/
gsNsTimeIntegrator.hpp
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/
gsNsTimeIntegrator.hpp
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/** @file gsNsTimeIntegrator.hpp
@brief A class providing time integration for incompressible Navier-Stokes.
This file is part of the G+Smo library.
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
Author(s):
O. Weeger (2012 - 2015, TU Kaiserslautern),
A.Shamanskiy (2016 - ...., TU Kaiserslautern)
*/
#pragma once
#include <gsElasticity/gsNsTimeIntegrator.h>
#include <gsElasticity/gsNsAssembler.h>
#include <gsElasticity/gsMassAssembler.h>
#include <gsElasticity/gsIterative.h>
namespace gismo
{
template <class T>
gsNsTimeIntegrator<T>::gsNsTimeIntegrator(gsNsAssembler<T> & stiffAssembler_,
gsMassAssembler<T> & massAssembler_,
gsMultiPatch<T> * ALEvelocity,
gsBoundaryInterface * ALEpatches)
: stiffAssembler(stiffAssembler_),
massAssembler(massAssembler_),
velocityALE(ALEvelocity),
interface(ALEpatches)
{
initialized = false;
m_options = defaultOptions();
m_ddof = stiffAssembler.allFixedDofs();
numIters = 0;
hasSavedState = false;
}
template <class T>
gsOptionList gsNsTimeIntegrator<T>::defaultOptions()
{
gsOptionList opt = Base::defaultOptions();
opt.addInt("Scheme","Time integration scheme",time_integration::implicit_nonlinear);
opt.addReal("Theta","Time integration parametrer: 0 - explicit Euler, 1 - implicit Euler, 0.5 - Crank-Nicolson",0.5);
opt.addInt("Verbosity","Amount of information printed to the terminal: none, some, all",solver_verbosity::none);
opt.addReal("AbsTol","Absolute tolerance for the convergence cretiria",1e-10);
opt.addReal("RelTol","Relative tolerance for the stopping criteria",1e-7);
opt.addSwitch("ALE","ALE deformation is applied to the flow domain",false);
return opt;
}
template <class T>
void gsNsTimeIntegrator<T>::initialize()
{
GISMO_ENSURE(solVector.rows() == stiffAssembler.numDofs(),"No initial conditions provided!");
stiffAssembler.assemble(solVector,m_ddof);
massAssembler.setFixedDofs(m_ddof);
massAssembler.assemble(true);
// IMEX stuff
oldSolVector = solVector;
oldTimeStep = 1.;
initialized = true;
}
template <class T>
void gsNsTimeIntegrator<T>::makeTimeStep(T timeStep)
{
if (!initialized)
initialize();
tStep = timeStep;
if (m_options.getInt("Scheme") == time_integration::implicit_nonlinear)
implicitNonlinear();
if (m_options.getInt("Scheme") == time_integration::implicit_linear)
implicitLinear();
}
template <class T>
void gsNsTimeIntegrator<T>::implicitLinear()
{
T theta = m_options.getReal("Theta");
index_t numDofsVel = massAssembler.numDofs();
stiffAssembler.options().setInt("Assembly",ns_assembly::ossen);
// rhs = M*u_n - dt*(1-theta)*A(u_n)*u_n + dt*(1-theta)*F_n + dt*theta*F_n+1
// rhs: dt*(1-theta)*F_n
m_system.rhs() = tStep*(1-theta)*stiffAssembler.rhs();
// rhs: -dt*(1-theta)*A(u_n)*u_n
m_system.rhs().middleRows(0,numDofsVel) -= tStep*(1-theta)*stiffAssembler.matrix().block(0,0,numDofsVel,numDofsVel) *
solVector.middleRows(0,numDofsVel);
// rhs: M*u_n
m_system.rhs().middleRows(0,numDofsVel) += massAssembler.matrix() *
solVector.middleRows(0,numDofsVel);
// rhs: M_FD*u_DDOFS_n
m_system.rhs().middleRows(0,numDofsVel) -= massAssembler.rhs();
gsMultiPatch<T> velocity, pressure;
stiffAssembler.constructSolution(solVector + tStep/oldTimeStep*(solVector-oldSolVector),
stiffAssembler.allFixedDofs(),velocity,pressure);
if (m_options.getSwitch("ALE"))
for (size_t p = 0; p < interface->patches.size(); ++p)
velocity.patch(interface->patches[p].second).coefs() -=
velocityALE->patch(interface->patches[p].first).coefs();
stiffAssembler.assemble(velocity,pressure);
massAssembler.setFixedDofs(stiffAssembler.allFixedDofs());
if (m_options.getSwitch("ALE"))
massAssembler.assemble();
else
massAssembler.eliminateFixedDofs();
// rhs: dt*theta*F_n+1
m_system.rhs() += tStep*theta*stiffAssembler.rhs();
// rhs: -M_FD*u_DDOFS_n+1
m_system.rhs().middleRows(0,numDofsVel) += massAssembler.rhs();
// matrix = M + dt*theta*A(u_exp)
m_system.matrix() = tStep*stiffAssembler.matrix();
// we need to modify the (0,0,numDofsVel,numDofsVel) block of the matrix.
// unfortunately, eigen provides only a read-only block interfaces.
