// *****************************************************************************
/*!
\file src/PDE/MultiMat/DGMultiMat.hpp
\copyright 2012-2015 J. Bakosi,
2016-2018 Los Alamos National Security, LLC.,
2019-2021 Triad National Security, LLC.
All rights reserved. See the LICENSE file for details.
\brief Compressible multi-material flow using discontinuous Galerkin
finite elements
\details This file implements calls to the physics operators governing
compressible multi-material flow (with velocity equilibrium) using
discontinuous Galerkin discretizations.
*/
// *****************************************************************************
#ifndef DGMultiMat_h
#define DGMultiMat_h
#include <cmath>
#include <algorithm>
#include <unordered_set>
#include <map>
#include <array>
#include "Macro.hpp"
#include "Exception.hpp"
#include "Vector.hpp"
#include "ContainerUtil.hpp"
#include "UnsMesh.hpp"
#include "Inciter/InputDeck/InputDeck.hpp"
#include "Integrate/Basis.hpp"
#include "Integrate/Quadrature.hpp"
#include "Integrate/Initialize.hpp"
#include "Integrate/Mass.hpp"
#include "Integrate/Surface.hpp"
#include "Integrate/Boundary.hpp"
#include "Integrate/Volume.hpp"
#include "Integrate/MultiMatTerms.hpp"
#include "Integrate/Source.hpp"
#include "Integrate/SolidTerms.hpp"
#include "RiemannChoice.hpp"
#include "MultiMat/MultiMatIndexing.hpp"
#include "Reconstruction.hpp"
#include "Limiter.hpp"
#include "Problem/FieldOutput.hpp"
#include "Problem/BoxInitialization.hpp"
#include "PrefIndicator.hpp"
#include "MultiMat/BCFunctions.hpp"
#include "MultiMat/MiscMultiMatFns.hpp"
namespace inciter {
extern ctr::InputDeck g_inputdeck;
namespace dg {
//! \brief MultiMat used polymorphically with tk::DGPDE
//! \details The template arguments specify policies and are used to configure
//! the behavior of the class. The policies are:
//! - Physics - physics configuration, see PDE/MultiMat/Physics.h
//! - Problem - problem configuration, see PDE/MultiMat/Problem.h
//! \note The default physics is Euler, set in inciter::deck::check_multimat()
template< class Physics, class Problem >
class MultiMat {
private:
using eq = tag::multimat;
public:
//! Constructor
explicit MultiMat() :
m_ncomp( g_inputdeck.get< tag::ncomp >() ),
m_nprim(nprim()),
m_riemann( multimatRiemannSolver(
g_inputdeck.get< tag::flux >() ) )
{
// associate boundary condition configurations with state functions
brigand::for_each< ctr::bclist::Keys >( ConfigBC( m_bc,
{ dirichlet
, symmetry
, invalidBC // Inlet BC not implemented
, invalidBC // Outlet BC not implemented
, farfieldOutlet
, extrapolate } ) );
// EoS initialization
initializeMaterialEoS( m_mat_blk );
}
//! Find the number of primitive quantities required for this PDE system
//! \return The number of primitive quantities required to be stored for
//! this PDE system
std::size_t nprim() const
{
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto& solidx = inciter::g_inputdeck.get<
tag::matidxmap, tag::solidx >();
// individual material pressures and three velocity components
std::size_t np(nmat+3);
for (std::size_t k=0; k<nmat; ++k) {
if (solidx[k] > 0) {
// individual material Cauchy stress tensor components
np += 6;
}
}
return np;
}
//! Find the number of materials set up for this PDE system
//! \return The number of materials set up for this PDE system
std::size_t nmat() const
{
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
return nmat;
}
//! Assign number of DOFs per equation in the PDE system
//! \param[in,out] numEqDof Array storing number of Dofs for each PDE
//! equation
void numEquationDofs(std::vector< std::size_t >& numEqDof) const
{
// all equation-dofs initialized to ndofs first
for (std::size_t i=0; i<m_ncomp; ++i) {
numEqDof.push_back(g_inputdeck.get< tag::ndof >());
}
// volume fractions are P0Pm (ndof = 1) for multi-material simulations
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
if(nmat > 1)
for (std::size_t k=0; k<nmat; ++k)
numEqDof[volfracIdx(nmat, k)] = 1;
}
//! Determine elements that lie inside the user-defined IC box
//! \param[in] geoElem Element geometry array
//! \param[in] nielem Number of internal elements
//! \param[in,out] inbox List of nodes at which box user ICs are set for
//! each IC box
void IcBoxElems( const tk::Fields& geoElem,
std::size_t nielem,
std::vector< std::unordered_set< std::size_t > >& inbox ) const
{
tk::BoxElems< eq >(geoElem, nielem, inbox);
}
//! Initalize the compressible flow equations, prepare for time integration
//! \param[in] L Block diagonal mass matrix
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in] inbox List of elements at which box user ICs are set for
//! each IC box
//! \param[in] elemblkid Element ids associated with mesh block ids where
//! user ICs are set
//! \param[in,out] unk Array of unknowns
//! \param[in] t Physical time
