* Lees Edwards */
advflux_t * flux; /* Advective fluxes */
int nall; /* Allocated sites */
double * h; /* Molecular Field */
beris_edw_t * target; /* Target memory */
};
static __constant__ beris_edw_param_t static_param;
/*****************************************************************************
*
* beris_edw_create
*
* Create; one-time initialisation of the constant noise matrices is
* also here.
*
*****************************************************************************/
__host__ int beris_edw_create(pe_t * pe, cs_t * cs, lees_edw_t * le,
beris_edw_t ** pobj) {
int ndevice;
int nsites = 0;
advflux_t * flx = NULL;
beris_edw_t * obj = NULL;
assert(pe);
assert(cs);
assert(le);
assert(pobj);
obj = (beris_edw_t *) calloc(1, sizeof(beris_edw_t));
assert(obj);
if (obj == NULL) pe_fatal(pe, "calloc(beris_edw) failed\n");
obj->param = (beris_edw_param_t *) calloc(1, sizeof(beris_edw_param_t));
if (obj->param == NULL) pe_fatal(pe, "calloc(beris_edw_param_t) failed\n");
advflux_le_create(pe, cs, le, NQAB, &flx);
assert(flx);
lees_edw_nsites(le, &nsites);
obj->nall = nsites;
if (nsites < 1 || INT_MAX/NQAB < nsites) {
pe_info(pe, "beris_edw_create: failure in int32_t indexing\n");
return -1;
}
obj->h = (double *) calloc(nsites*NQAB, sizeof(double));
assert(obj->h);
obj->cs = cs;
obj->le = le;
obj->flux = flx;
beris_edw_tmatrix(obj->param->tmatrix);
/* Allocate a target copy, or alias */
tdpGetDeviceCount(&ndevice);
if (ndevice == 0) {
obj->target = obj;
}
else {
double * htmp = NULL;
beris_edw_param_t * tmp;
lees_edw_t * letarget = NULL;
tdpAssert(tdpMalloc((void **) &obj->target, sizeof(beris_edw_t)));
tdpAssert(tdpMemset(obj->target, 0, sizeof(beris_edw_t)));
tdpGetSymbolAddress((void **) &tmp, tdpSymbol(static_param));
tdpAssert(tdpMemcpy(&obj->target->param, &tmp, sizeof(beris_edw_param_t *),
tdpMemcpyHostToDevice));
lees_edw_target(le, &letarget);
tdpAssert(tdpMemcpy(&obj->target->le, &letarget, sizeof(lees_edw_t *),
tdpMemcpyHostToDevice));
tdpAssert(tdpMemcpy(&obj->target->flux, &flx->target, sizeof(advflux_t *),
tdpMemcpyHostToDevice));
tdpAssert(tdpMemcpy(&obj->target->nall, &obj->nall, sizeof(int),
tdpMemcpyHostToDevice));
tdpAssert(tdpMalloc((void **) &htmp, nsites*NQAB*sizeof(double)));
tdpAssert(tdpMemcpy(&obj->target->h, &htmp, sizeof(double *),
tdpMemcpyHostToDevice));
}
*pobj = obj;
return 0;
}
/*****************************************************************************
*
* beris_edw_free
*
*****************************************************************************/
__host__ int beris_edw_free(beris_edw_t * be) {
int ndevice;
assert(be);
tdpGetDeviceCount(&ndevice);
if (ndevice > 0) {
double * htmp;
tdpAssert(tdpMemcpy(&htmp, &be->target->h, sizeof(double *),
tdpMemcpyDeviceToHost));
tdpAssert(tdpFree(htmp));
tdpAssert(tdpFree(be->target));
}
advflux_free(be->flux);
free(be->h);
free(be->param);
free(be);
return 0;
}
/*****************************************************************************
*
* beris_edw_param_commit
*
*****************************************************************************/
__host__ int beris_edw_param_commit(beris_edw_t * be) {
double kt;
physics_t * phys = NULL;
assert(be);
physics_ref(&phys);
physics_kt(phys, &kt);
be->param->var = sqrt(2.0*kt*be->param->gamma);
tdpMemcpyToSymbol(tdpSymbol(static_param), be->param,
sizeof(beris_edw_param_t), 0, tdpMemcpyHostToDevice);
return 0;
}
/*****************************************************************************
*
* beris_edw_param_set
*
*****************************************************************************/
__host__ int beris_edw_param_set(beris_edw_t * be, beris_edw_param_t * vals) {
assert(be);
assert(vals);
*be->param = *vals;
return 0;
}
/*****************************************************************************
*
* beris_edw_update
*
* Driver routine for the update.