// the following is an ugly way to overcome this
gsSparseMatrix<T> tempVelocityBlock = m_system.matrix().block(0,0,numDofsVel,numDofsVel);
tempVelocityBlock *= (theta-1);
tempVelocityBlock += massAssembler.matrix();
tempVelocityBlock.conservativeResize(stiffAssembler.numDofs(),numDofsVel);
m_system.matrix().leftCols(numDofsVel) += tempVelocityBlock;
m_system.matrix().makeCompressed();
oldSolVector = solVector;
oldTimeStep = tStep;
m_ddof = stiffAssembler.allFixedDofs();
numIters = 1;
#ifdef GISMO_WITH_PARDISO
gsSparseSolver<>::PardisoLU solver(m_system.matrix());
solVector = solver.solve(m_system.rhs());
#else
gsSparseSolver<>::LU solver(m_system.matrix());
solVector = solver.solve(m_system.rhs());
#endif
}
template <class T>
void gsNsTimeIntegrator<T>::implicitNonlinear()
{
stiffAssembler.options().setInt("Assembly",ns_assembly::newton_next);
T theta = m_options.getReal("Theta");
index_t numDofsVel = massAssembler.numDofs();
constRHS = tStep*(1-theta)*stiffAssembler.rhs();
constRHS.middleRows(0,numDofsVel).noalias() -= tStep*(1-theta)*stiffAssembler.matrix().block(0,0,numDofsVel,numDofsVel)*solVector.middleRows(0,numDofsVel);
constRHS.middleRows(0,numDofsVel).noalias() += massAssembler.matrix()*solVector.middleRows(0,numDofsVel);
constRHS.middleRows(0,numDofsVel).noalias() -= massAssembler.rhs();
massAssembler.setFixedDofs(stiffAssembler.allFixedDofs());
if (m_options.getSwitch("ALE"))
massAssembler.assemble();
else
massAssembler.eliminateFixedDofs();
constRHS.middleRows(0,numDofsVel).noalias() += massAssembler.rhs();
gsIterative<T> solver(*this,solVector,m_ddof);
solver.options().setInt("Verbosity",m_options.getInt("Verbosity"));
solver.options().setInt("Solver",linear_solver::LU);
solver.options().setInt("IterType",iteration_type::next);
solver.options().setReal("AbsTol",m_options.getReal("AbsTol"));
solver.options().setReal("RelTol",m_options.getReal("RelTol"));
solver.solve();
solVector = solver.solution();
m_ddof = stiffAssembler.allFixedDofs();
numIters = solver.numberIterations();
}
template <class T>
bool gsNsTimeIntegrator<T>::assemble(const gsMatrix<T> & solutionVector,
const std::vector<gsMatrix<T> > & fixedDoFs)
{
T theta = m_options.getReal("Theta");
gsMultiPatch<T> velocity, pressure;
stiffAssembler.constructSolution(solutionVector,fixedDoFs,velocity,pressure);
if (m_options.getSwitch("ALE"))
for (size_t p = 0; p < interface->patches.size(); ++p)
velocity.patch(interface->patches[p].second).coefs() -=
velocityALE->patch(interface->patches[p].first).coefs();
stiffAssembler.assemble(velocity,pressure);
m_system.matrix() = tStep*stiffAssembler.matrix();
index_t numDofsVel = massAssembler.numDofs();
gsSparseMatrix<T> tempVelocityBlock = m_system.matrix().block(0,0,numDofsVel,numDofsVel);
tempVelocityBlock *= (theta-1);
tempVelocityBlock += massAssembler.matrix();
tempVelocityBlock.conservativeResize(stiffAssembler.numDofs(),numDofsVel);
m_system.matrix().leftCols(numDofsVel) += tempVelocityBlock;
m_system.matrix().makeCompressed();
m_system.rhs() = tStep*theta*stiffAssembler.rhs() + constRHS;
return true;
}
template <class T>
void gsNsTimeIntegrator<T>::constructSolution(gsMultiPatch<T> & velocity, gsMultiPatch<T> & pressure) const
{
stiffAssembler.constructSolution(solVector,m_ddof,velocity,pressure);
}
template <class T>
gsBaseAssembler<T> & gsNsTimeIntegrator<T>::mAssembler() { return massAssembler; }
template <class T>
gsBaseAssembler<T> & gsNsTimeIntegrator<T>::assembler() { return stiffAssembler; }
template <class T>
void gsNsTimeIntegrator<T>::saveState()
{
if (!initialized)
initialize();
velVecSaved = solVector;
oldVecSaved = oldSolVector;
massRhsSaved = massAssembler.rhs();
stiffRhsSaved = stiffAssembler.rhs();
stiffMatrixSaved = stiffAssembler.matrix();
ddofsSaved = m_ddof;
hasSavedState = true;
}
template <class T>
void gsNsTimeIntegrator<T>::recoverState()
{
GISMO_ENSURE(hasSavedState,"No state saved!");
solVector = velVecSaved;
oldSolVector = oldVecSaved;
massAssembler.setRHS(massRhsSaved);
stiffAssembler.setMatrix(stiffMatrixSaved);
stiffAssembler.setRHS(stiffRhsSaved);
m_ddof = ddofsSaved;
}
} // namespace ends