//! \param[in] nielem Number of internal elements
void initialize( const tk::Fields& L,
const std::vector< std::size_t >& inpoel,
const tk::UnsMesh::Coords& coord,
const std::vector< std::unordered_set< std::size_t > >& inbox,
const std::unordered_map< std::size_t, std::set< std::size_t > >&
elemblkid,
tk::Fields& unk,
tk::real t,
const std::size_t nielem ) const
{
tk::initialize( m_ncomp, m_mat_blk, L, inpoel, coord,
Problem::initialize, unk, t, nielem );
const auto rdof = g_inputdeck.get< tag::rdof >();
const auto& ic = g_inputdeck.get< tag::ic >();
const auto& icbox = ic.get< tag::box >();
const auto& icmbk = ic.get< tag::meshblock >();
const auto& bgpre = ic.get< tag::pressure >();
const auto& bgtemp = ic.get< tag::temperature >();
// Set initial conditions inside user-defined IC boxes and mesh blocks
std::vector< tk::real > s(m_ncomp, 0.0);
for (std::size_t e=0; e<nielem; ++e) {
// inside user-defined box
if (!icbox.empty()) {
std::size_t bcnt = 0;
for (const auto& b : icbox) { // for all boxes
if (inbox.size() > bcnt && inbox[bcnt].find(e) != inbox[bcnt].end())
{
std::vector< tk::real > box
{ b.template get< tag::xmin >(), b.template get< tag::xmax >(),
b.template get< tag::ymin >(), b.template get< tag::ymax >(),
b.template get< tag::zmin >(), b.template get< tag::zmax >() };
auto V_ex = (box[1]-box[0]) * (box[3]-box[2]) * (box[5]-box[4]);
for (std::size_t c=0; c<m_ncomp; ++c) {
auto mark = c*rdof;
s[c] = unk(e,mark);
// set high-order DOFs to zero
for (std::size_t i=1; i<rdof; ++i)
unk(e,mark+i) = 0.0;
}
initializeBox<ctr::boxList>( m_mat_blk, V_ex, t, b, bgpre,
bgtemp, s );
// store box-initialization in solution vector
for (std::size_t c=0; c<m_ncomp; ++c) {
auto mark = c*rdof;
unk(e,mark) = s[c];
}
}
++bcnt;
}
}
// inside user-specified mesh blocks
if (!icmbk.empty()) {
for (const auto& b : icmbk) { // for all blocks
auto blid = b.get< tag::blockid >();
auto V_ex = b.get< tag::volume >();
if (elemblkid.find(blid) != elemblkid.end()) {
const auto& elset = tk::cref_find(elemblkid, blid);
if (elset.find(e) != elset.end()) {
initializeBox<ctr::meshblockList>( m_mat_blk, V_ex, t, b,
bgpre, bgtemp, s );
// store initialization in solution vector
for (std::size_t c=0; c<m_ncomp; ++c) {
auto mark = c*rdof;
unk(e,mark) = s[c];
}
}
}
}
}
}
}
//! Compute the left hand side block-diagonal mass matrix
//! \param[in] geoElem Element geometry array
//! \param[in,out] l Block diagonal mass matrix
void lhs( const tk::Fields& geoElem, tk::Fields& l ) const {
const auto ndof = g_inputdeck.get< tag::ndof >();
// Unlike Compflow and Transport, there is a weak reconstruction about
// conservative variable after limiting function which will require the
// size of left hand side vector to be rdof
tk::mass( m_ncomp, ndof, geoElem, l );
}
//! Update the interface cells to first order dofs
//! \param[in] unk Array of unknowns
//! \param[in] nielem Number of internal elements
// //! \param[in,out] ndofel Array of dofs
//! \details This function resets the high-order terms in interface cells.
void updateInterfaceCells( tk::Fields& unk,
std::size_t nielem,
std::vector< std::size_t >& /*ndofel*/ ) const
{
auto intsharp =
g_inputdeck.get< tag::multimat, tag::intsharp >();
// If this cell is not material interface, return this function
if(not intsharp) return;
auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto& solidx = g_inputdeck.get<
tag::matidxmap, tag::solidx >();
for (std::size_t e=0; e<nielem; ++e) {
std::vector< std::size_t > matInt(nmat, 0);
std::vector< tk::real > alAvg(nmat, 0.0);
for (std::size_t k=0; k<nmat; ++k)
alAvg[k] = unk(e, volfracDofIdx(nmat,k,rdof,0));
auto intInd = interfaceIndicator(nmat, alAvg, matInt);
// interface cells cannot be high-order
if (intInd) {
//ndofel[e] = 1;
for (std::size_t k=0; k<nmat; ++k) {
if (matInt[k]) {
for (std::size_t i=1; i<rdof; ++i) {
unk(e, densityDofIdx(nmat,k,rdof,i)) = 0.0;
unk(e, energyDofIdx(nmat,k,rdof,i)) = 0.0;
}
if (solidx[k] > 0) {
for (std::size_t i=0; i<3; ++i)
for (std::size_t j=0; j<3; ++j)
for (std::size_t idof=1; idof<rdof; ++idof) {
unk(e, deformDofIdx(nmat,solidx[k],i,j,rdof,idof)) = 0.0;
}
}
}
}
for (std::size_t idir=0; idir<3; ++idir) {
for (std::size_t i=1; i<rdof; ++i) {
unk(e, momentumDofIdx(nmat,idir,rdof,i)) = 0.0;
}
}
}
}
}
//! Update the primitives for this PDE system
//! \param[in] unk Array of unknowns
//! \param[in] L The left hand side block-diagonal mass matrix
//! \param[in] geoElem Element geometry array
//! \param[in,out] prim Array of primitives
//! \param[in] nielem Number of internal elements
//! \details This function computes and stores the dofs for primitive
//! quantities, which are required for obtaining reconstructed states used
//! in the Riemann solver. See /PDE/Riemann/AUSM.hpp, where the
//! normal velocity for advection is calculated from independently
//! reconstructed velocities.