*
* Compute advective fluxes (plus appropriate boundary conditions),
* and perform update for one time step.
*
* hydro is allowed to be NULL, in which case we only have relaxational
* dynamics.
*
*****************************************************************************/
__host__ int beris_edw_update(beris_edw_t * be,
fe_t * fe,
field_t * fq,
field_grad_t * fq_grad,
hydro_t * hydro,
colloids_info_t * cinfo,
map_t * map,
noise_t * noise) {
assert(be);
assert(fq);
assert(map);
if (hydro) {
beris_edw_fix_swd(be, cinfo, hydro, map);
hydro_lees_edwards(hydro);
advection_x(be->flux, hydro, fq);
advection_bcs_no_normal_flux(be->flux, map);
}
beris_edw_h_driver(be, fe);
beris_edw_update_driver(be, fq, fq_grad, hydro, map, noise);
return 0;
}
/*****************************************************************************
*
* beris_edw_update_host
*
* Update q via Euler forward step. Note here we only update the
* 5 independent elements of the Q tensor.
*
* hydro is allowed to be NULL, in which case we only have relaxational
* dynamics.
*
* This is a explicit (ic,jc,kc) loop version retained for reference.
*
* TODO: The assert(0) in the noise section indicates this requires
* a test. The rest of the code is unaffected.
*
*****************************************************************************/
__host__ int beris_edw_update_host(beris_edw_t * be, fe_t * fe, field_t * fq,
hydro_t * hydro, advflux_t * flux,
map_t * map, noise_t * noise) {
int ic, jc, kc;
int ia, ib, id;
int index, indexj, indexk;
int nlocal[3];
int status;
double q[3][3];
double w[3][3];
double d[3][3];
double h[3][3];
double s[3][3];
double omega[3][3];
double trace_qw;
double xi;
double gamma;
double chi[NQAB], chi_qab[3][3];
double tmatrix[3][3][NQAB] = {0};
double var = 0.0;
const double dt = 1.0;
const double r3 = 1.0/3.0;
KRONECKER_DELTA_CHAR(d_);
assert(be);
assert(fe);
assert(fe->func->htensor);
assert(fq);
assert(flux);
assert(map);
xi = be->param->xi;
gamma = be->param->gamma;
var = be->param->var;
for (ia = 0; ia < 3; ia++) {
for (ib = 0; ib < 3; ib++) {
s[ia][ib] = 0.0;
chi_qab[ia][ib] = 0.0;
}
}
/* Get kBT, variance of noise and set basis of traceless,
* symmetric matrices for contraction */
if (be->param->noise) {
assert(0); /* check noise kt */
beris_edw_tmatrix(tmatrix);
}
lees_edw_nlocal(be->le, nlocal);
for (ic = 1; ic <= nlocal[X]; ic++) {
for (jc = 1; jc <= nlocal[Y]; jc++) {
for (kc = 1; kc <= nlocal[Z]; kc++) {
index = lees_edw_index(be->le, ic, jc, kc);
map_status(map, index, &status);
if (status != MAP_FLUID) continue;
field_tensor(fq, index, q);
fe->func->htensor(fe, index, h);
if (hydro) {
/* Velocity gradient tensor, symmetric and antisymmetric parts */
hydro_u_gradient_tensor(hydro, ic, jc, kc, w);
trace_qw = 0.0;
for (ia = 0; ia < 3; ia++) {
for (ib = 0; ib < 3; ib++) {
trace_qw += q[ia][ib]*w[ib][ia];
d[ia][ib] = 0.5*(w[ia][ib] + w[ib][ia]);
omega[ia][ib] = 0.5*(w[ia][ib] - w[ib][ia]);