void updatePrimitives( const tk::Fields& unk,
const tk::Fields& L,
const tk::Fields& geoElem,
tk::Fields& prim,
std::size_t nielem ) const
{
const auto rdof = g_inputdeck.get< tag::rdof >();
const auto ndof = g_inputdeck.get< tag::ndof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto& solidx = g_inputdeck.get< tag::matidxmap, tag::solidx >();
Assert( unk.nunk() == prim.nunk(), "Number of unknowns in solution "
"vector and primitive vector at recent time step incorrect" );
Assert( unk.nprop() == rdof*m_ncomp, "Number of components in solution "
"vector must equal "+ std::to_string(rdof*m_ncomp) );
Assert( prim.nprop() == rdof*m_nprim, "Number of components in vector of "
"primitive quantities must equal "+ std::to_string(rdof*m_nprim) );
for (std::size_t e=0; e<nielem; ++e)
{
std::vector< tk::real > R(m_nprim*ndof, 0.0);
auto ng = tk::NGvol(ndof);
// arrays for quadrature points
std::array< std::vector< tk::real >, 3 > coordgp;
std::vector< tk::real > wgp;
coordgp[0].resize( ng );
coordgp[1].resize( ng );
coordgp[2].resize( ng );
wgp.resize( ng );
tk::GaussQuadratureTet( ng, coordgp, wgp );
// Loop over quadrature points in element e
for (std::size_t igp=0; igp<ng; ++igp)
{
// Compute the basis function
auto B =
tk::eval_basis( ndof, coordgp[0][igp], coordgp[1][igp], coordgp[2][igp] );
auto w = wgp[igp] * geoElem(e, 0);
auto state = tk::eval_state( m_ncomp, rdof, ndof, e, unk, B );
// bulk density at quadrature point
tk::real rhob(0.0);
for (std::size_t k=0; k<nmat; ++k)
rhob += state[densityIdx(nmat, k)];
// velocity vector at quadrature point
std::array< tk::real, 3 >
vel{ state[momentumIdx(nmat, 0)]/rhob,
state[momentumIdx(nmat, 1)]/rhob,
state[momentumIdx(nmat, 2)]/rhob };
std::vector< tk::real > pri(m_nprim, 0.0);
// Evaluate material pressure at quadrature point
for(std::size_t imat = 0; imat < nmat; imat++)
{
auto alphamat = state[volfracIdx(nmat, imat)];
auto arhomat = state[densityIdx(nmat, imat)];
auto arhoemat = state[energyIdx(nmat, imat)];
auto gmat = getDeformGrad(nmat, imat, state);
pri[pressureIdx(nmat,imat)] = m_mat_blk[imat].compute<
EOS::pressure >( arhomat, vel[0], vel[1], vel[2], arhoemat,
alphamat, imat, gmat );
pri[pressureIdx(nmat,imat)] = constrain_pressure( m_mat_blk,
pri[pressureIdx(nmat,imat)], arhomat, alphamat, imat);
if (solidx[imat] > 0) {
auto asigmat = m_mat_blk[imat].computeTensor< EOS::CauchyStress >(
arhomat, vel[0], vel[1], vel[2], arhoemat,
alphamat, imat, gmat );
pri[stressIdx(nmat,solidx[imat],0)] = asigmat[0][0];
pri[stressIdx(nmat,solidx[imat],1)] = asigmat[1][1];
pri[stressIdx(nmat,solidx[imat],2)] = asigmat[2][2];
pri[stressIdx(nmat,solidx[imat],3)] = asigmat[0][1];
pri[stressIdx(nmat,solidx[imat],4)] = asigmat[0][2];
pri[stressIdx(nmat,solidx[imat],5)] = asigmat[1][2];
}
}
// Evaluate bulk velocity at quadrature point
for (std::size_t idir=0; idir<3; ++idir) {
pri[velocityIdx(nmat,idir)] = vel[idir];
}
for(std::size_t k = 0; k < m_nprim; k++)
{
auto mark = k * ndof;
for(std::size_t idof = 0; idof < ndof; idof++)
R[mark+idof] += w * pri[k] * B[idof];
}
}
// Update the DG solution of primitive variables
for(std::size_t k = 0; k < m_nprim; k++)
{
auto mark = k * ndof;
auto rmark = k * rdof;
for(std::size_t idof = 0; idof < ndof; idof++)
{
prim(e, rmark+idof) = R[mark+idof] / L(e, mark+idof);
if(fabs(prim(e, rmark+idof)) < 1e-16)
prim(e, rmark+idof) = 0;
}
}
}
}
//! Clean up the state of trace materials for this PDE system
//! \param[in] t Physical time
//! \param[in] geoElem Element geometry array
//! \param[in,out] unk Array of unknowns
//! \param[in,out] prim Array of primitives
//! \param[in] nielem Number of internal elements
//! \details This function cleans up the state of materials present in trace
//! quantities in each cell. Specifically, the state of materials with
//! very low volume-fractions in a cell is replaced by the state of the
//! material which is present in the largest quantity in that cell. This
//! becomes necessary when shocks pass through cells which contain a very
//! small amount of material. The state of that tiny material might
//! become unphysical and cause solution to diverge; thus requiring such
//! a "reset".
void cleanTraceMaterial( tk::real t,
const tk::Fields& geoElem,
tk::Fields& unk,
tk::Fields& prim,
std::size_t nielem ) const
{
[[maybe_unused]] const auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
Assert( unk.nunk() == prim.nunk(), "Number of unknowns in solution "
"vector and primitive vector at recent time step incorrect" );
Assert( unk.nprop() == rdof*m_ncomp, "Number of components in solution "
"vector must equal "+ std::to_string(rdof*m_ncomp) );
Assert( prim.nprop() == rdof*m_nprim, "Number of components in vector of "
"primitive quantities must equal "+ std::to_string(rdof*m_nprim) );
auto neg_density = cleanTraceMultiMat(t, nielem, m_mat_blk, geoElem, nmat,
unk, prim);
if (neg_density) Throw("Negative partial density.");
}
//! Reconstruct second-order solution from first-order
//! \param[in] geoElem Element geometry array
//! \param[in] fd Face connectivity and boundary conditions object
//! \param[in] esup Elements-surrounding-nodes connectivity
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in,out] U Solution vector at recent time step
//! \param[in,out] P Vector of primitives at recent time step
void reconstruct( tk::real,
const tk::Fields&,
const tk::Fields& geoElem,
const inciter::FaceData& fd,
const std::map< std::size_t, std::vector< std::size_t > >&
esup,
const std::vector< std::size_t >& inpoel,
const tk::UnsMesh::Coords& coord,
tk::Fields& U,
tk::Fields& P ) const
{
const auto rdof = g_inputdeck.get< tag::rdof >();
const auto ndof = g_inputdeck.get< tag::ndof >();
bool is_p0p1(false);
if (rdof == 4 && ndof == 1)
is_p0p1 = true;
const auto nelem = fd.Esuel().size()/4;
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
Assert( U.nprop() == rdof*m_ncomp, "Number of components in solution "
"vector must equal "+ std::to_string(rdof*m_ncomp) );
//----- reconstruction of conserved quantities -----
//--------------------------------------------------
// specify how many variables need to be reconstructed
std::vector< std::size_t > vars;
for (std::size_t c=0; c<m_ncomp; ++c) vars.push_back(c);
// If DG is applied, reconstruct only volume fractions
if (!is_p0p1 && ndof > 1)
{
vars.clear();
for (std::size_t k=0; k<nmat; ++k) vars.push_back(volfracIdx(nmat, k));
}
// 1. solve 3x3 least-squares system
for (std::size_t e=0; e<nelem; ++e)
{
// Reconstruct second-order dofs of volume-fractions in Taylor space
// using nodal-stencils, for a good interface-normal estimate
tk::recoLeastSqExtStencil( rdof, e, esup, inpoel, geoElem, U, vars );
}
// 2. transform reconstructed derivatives to Dubiner dofs
tk::transform_P0P1(rdof, nelem, inpoel, coord, U, vars);
//----- reconstruction of primitive quantities -----
//--------------------------------------------------
// For multimat, conserved and primitive quantities are reconstructed
// separately.
if (is_p0p1) {
vars.clear();
for (std::size_t c=0; c<m_nprim; ++c) vars.push_back(c);
// 1.
for (std::size_t e=0; e<nelem; ++e)
{
// Reconstruct second-order dofs of volume-fractions in Taylor space
// using nodal-stencils, for a good interface-normal estimate
tk::recoLeastSqExtStencil( rdof, e, esup, inpoel, geoElem, P, vars );
}
// 2.
tk::transform_P0P1(rdof, nelem, inpoel, coord, P, vars);
}
}
//! Limit second-order solution, and primitive quantities separately
//! \param[in] t Physical time
//! \param[in] geoFace Face geometry array
//! \param[in] geoElem Element geometry array
//! \param[in] fd Face connectivity and boundary conditions object
//! \param[in] esup Elements-surrounding-nodes connectivity
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in] ndofel Vector of local number of degrees of freedome
//! \param[in] gid Local->global node id map
//! \param[in] bid Local chare-boundary node ids (value) associated to
//! global node ids (key)
//! \param[in] uNodalExtrm Chare-boundary nodal extrema for conservative
//! variables
//! \param[in] pNodalExtrm Chare-boundary nodal extrema for primitive
//! variables
//! \param[in] mtInv Inverse of Taylor mass matrix
//! \param[in,out] U Solution vector at recent time step
//! \param[in,out] P Vector of primitives at recent time step
//! \param[in,out] shockmarker Vector of shock-marker values
void limit( [[maybe_unused]] tk::real t,
const tk::Fields& geoFace,
const tk::Fields& geoElem,
const inciter::FaceData& fd,
const std::map< std::size_t, std::vector< std::size_t > >& esup,
const std::vector< std::size_t >& inpoel,
const tk::UnsMesh::Coords& coord,
const std::vector< std::size_t >& ndofel,
const std::vector< std::size_t >& gid,
const std::unordered_map< std::size_t, std::size_t >& bid,
const std::vector< std::vector<tk::real> >& uNodalExtrm,
const std::vector< std::vector<tk::real> >& pNodalExtrm,
const std::vector< std::vector<tk::real> >& mtInv,
tk::Fields& U,
tk::Fields& P,
std::vector< std::size_t >& shockmarker ) const
{
Assert( U.nunk() == P.nunk(), "Number of unknowns in solution "
"vector and primitive vector at recent time step incorrect" );
const auto limiter = g_inputdeck.get< tag::limiter >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto rdof = g_inputdeck.get< tag::rdof >();
const auto& solidx = g_inputdeck.get<
tag::matidxmap, tag::solidx >();
// limit vectors of conserved and primitive quantities
if (limiter == ctr::LimiterType::SUPERBEEP1)
{
SuperbeeMultiMat_P1( fd.Esuel(), inpoel, ndofel,
coord, solidx, U, P, nmat );
}
else if (limiter == ctr::LimiterType::VERTEXBASEDP1 && rdof == 4)
{
VertexBasedMultiMat_P1( esup, inpoel, ndofel, fd.Esuel().size()/4,
m_mat_blk, fd, geoFace, geoElem, coord, flux, solidx, U, P,
nmat, shockmarker );
}
else if (limiter == ctr::LimiterType::VERTEXBASEDP1 && rdof == 10)
{
VertexBasedMultiMat_P2( esup, inpoel, ndofel, fd.Esuel().size()/4,
m_mat_blk, fd, geoFace, geoElem, coord, gid, bid,
uNodalExtrm, pNodalExtrm, mtInv, flux, solidx, U, P, nmat,
shockmarker );
}
else if (limiter != ctr::LimiterType::NOLIMITER)
{
Throw("Limiter type not configured for multimat.");
}
}
//! Apply CPL to the conservative variable solution for this PDE system
//! \param[in] prim Array of primitive variables
//! \param[in] geoElem Element geometry array
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in,out] unk Array of conservative variables
//! \param[in] nielem Number of internal elements
//! \details This function applies CPL to obtain consistent dofs for
//! conservative quantities based on the limited primitive quantities.