}
}
for (ia = 0; ia < 3; ia++) {
for (ib = 0; ib < 3; ib++) {
s[ia][ib] = -2.0*xi*(q[ia][ib] + r3*d_[ia][ib])*trace_qw;
for (id = 0; id < 3; id++) {
s[ia][ib] +=
(xi*d[ia][id] + omega[ia][id])*(q[id][ib] + r3*d_[id][ib])
+ (q[ia][id] + r3*d_[ia][id])*(xi*d[id][ib] - omega[id][ib]);
}
}
}
}
/* Fluctuating tensor order parameter */
if (be->param->noise) {
noise_reap_n(noise, index, NQAB, chi);
for (id = 0; id < NQAB; id++) {
chi[id] = var*chi[id];
}
for (ia = 0; ia < 3; ia++) {
for (ib = 0; ib < 3; ib++) {
chi_qab[ia][ib] = 0.0;
for (id = 0; id < NQAB; id++) {
chi_qab[ia][ib] += chi[id]*tmatrix[ia][ib][id];
}
}
}
}
/* Here's the full hydrodynamic update. */
indexj = lees_edw_index(be->le, ic, jc-1, kc);
indexk = lees_edw_index(be->le, ic, jc, kc-1);
q[X][X] += dt*(s[X][X] + gamma*h[X][X] + chi_qab[X][X]
- flux->fe[addr_rank1(flux->nsite, NQAB, index, XX)]
+ flux->fw[addr_rank1(flux->nsite, NQAB, index, XX)]
- flux->fy[addr_rank1(flux->nsite, NQAB, index, XX)]
+ flux->fy[addr_rank1(flux->nsite, NQAB, indexj, XX)]
- flux->fz[addr_rank1(flux->nsite, NQAB, index, XX)]
+ flux->fz[addr_rank1(flux->nsite, NQAB, indexk, XX)]);
q[X][Y] += dt*(s[X][Y] + gamma*h[X][Y] + chi_qab[X][Y]
- flux->fe[addr_rank1(flux->nsite, NQAB, index, XY)]
+ flux->fw[addr_rank1(flux->nsite, NQAB, index, XY)]
- flux->fy[addr_rank1(flux->nsite, NQAB, index, XY)]
+ flux->fy[addr_rank1(flux->nsite, NQAB, indexj, XY)]
- flux->fz[addr_rank1(flux->nsite, NQAB, index, XY)]
+ flux->fz[addr_rank1(flux->nsite, NQAB, indexk, XY)]);
q[X][Z] += dt*(s[X][Z] + gamma*h[X][Z] + chi_qab[X][Z]
- flux->fe[addr_rank1(flux->nsite, NQAB, index, XZ)]
+ flux->fw[addr_rank1(flux->nsite, NQAB, index, XZ)]
- flux->fy[addr_rank1(flux->nsite, NQAB, index, XZ)]
+ flux->fy[addr_rank1(flux->nsite, NQAB, indexj, XZ)]
- flux->fz[addr_rank1(flux->nsite, NQAB, index, XZ)]
+ flux->fz[addr_rank1(flux->nsite, NQAB, indexk, XZ)]);
q[Y][Y] += dt*(s[Y][Y] + gamma*h[Y][Y] + chi_qab[Y][Y]
- flux->fe[addr_rank1(flux->nsite, NQAB, index, YY)]
+ flux->fw[addr_rank1(flux->nsite, NQAB, index, YY)]
- flux->fy[addr_rank1(flux->nsite, NQAB, index, YY)]
+ flux->fy[addr_rank1(flux->nsite, NQAB, indexj, YY)]
- flux->fz[addr_rank1(flux->nsite, NQAB, index, YY)]
+ flux->fz[addr_rank1(flux->nsite, NQAB, indexk, YY)]);
q[Y][Z] += dt*(s[Y][Z] + gamma*h[Y][Z] + chi_qab[Y][Z]
- flux->fe[addr_rank1(flux->nsite, NQAB, index, YZ)]
+ flux->fw[addr_rank1(flux->nsite, NQAB, index, YZ)]
- flux->fy[addr_rank1(flux->nsite, NQAB, index, YZ)]
+ flux->fy[addr_rank1(flux->nsite, NQAB, indexj, YZ)]
- flux->fz[addr_rank1(flux->nsite, NQAB, index, YZ)]
+ flux->fz[addr_rank1(flux->nsite, NQAB, indexk, YZ)]);
field_tensor_set(fq, index, q);
/* Next site */
}
}
}
return 0;
}
/*****************************************************************************
*
* beris_edw_update_driver
*
* Update q via Euler forward step. Note here we only update the
* 5 independent elements of the Q tensor.