//! See Pandare et al. (2023). On the Design of Stable,
//! Consistent, and Conservative High-Order Methods for Multi-Material
//! Hydrodynamics. J Comp Phys, 112313.
void CPL( const tk::Fields& prim,
const tk::Fields& geoElem,
const std::vector< std::size_t >& inpoel,
const tk::UnsMesh::Coords& coord,
tk::Fields& unk,
std::size_t nielem ) const
{
[[maybe_unused]] const auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
Assert( unk.nunk() == prim.nunk(), "Number of unknowns in solution "
"vector and primitive vector at recent time step incorrect" );
Assert( unk.nprop() == rdof*m_ncomp, "Number of components in solution "
"vector must equal "+ std::to_string(rdof*m_ncomp) );
Assert( prim.nprop() == rdof*m_nprim, "Number of components in vector of "
"primitive quantities must equal "+ std::to_string(rdof*m_nprim) );
correctLimConservMultiMat(nielem, m_mat_blk, nmat, inpoel,
coord, geoElem, prim, unk);
}
//! Return cell-average deformation gradient tensor
//! \param[in] unk Solution vector at recent time step
//! \param[in] nielem Number of internal elements
//! \details This function returns the bulk cell-average inverse
//! deformation gradient tensor
std::array< std::vector< tk::real >, 9 > cellAvgDeformGrad(
const tk::Fields& unk,
std::size_t nielem ) const
{
const auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto& solidx = g_inputdeck.get< tag::matidxmap, tag::solidx >();
std::array< std::vector< tk::real >, 9 > gb;
if (inciter::haveSolid(nmat, solidx)) {
for (auto& gij : gb)
gij.resize(nielem, 0.0);
for (std::size_t e=0; e<nielem; ++e) {
for (std::size_t k=0; k<nmat; ++k) {
if (solidx[k] > 0) {
for (std::size_t i=0; i<3; ++i)
for (std::size_t j=0; j<3; ++j)
gb[3*i+j][e] += unk(e, volfracDofIdx(nmat,k,rdof,0)) *
unk(e,deformDofIdx(nmat,solidx[k],i,j,rdof,0));
}
}
}
}
return gb;
}
//! Compute right hand side
//! \param[in] t Physical time
//! \param[in] geoFace Face geometry array
//! \param[in] geoElem Element geometry array
//! \param[in] fd Face connectivity and boundary conditions object
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in] U Solution vector at recent time step
//! \param[in] P Primitive vector at recent time step
//! \param[in] ndofel Vector of local number of degrees of freedom
//! \param[in] dt Delta time
//! \param[in,out] R Right-hand side vector computed
void rhs( tk::real t,
const tk::Fields& geoFace,
const tk::Fields& geoElem,
const inciter::FaceData& fd,
const std::vector< std::size_t >& inpoel,
const std::vector< std::unordered_set< std::size_t > >&,
const tk::UnsMesh::Coords& coord,
const tk::Fields& U,
const tk::Fields& P,
const std::vector< std::size_t >& ndofel,
const tk::real dt,
tk::Fields& R ) const
{
const auto ndof = g_inputdeck.get< tag::ndof >();
const auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto intsharp =
g_inputdeck.get< tag::multimat, tag::intsharp >();
const auto& solidx = inciter::g_inputdeck.get<
tag::matidxmap, tag::solidx >();
auto nsld = numSolids(nmat, solidx);
const auto nelem = fd.Esuel().size()/4;
Assert( U.nunk() == P.nunk(), "Number of unknowns in solution "
"vector and primitive vector at recent time step incorrect" );
Assert( U.nunk() == R.nunk(), "Number of unknowns in solution "
"vector and right-hand side at recent time step incorrect" );
Assert( U.nprop() == rdof*m_ncomp, "Number of components in solution "
"vector must equal "+ std::to_string(rdof*m_ncomp) );
Assert( P.nprop() == rdof*m_nprim, "Number of components in primitive "
"vector must equal "+ std::to_string(rdof*m_nprim) );
Assert( R.nprop() == ndof*m_ncomp, "Number of components in right-hand "
"side vector must equal "+ std::to_string(ndof*m_ncomp) );
Assert( fd.Inpofa().size()/3 == fd.Esuf().size()/2,
"Mismatch in inpofa size" );
// set rhs to zero
R.fill(0.0);
// Allocate space for Riemann derivatives used in non-conservative terms.
// The following Riemann derivatives are stored, in order:
// 1) 3*nmat terms: derivatives of partial pressure of each material,
// for the energy equations.
// 2) ndof terms: derivatives of Riemann velocity times the basis
// function, for the volume fraction equations.
// 3) nmat*3*3*9 terms: 3 derivatives of u_l*g_ij for each material, for
// the deformation gradient equations.