*
* hydro is allowed to be NULL, in which case we only have relaxational
* dynamics.
*
*****************************************************************************/
__host__ int beris_edw_update_driver(beris_edw_t * be,
field_t * fq,
field_grad_t * fq_grad,
hydro_t * hydro,
map_t * map,
noise_t * noise) {
int nlocal[3];
hydro_t * hydrotarget = NULL;
noise_t * noisetarget = NULL;
assert(be);
assert(fq);
assert(map);
cs_nlocal(be->cs, nlocal);
{
dim3 nblk = {};
dim3 ntpb = {};
cs_limits_t lim = {1, nlocal[X], 1, nlocal[Y], 1, nlocal[Z]};
kernel_3d_v_t k3v = kernel_3d_v(be->cs, lim, NSIMDVL);
kernel_3d_launch_param(k3v.kiterations, &nblk, &ntpb);
beris_edw_param_commit(be);
if (hydro) hydrotarget = hydro->target;
if (noise) noisetarget = noise->target;
TIMER_start(BP_BE_UPDATE_KERNEL);
tdpLaunchKernel(beris_edw_kernel_v, nblk, ntpb, 0, 0,
k3v, be->target, fq->target, fq_grad->target,
hydrotarget, be->flux->target, map->target, noisetarget);
tdpAssert(tdpPeekAtLastError());
tdpAssert(tdpDeviceSynchronize());
TIMER_stop(BP_BE_UPDATE_KERNEL);
}
return 0;
}
/*****************************************************************************
*
* beris_edw_kernel
*
*****************************************************************************/
__global__ void beris_edw_kernel_v(kernel_3d_v_t k3v, beris_edw_t * be,
field_t * fq, field_grad_t * fqgrad,
hydro_t * hydro, advflux_t * flux,
map_t * map, noise_t * noise) {
int kindex = 0;
const double dt = 1.0;
const double r3 = (1.0/3.0);
KRONECKER_DELTA_CHAR(d_);
assert(be);
assert(fq);
assert(fqgrad);
assert(flux);
assert(map);
for_simt_parallel(kindex, k3v.kiterations, NSIMDVL) {
int iv;
int index;
int ic[NSIMDVL], jc[NSIMDVL], kc[NSIMDVL];
int indexj[NSIMDVL], indexk[NSIMDVL];
int maskv[NSIMDVL];
int status = 0;
double q[3][3][NSIMDVL];
double w[3][3][NSIMDVL] = {0};
double d[3][3][NSIMDVL];
double s[3][3][NSIMDVL];
double omega[3][3][NSIMDVL];
double trace_qw[NSIMDVL];
double chi[NQAB], chi_qab[3][3][NSIMDVL];
double tr[NSIMDVL];
index = k3v.kindex0 + kindex;
kernel_3d_v_coords(&k3v, kindex, ic, jc, kc);
kernel_3d_v_mask(&k3v, ic, jc, kc, maskv);
for (int ia = 0; ia < 3; ia++) {
for (int ib = 0; ib < 3; ib++) {
for_simd_v(iv, NSIMDVL) s[ia][ib][iv] = 0.0;
for_simd_v(iv, NSIMDVL) chi_qab[ia][ib][iv] = 0.0;
}
}
/* Mask out non-fluid sites. */
/* No vectorisation here at the moment */
for (iv = 0; iv < NSIMDVL; iv++) {
if (maskv[iv]) map_status(map, index+iv, &status);
if (maskv[iv] && status != MAP_FLUID) maskv[iv] = 0;
}
/* Expand q tensor */
for_simd_v(iv, NSIMDVL) q[X][X][iv] = fq->data[addr_rank1(fq->nsites,NQAB,index+iv,XX)];
for_simd_v(iv, NSIMDVL) q[X][Y][iv] = fq->data[addr_rank1(fq->nsites,NQAB,index+iv,XY)];
for_simd_v(iv, NSIMDVL) q[X][Z][iv] = fq->data[addr_rank1(fq->nsites,NQAB,index+iv,XZ)];
for_simd_v(iv, NSIMDVL) q[Y][X][iv] = q[X][Y][iv];
for_simd_v(iv, NSIMDVL) q[Y][Y][iv] = fq->data[addr_rank1(fq->nsites,NQAB,index+iv,YY)];
for_simd_v(iv, NSIMDVL) q[Y][Z][iv] = fq->data[addr_rank1(fq->nsites,NQAB,index+iv,YZ)];
for_simd_v(iv, NSIMDVL) q[Z][X][iv] = q[X][Z][iv];
for_simd_v(iv, NSIMDVL) q[Z][Y][iv] = q[Y][Z][iv];
for_simd_v(iv, NSIMDVL) q[Z][Z][iv] = 0.0 - q[X][X][iv] - q[Y][Y][iv];
if (hydro) {
/* Velocity gradient tensor, symmetric and antisymmetric parts */
int im1[NSIMDVL];
int ip1[NSIMDVL];
for_simd_v(iv, NSIMDVL) im1[iv] = lees_edw_ic_to_buff(be->le, ic[iv], -1);
for_simd_v(iv, NSIMDVL) ip1[iv] = lees_edw_ic_to_buff(be->le, ic[iv], +1);
for_simd_v(iv, NSIMDVL) im1[iv] = lees_edw_index(be->le, im1[iv], jc[iv], kc[iv]);
for_simd_v(iv, NSIMDVL) ip1[iv] = lees_edw_index(be->le, ip1[iv], jc[iv], kc[iv]);
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
w[X][X][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], X)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], X)]);
}
}
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
w[Y][X][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], Y)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], Y)]);
}
}
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
w[Z][X][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], Z)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], Z)]);
}
}
for_simd_v(iv, NSIMDVL) {
im1[iv] = lees_edw_index(be->le, ic[iv], jc[iv] - maskv[iv], kc[iv]);
}
for_simd_v(iv, NSIMDVL) {
ip1[iv] = lees_edw_index(be->le, ic[iv], jc[iv] + maskv[iv], kc[iv]);
}
for_simd_v(iv, NSIMDVL) {
w[X][Y][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], X)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], X)]);
}
for_simd_v(iv, NSIMDVL) {
w[Y][Y][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], Y)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], Y)]);
}
for_simd_v(iv, NSIMDVL) {
w[Z][Y][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], Z)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], Z)]);
}
for_simd_v(iv, NSIMDVL) {
im1[iv] = lees_edw_index(be->le, ic[iv], jc[iv], kc[iv] - maskv[iv]);
}
for_simd_v(iv, NSIMDVL) {
ip1[iv] = lees_edw_index(be->le, ic[iv], jc[iv], kc[iv] + maskv[iv]);
}
for_simd_v(iv, NSIMDVL) {
w[X][Z][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], X)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], X)]);
}
for_simd_v(iv, NSIMDVL) {
w[Y][Z][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], Y)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], Y)]);
}
for_simd_v(iv, NSIMDVL) {
w[Z][Z][iv] = 0.5*
(hydro->u->data[addr_rank1(hydro->nsite, NHDIM, ip1[iv], Z)] -