// 4) 3*nsld terms: 3 derivatives of \alpha \sigma_ij for each solid
// material, for the energy equations.
std::vector< std::vector< tk::real > >
riemannDeriv(3*nmat+ndof+3*nsld, std::vector<tk::real>(U.nunk(),0.0));
// vectors to store the data of riemann velocity used for reconstruction
// in volume fraction equation
std::vector< std::vector< tk::real > > vriem( U.nunk() );
std::vector< std::vector< tk::real > > riemannLoc( U.nunk() );
// configure a no-op lambda for prescribed velocity
auto velfn = []( ncomp_t, tk::real, tk::real, tk::real, tk::real ){
return tk::VelFn::result_type(); };
// compute internal surface flux integrals
tk::surfInt( nmat, m_mat_blk, t, ndof, rdof, inpoel, solidx,
coord, fd, geoFace, geoElem, m_riemann, velfn, U, P, ndofel,
dt, R, vriem, riemannLoc, riemannDeriv, intsharp );
// compute optional source term
tk::srcInt( m_mat_blk, t, ndof, fd.Esuel().size()/4, inpoel,
coord, geoElem, Problem::src, ndofel, R, nmat );
if(ndof > 1)
// compute volume integrals
tk::volInt( nmat, t, m_mat_blk, ndof, rdof, nelem,
inpoel, coord, geoElem, flux, velfn, U, P, ndofel, R,
intsharp );
// compute boundary surface flux integrals
for (const auto& b : m_bc)
tk::bndSurfInt( nmat, m_mat_blk, ndof, rdof,
b.first, fd, geoFace, geoElem, inpoel, coord, t,
m_riemann, velfn, b.second, U, P, ndofel, R, vriem,
riemannLoc, riemannDeriv, intsharp );
Assert( riemannDeriv.size() == 3*nmat+ndof+3*nsld, "Size of "
"Riemann derivative vector incorrect" );
// get derivatives from riemannDeriv
for (std::size_t k=0; k<riemannDeriv.size(); ++k)
{
Assert( riemannDeriv[k].size() == U.nunk(), "Riemann derivative vector "
"for non-conservative terms has incorrect size" );
for (std::size_t e=0; e<U.nunk(); ++e)
riemannDeriv[k][e] /= geoElem(e, 0);
}
// compute volume integrals of non-conservative terms
tk::nonConservativeInt( nmat, m_mat_blk, ndof, rdof, nelem,
inpoel, coord, geoElem, U, P, riemannDeriv,
ndofel, R, intsharp );
// Code below commented until details about the form of these terms in the
// \alpha_k g_k equations are sorted out.
// // Compute integrals for inverse deformation in solid materials
// if (inciter::haveSolid(nmat, solidx))
// tk::solidTermsVolInt( nmat, m_mat_blk, ndof, rdof, nelem,
// inpoel, coord, geoElem, U, P, ndofel, dt, R);
// compute finite pressure relaxation terms
if (g_inputdeck.get< tag::multimat, tag::prelax >())
{
const auto ct = g_inputdeck.get< tag::multimat,
tag::prelax_timescale >();
tk::pressureRelaxationInt( nmat, m_mat_blk, ndof,
rdof, nelem, inpoel, coord, geoElem, U, P,
ndofel, ct, R, intsharp );
}
}
//! Evaluate the adaptive indicator and mark the ndof for each element
//! \param[in] nunk Number of unknowns
//! \param[in] coord Array of nodal coordinates
//! \param[in] inpoel Element-node connectivity
//! \param[in] fd Face connectivity and boundary conditions object
//! \param[in] unk Array of unknowns
//! \param[in] prim Array of primitive quantities
//! \param[in] indicator p-refinement indicator type
//! \param[in] ndof Number of degrees of freedom in the solution
//! \param[in] ndofmax Max number of degrees of freedom for p-refinement
//! \param[in] tolref Tolerance for p-refinement
//! \param[in,out] ndofel Vector of local number of degrees of freedome
void eval_ndof( std::size_t nunk,
[[maybe_unused]] const tk::UnsMesh::Coords& coord,
[[maybe_unused]] const std::vector< std::size_t >& inpoel,
const inciter::FaceData& fd,
const tk::Fields& unk,
const tk::Fields& prim,
inciter::ctr::PrefIndicatorType indicator,
std::size_t ndof,
std::size_t ndofmax,
tk::real tolref,
std::vector< std::size_t >& ndofel ) const
{
const auto& esuel = fd.Esuel();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
if(indicator == inciter::ctr::PrefIndicatorType::SPECTRAL_DECAY)
spectral_decay(nmat, nunk, esuel, unk, prim, ndof, ndofmax, tolref,
ndofel);
else
Throw( "No such adaptive indicator type" );
}
//! Compute the minimum time step size
//! \param[in] fd Face connectivity and boundary conditions object
//! \param[in] geoFace Face geometry array
//! \param[in] geoElem Element geometry array
// //! \param[in] ndofel Vector of local number of degrees of freedom
//! \param[in] U Solution vector at recent time step
//! \param[in] P Vector of primitive quantities at recent time step
//! \param[in] nielem Number of internal elements
//! \return Minimum time step size
//! \details The allowable dt is calculated by looking at the maximum
//! wave-speed in elements surrounding each face, times the area of that
//! face. Once the maximum of this quantity over the mesh is determined,
//! the volume of each cell is divided by this quantity. A minimum of this
//! ratio is found over the entire mesh, which gives the allowable dt.
tk::real dt( const std::array< std::vector< tk::real >, 3 >&,
const std::vector< std::size_t >&,
const inciter::FaceData& fd,
const tk::Fields& geoFace,
const tk::Fields& geoElem,
const std::vector< std::size_t >& /*ndofel*/,
const tk::Fields& U,
const tk::Fields& P,
const std::size_t nielem ) const
{
const auto ndof = g_inputdeck.get< tag::ndof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
auto mindt = timeStepSizeMultiMat( m_mat_blk, fd.Esuf(), geoFace, geoElem,
nielem, nmat, U, P);
tk::real dgp = 0.0;
if (ndof == 4)
{
dgp = 1.0;
}
else if (ndof == 10)
{
dgp = 2.0;
}
// Scale smallest dt with CFL coefficient and the CFL is scaled by (2*p+1)
// where p is the order of the DG polynomial by linear stability theory.
mindt /= (2.0*dgp + 1.0);
return mindt;
}
//! Extract the velocity field at cell nodes. Currently unused.