hydro->u->data[addr_rank1(hydro->nsite, NHDIM, im1[iv], Z)]);
}
/* Enforce tracelessness */
for_simd_v(iv, NSIMDVL) tr[iv] = r3*(w[X][X][iv] + w[Y][Y][iv] + w[Z][Z][iv]);
for_simd_v(iv, NSIMDVL) w[X][X][iv] -= tr[iv];
for_simd_v(iv, NSIMDVL) w[Y][Y][iv] -= tr[iv];
for_simd_v(iv, NSIMDVL) w[Z][Z][iv] -= tr[iv];
for_simd_v(iv, NSIMDVL) trace_qw[iv] = 0.0;
for (int ia = 0; ia < 3; ia++) {
for (int ib = 0; ib < 3; ib++) {
for_simd_v(iv, NSIMDVL) trace_qw[iv] += q[ia][ib][iv]*w[ib][ia][iv];
for_simd_v(iv, NSIMDVL) d[ia][ib][iv] = 0.5*(w[ia][ib][iv] + w[ib][ia][iv]);
for_simd_v(iv, NSIMDVL) omega[ia][ib][iv] = 0.5*(w[ia][ib][iv] - w[ib][ia][iv]);
}
}
for (int ia = 0; ia < 3; ia++) {
for (int ib = 0; ib < 3; ib++) {
for_simd_v(iv, NSIMDVL) {
s[ia][ib][iv] =
-2.0*be->param->xi*(q[ia][ib][iv] + r3*d_[ia][ib])*trace_qw[iv];
}
for (int id = 0; id < 3; id++) {
for_simd_v(iv, NSIMDVL) {
s[ia][ib][iv] +=
(be->param->xi*d[ia][id][iv] + omega[ia][id][iv])
*(q[id][ib][iv] + r3*d_[id][ib])
+ (q[ia][id][iv] + r3*d_[ia][id])
*(be->param->xi*d[id][ib][iv] - omega[id][ib][iv]);
}
}
}
}
}
/* Fluctuating tensor order parameter */
if (be->param->noise) {
for_simd_v(iv, NSIMDVL) {
noise_reap_n(noise, index+iv, NQAB, chi);
for (int id = 0; id < NQAB; id++) {
chi[id] = be->param->var*chi[id];
}
for (int ia = 0; ia < 3; ia++) {
for (int ib = 0; ib < 3; ib++) {
chi_qab[ia][ib][iv] = 0.0;
for (int id = 0; id < NQAB; id++) {
chi_qab[ia][ib][iv] += chi[id]*be->param->tmatrix[ia][ib][id];
}
}
}
}
}
/* Here's the full hydrodynamic update. */
/* The divergence of advective fluxes involves (jc-1) and (kc-1)
* which are masked out if not a valid kernel site */
for_simd_v(iv, NSIMDVL) {
indexj[iv] = lees_edw_index(be->le, ic[iv], jc[iv] - maskv[iv], kc[iv]);
}
for_simd_v(iv, NSIMDVL) {
indexk[iv] = lees_edw_index(be->le, ic[iv], jc[iv], kc[iv] - maskv[iv]);
}
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
q[X][X][iv] += dt*
(s[X][X][iv]
+ chi_qab[X][X][iv]
+ be->param->gamma*be->h[addr_rank1(be->nall, NQAB, index+iv, XX)]
- flux->fe[addr_rank1(flux->nsite,NQAB,index + iv,XX)]
+ flux->fw[addr_rank1(flux->nsite,NQAB,index + iv,XX)]
- flux->fy[addr_rank1(flux->nsite,NQAB,index + iv,XX)]
+ flux->fy[addr_rank1(flux->nsite,NQAB,indexj[iv],XX)]
- flux->fz[addr_rank1(flux->nsite,NQAB,index + iv,XX)]
+ flux->fz[addr_rank1(flux->nsite,NQAB,indexk[iv],XX)]);
}
}
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
q[X][Y][iv] += dt*
(s[X][Y][iv]
+ chi_qab[X][Y][iv]
+ be->param->gamma*be->h[addr_rank1(be->nall, NQAB, index+iv, XY)]
- flux->fe[addr_rank1(flux->nsite,NQAB,index + iv,XY)]
+ flux->fw[addr_rank1(flux->nsite,NQAB,index + iv,XY)]
- flux->fy[addr_rank1(flux->nsite,NQAB,index + iv,XY)]
+ flux->fy[addr_rank1(flux->nsite,NQAB,indexj[iv],XY)]