//! \param[in] U Solution vector at recent time step
//! \param[in] N Element node indices
//! \return Array of the four values of the velocity field
std::array< std::array< tk::real, 4 >, 3 >
velocity( const tk::Fields& U,
const std::array< std::vector< tk::real >, 3 >&,
const std::array< std::size_t, 4 >& N ) const
{
const auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
std::array< std::array< tk::real, 4 >, 3 > v;
v[0] = U.extract( momentumDofIdx(nmat, 0, rdof, 0), N );
v[1] = U.extract( momentumDofIdx(nmat, 1, rdof, 0), N );
v[2] = U.extract( momentumDofIdx(nmat, 2, rdof, 0), N );
std::vector< std::array< tk::real, 4 > > ar;
ar.resize(nmat);
for (std::size_t k=0; k<nmat; ++k)
ar[k] = U.extract( densityDofIdx(nmat, k, rdof, 0), N );
std::array< tk::real, 4 > r{{ 0.0, 0.0, 0.0, 0.0 }};
for (std::size_t i=0; i<r.size(); ++i) {
for (std::size_t k=0; k<nmat; ++k)
r[i] += ar[k][i];
}
std::transform( r.begin(), r.end(), v[0].begin(), v[0].begin(),
[]( tk::real s, tk::real& d ){ return d /= s; } );
std::transform( r.begin(), r.end(), v[1].begin(), v[1].begin(),
[]( tk::real s, tk::real& d ){ return d /= s; } );
std::transform( r.begin(), r.end(), v[2].begin(), v[2].begin(),
[]( tk::real s, tk::real& d ){ return d /= s; } );
return v;
}
//! Return a map that associates user-specified strings to functions
//! \return Map that associates user-specified strings to functions that
//! compute relevant quantities to be output to file
std::map< std::string, tk::GetVarFn > OutVarFn() const
{ return MultiMatOutVarFn(); }
//! Return analytic field names to be output to file
//! \return Vector of strings labelling analytic fields output in file
std::vector< std::string > analyticFieldNames() const {
auto nmat = g_inputdeck.get< eq, tag::nmat >();
return MultiMatFieldNames(nmat);
}
//! Return time history field names to be output to file
//! \return Vector of strings labelling time history fields output in file
std::vector< std::string > histNames() const {
return MultiMatHistNames();
}
//! Return surface field output going to file
std::vector< std::vector< tk::real > >
surfOutput( const std::map< int, std::vector< std::size_t > >&,
tk::Fields& ) const
{
std::vector< std::vector< tk::real > > s; // punt for now
return s;
}
//! Return time history field output evaluated at time history points
//! \param[in] h History point data
//! \param[in] inpoel Element-node connectivity
//! \param[in] coord Array of nodal coordinates
//! \param[in] U Array of unknowns
//! \param[in] P Array of primitive quantities
//! \return Vector of time history output of bulk flow quantities (density,
//! velocity, total energy, and pressure) evaluated at time history points
std::vector< std::vector< tk::real > >
histOutput( const std::vector< HistData >& h,
const std::vector< std::size_t >& inpoel,
const tk::UnsMesh::Coords& coord,
const tk::Fields& U,
const tk::Fields& P ) const
{
const auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto& x = coord[0];
const auto& y = coord[1];
const auto& z = coord[2];
std::vector< std::vector< tk::real > > Up(h.size());
std::size_t j = 0;
for (const auto& p : h) {
auto e = p.get< tag::elem >();
auto chp = p.get< tag::coord >();
// Evaluate inverse Jacobian
std::array< std::array< tk::real, 3>, 4 > cp{{
{{ x[inpoel[4*e ]], y[inpoel[4*e ]], z[inpoel[4*e ]] }},
{{ x[inpoel[4*e+1]], y[inpoel[4*e+1]], z[inpoel[4*e+1]] }},
{{ x[inpoel[4*e+2]], y[inpoel[4*e+2]], z[inpoel[4*e+2]] }},
{{ x[inpoel[4*e+3]], y[inpoel[4*e+3]], z[inpoel[4*e+3]] }} }};
auto J = tk::inverseJacobian( cp[0], cp[1], cp[2], cp[3] );
// evaluate solution at history-point
std::array< tk::real, 3 > dc{{chp[0]-cp[0][0], chp[1]-cp[0][1],
chp[2]-cp[0][2]}};
auto B = tk::eval_basis(rdof, tk::dot(J[0],dc), tk::dot(J[1],dc),
tk::dot(J[2],dc));
auto uhp = eval_state(m_ncomp, rdof, rdof, e, U, B);
auto php = eval_state(m_nprim, rdof, rdof, e, P, B);
// store solution in history output vector
Up[j].resize(6, 0.0);
for (std::size_t k=0; k<nmat; ++k) {
Up[j][0] += uhp[densityIdx(nmat,k)];
Up[j][4] += uhp[energyIdx(nmat,k)];
Up[j][5] += php[pressureIdx(nmat,k)];
}
Up[j][1] = php[velocityIdx(nmat,0)];
Up[j][2] = php[velocityIdx(nmat,1)];
Up[j][3] = php[velocityIdx(nmat,2)];
++j;
}
return Up;
}
//! Return names of integral variables to be output to diagnostics file
//! \return Vector of strings labelling integral variables output
std::vector< std::string > names() const
{
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
return MultiMatDiagNames(nmat);
}
//! Return analytic solution (if defined by Problem) at xi, yi, zi, t
//! \param[in] xi X-coordinate at which to evaluate the analytic solution
//! \param[in] yi Y-coordinate at which to evaluate the analytic solution