- flux->fz[addr_rank1(flux->nsite,NQAB,index + iv,XY)]
+ flux->fz[addr_rank1(flux->nsite,NQAB,indexk[iv],XY)]);
}
}
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
q[X][Z][iv] += dt*
(s[X][Z][iv]
+ chi_qab[X][Z][iv]
+ be->param->gamma*be->h[addr_rank1(be->nall, NQAB, index+iv, XZ)]
- flux->fe[addr_rank1(flux->nsite,NQAB,index + iv,XZ)]
+ flux->fw[addr_rank1(flux->nsite,NQAB,index + iv,XZ)]
- flux->fy[addr_rank1(flux->nsite,NQAB,index + iv,XZ)]
+ flux->fy[addr_rank1(flux->nsite,NQAB,indexj[iv],XZ)]
- flux->fz[addr_rank1(flux->nsite,NQAB,index + iv,XZ)]
+ flux->fz[addr_rank1(flux->nsite,NQAB,indexk[iv],XZ)]);
}
}
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
q[Y][Y][iv] += dt*
(s[Y][Y][iv]
+ chi_qab[Y][Y][iv]
+ be->param->gamma*be->h[addr_rank1(be->nall, NQAB, index+iv, YY)]
- flux->fe[addr_rank1(flux->nsite,NQAB,index + iv,YY)]
+ flux->fw[addr_rank1(flux->nsite,NQAB,index + iv,YY)]
- flux->fy[addr_rank1(flux->nsite,NQAB,index + iv,YY)]
+ flux->fy[addr_rank1(flux->nsite,NQAB,indexj[iv],YY)]
- flux->fz[addr_rank1(flux->nsite,NQAB,index + iv,YY)]
+ flux->fz[addr_rank1(flux->nsite,NQAB,indexk[iv],YY)]);
}
}
for_simd_v(iv, NSIMDVL) {
if (maskv[iv]) {
q[Y][Z][iv] += dt*
(s[Y][Z][iv]
+ chi_qab[Y][Z][iv]
+ be->param->gamma*be->h[addr_rank1(be->nall, NQAB, index+iv, YZ)]
- flux->fe[addr_rank1(flux->nsite,NQAB,index + iv,YZ)]
+ flux->fw[addr_rank1(flux->nsite,NQAB,index + iv,YZ)]
- flux->fy[addr_rank1(flux->nsite,NQAB,index + iv,YZ)]
+ flux->fy[addr_rank1(flux->nsite,NQAB,indexj[iv],YZ)]
- flux->fz[addr_rank1(flux->nsite,NQAB,index + iv,YZ)]
+ flux->fz[addr_rank1(flux->nsite,NQAB,indexk[iv],YZ)]);
}
}
for_simd_v(iv, NSIMDVL) fq->data[addr_rank1(fq->nsites,NQAB,index+iv,XX)] = q[X][X][iv];
for_simd_v(iv, NSIMDVL) fq->data[addr_rank1(fq->nsites,NQAB,index+iv,XY)] = q[X][Y][iv];
for_simd_v(iv, NSIMDVL) fq->data[addr_rank1(fq->nsites,NQAB,index+iv,XZ)] = q[X][Z][iv];
for_simd_v(iv, NSIMDVL) fq->data[addr_rank1(fq->nsites,NQAB,index+iv,YY)] = q[Y][Y][iv];
for_simd_v(iv, NSIMDVL) fq->data[addr_rank1(fq->nsites,NQAB,index+iv,YZ)] = q[Y][Z][iv];
/* Next sites. */
}
return;
}
/*****************************************************************************
*
* beris_edw_tmatrix
*
* Sets the elements of the traceless, symmetric base matrices
* following Bhattacharjee et al. There are five:
*
* T^0_ab = sqrt(3/2) [ z_a z_b ]
* T^1_ab = sqrt(1/2) ( x_a x_b - y_a y_b ) a simple dyadic product
* T^2_ab = sqrt(2) [ x_a y_b ]
* T^3_ab = sqrt(2) [ x_a z_b ]
* T^4_ab = sqrt(2) [ y_a z_b ]
*
* Where x, y, z, are unit vectors, and the square brackets should
* be interpreted as
* [t_ab] = (1/2) (t_ab + t_ba) - (1/3) Tr (t_ab) d_ab.
*
* Note the contraction T^i_ab T^j_ab = d_ij.