//! \param[in] zi Z-coordinate at which to evaluate the analytic solution
//! \param[in] t Physical time at which to evaluate the analytic solution
//! \return Vector of analytic solution at given location and time
std::vector< tk::real >
analyticSolution( tk::real xi, tk::real yi, tk::real zi, tk::real t ) const
{ return Problem::analyticSolution( m_ncomp, m_mat_blk, xi, yi, zi, t ); }
//! Return analytic solution for conserved variables
//! \param[in] xi X-coordinate at which to evaluate the analytic solution
//! \param[in] yi Y-coordinate at which to evaluate the analytic solution
//! \param[in] zi Z-coordinate at which to evaluate the analytic solution
//! \param[in] t Physical time at which to evaluate the analytic solution
//! \return Vector of analytic solution at given location and time
std::vector< tk::real >
solution( tk::real xi, tk::real yi, tk::real zi, tk::real t ) const
{ return Problem::initialize( m_ncomp, m_mat_blk, xi, yi, zi, t ); }
//! Return cell-averaged specific total energy for an element
//! \param[in] e Element id for which total energy is required
//! \param[in] unk Vector of conserved quantities
//! \return Cell-averaged specific total energy for given element
tk::real sp_totalenergy(std::size_t e, const tk::Fields& unk) const
{
const auto rdof = g_inputdeck.get< tag::rdof >();
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
tk::real sp_te(0.0);
// sum each material total energy
for (std::size_t k=0; k<nmat; ++k) {
sp_te += unk(e, energyDofIdx(nmat,k,rdof,0));
}
return sp_te;
}
private:
//! Number of components in this PDE system
const ncomp_t m_ncomp;
//! Number of primitive quantities stored in this PDE system
const ncomp_t m_nprim;
//! Riemann solver
tk::RiemannFluxFn m_riemann;
//! BC configuration
BCStateFn m_bc;
//! EOS material block
std::vector< EOS > m_mat_blk;
//! Evaluate conservative part of physical flux function for this PDE system
//! \param[in] ncomp Number of scalar components in this PDE system
//! \param[in] ugp Numerical solution at the Gauss point at which to
//! evaluate the flux
//! \return Flux vectors for all components in this PDE system
//! \note The function signature must follow tk::FluxFn
static tk::FluxFn::result_type
flux( ncomp_t ncomp,
const std::vector< EOS >& mat_blk,
const std::vector< tk::real >& ugp,
const std::vector< std::array< tk::real, 3 > >& )
{
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
return tk::fluxTerms(ncomp, nmat, mat_blk, ugp);
}
//! \brief Boundary state function providing the left and right state of a
//! face at Dirichlet boundaries
//! \param[in] ncomp Number of scalar components in this PDE system
//! \param[in] mat_blk EOS material block
//! \param[in] ul Left (domain-internal) state
//! \param[in] x X-coordinate at which to compute the states
//! \param[in] y Y-coordinate at which to compute the states
//! \param[in] z Z-coordinate at which to compute the states
//! \param[in] t Physical time
//! \return Left and right states for all scalar components in this PDE
//! system
//! \note The function signature must follow tk::StateFn. For multimat, the
//! left or right state is the vector of conserved quantities, followed by
//! the vector of primitive quantities appended to it.
static tk::StateFn::result_type
dirichlet( ncomp_t ncomp,
const std::vector< EOS >& mat_blk,
const std::vector< tk::real >& ul, tk::real x, tk::real y,
tk::real z, tk::real t, const std::array< tk::real, 3 >& )
{
auto nmat = g_inputdeck.get< tag::multimat, tag::nmat >();
const auto& solidx = g_inputdeck.get<
tag::matidxmap, tag::solidx >();
[[maybe_unused]] auto nsld = numSolids(nmat, solidx);
auto ur = Problem::initialize( ncomp, mat_blk, x, y, z, t );
Assert( ur.size() == ncomp, "Incorrect size for boundary state vector" );
ur.resize(ul.size());
tk::real rho(0.0);
for (std::size_t k=0; k<nmat; ++k)
rho += ur[densityIdx(nmat, k)];
// get primitives in boundary state
// velocity
ur[ncomp+velocityIdx(nmat, 0)] = ur[momentumIdx(nmat, 0)] / rho;
ur[ncomp+velocityIdx(nmat, 1)] = ur[momentumIdx(nmat, 1)] / rho;
ur[ncomp+velocityIdx(nmat, 2)] = ur[momentumIdx(nmat, 2)] / rho;
// material pressures
for (std::size_t k=0; k<nmat; ++k)
{
auto gk = getDeformGrad(nmat, k, ur);
ur[ncomp+pressureIdx(nmat, k)] = mat_blk[k].compute< EOS::pressure >(
ur[densityIdx(nmat, k)], ur[ncomp+velocityIdx(nmat, 0)],
ur[ncomp+velocityIdx(nmat, 1)], ur[ncomp+velocityIdx(nmat, 2)],
ur[energyIdx(nmat, k)], ur[volfracIdx(nmat, k)], k, gk );
}
Assert( ur.size() == ncomp+nmat+3+nsld*6, "Incorrect size for appended "
"boundary state vector" );
return {{ std::move(ul), std::move(ur) }};
}
// Other boundary condition types that do not depend on "Problem" should be
// added in BCFunctions.hpp
};
} // dg::
} // inciter::
#endif // DGMultiMat_h