*
*****************************************************************************/
__host__ __device__ int beris_edw_tmatrix(double t[3][3][NQAB]) {
int ia, ib, id;
const double r3 = (1.0/3.0);
for (ia = 0; ia < 3; ia++) {
for (ib = 0; ib < 3; ib++) {
for (id = 0; id < NQAB; id++) {
t[ia][ib][id] = 0.0;
}
}
}
t[X][X][XX] = sqrt(3.0/2.0)*(0.0 - r3);
t[Y][Y][XX] = sqrt(3.0/2.0)*(0.0 - r3);
t[Z][Z][XX] = sqrt(3.0/2.0)*(1.0 - r3);
t[X][X][XY] = sqrt(1.0/2.0)*(1.0 - 0.0);
t[Y][Y][XY] = sqrt(1.0/2.0)*(0.0 - 1.0);
t[X][Y][XZ] = sqrt(2.0)*(1.0/2.0);
t[Y][X][XZ] = t[X][Y][XZ];
t[X][Z][YY] = sqrt(2.0)*(1.0/2.0);
t[Z][X][YY] = t[X][Z][YY];
t[Y][Z][YZ] = sqrt(2.0)*(1.0/2.0);
t[Z][Y][YZ] = t[Y][Z][YZ];
return 0;
}
/*****************************************************************************
*
* beris_edw_h_driver
*
*****************************************************************************/
__host__ int beris_edw_h_driver(beris_edw_t * be, fe_t * fe) {
int nlocal[3] = {0};
fe_t * fe_target = NULL;
assert(be);
assert(fe);
cs_nlocal(be->cs, nlocal);
{
dim3 nblk = {};
dim3 ntpb = {};
cs_limits_t lim = {1, nlocal[X], 1, nlocal[Y], 1, nlocal[Z]};
kernel_3d_v_t k3v = kernel_3d_v(be->cs, lim, NSIMDVL);
TIMER_start(TIMER_BE_MOL_FIELD);
kernel_3d_launch_param(k3v.kiterations, &nblk, &ntpb);
fe->func->target(fe, &fe_target);
tdpLaunchKernel(beris_edw_h_kernel_v, nblk, ntpb, 0, 0,
k3v, be->target, fe_target);
tdpAssert(tdpPeekAtLastError());
tdpAssert(tdpDeviceSynchronize());
TIMER_stop(TIMER_BE_MOL_FIELD);
}
return 0;
}
/*****************************************************************************
*
* beris_edw_h_kernel_v
*
* Compute and store the relevant molecular field
*
*****************************************************************************/
__global__ void beris_edw_h_kernel_v(kernel_3d_v_t k3v, beris_edw_t * be,
fe_t * fe) {
int kindex = 0;
assert(be);
assert(fe);
assert(fe->func->htensor_v);
for_simt_parallel(kindex, k3v.kiterations, NSIMDVL) {
int iv;
double h[3][3][NSIMDVL];
int index = k3v.kindex0 + kindex;
fe->func->htensor_v(fe, index, h);
for_simd_v(iv, NSIMDVL) {
be->h[addr_rank1(be->nall, NQAB, index + iv, XX)] = h[X][X][iv];
}
for_simd_v(iv, NSIMDVL) {
be->h[addr_rank1(be->nall, NQAB, index + iv, XY)] = h[X][Y][iv];
}
for_simd_v(iv, NSIMDVL) {
be->h[addr_rank1(be->nall, NQAB, index + iv, XZ)] = h[X][Z][iv];
}
for_simd_v(iv, NSIMDVL) {
be->h[addr_rank1(be->nall, NQAB, index + iv, YY)] = h[Y][Y][iv];
}
for_simd_v(iv, NSIMDVL) {
be->h[addr_rank1(be->nall, NQAB, index + iv, YZ)] = h[Y][Z][iv];
}
}
return;
}
/*****************************************************************************
*
* beris_fix_swd
*
* The velocity gradient tensor used in the Beris-Edwards equations
* requires some approximation to the velocity at solid lattice sites.
*
* This makes an approximation only at solid sites (so cannot change
* advective fluxes).
*
*****************************************************************************/
int beris_edw_fix_swd(beris_edw_t * be, colloids_info_t * cinfo,
hydro_t * hydro, map_t * map) {
int nlocal[3];
int noffset[3];
int nextra;
assert(be);