Transient incompressible Navier Stokes solver in a split scheme formulation. More...

#include <navier_solver.hpp>

Collaboration diagram for mfem::navier::NavierSolver:

Public Member Functions
	NavierSolver (ParMesh *mesh, int order, double kin_vis)
	Initialize data structures, set FE space order and kinematic viscosity. More...

void	Setup (double dt)
	Initialize forms, solvers and preconditioners. More...

void	Step (double &time, double dt, int cur_step, bool provisional=false)
	Compute solution at the next time step t+dt. More...

ParGridFunction *	GetProvisionalVelocity ()
	Return a pointer to the provisional velocity ParGridFunction. More...

ParGridFunction *	GetCurrentVelocity ()
	Return a pointer to the current velocity ParGridFunction. More...

ParGridFunction *	GetCurrentPressure ()
	Return a pointer to the current pressure ParGridFunction. More...

void	AddVelDirichletBC (VectorCoefficient *coeff, Array< int > &attr)
	Add a Dirichlet boundary condition to the velocity field. More...

void	AddVelDirichletBC (VecFuncT *f, Array< int > &attr)

void	AddPresDirichletBC (Coefficient *coeff, Array< int > &attr)
	Add a Dirichlet boundary condition to the pressure field. More...

void	AddPresDirichletBC (ScalarFuncT *f, Array< int > &attr)

void	AddAccelTerm (VectorCoefficient *coeff, Array< int > &attr)
	Add an acceleration term to the RHS of the equation. More...

void	AddAccelTerm (VecFuncT *f, Array< int > &attr)

void	EnablePA (bool pa)
	Enable partial assembly for every operator. More...

void	EnableNI (bool ni)

void	PrintTimingData ()
	Print timing summary of the solving routine. More...

	~NavierSolver ()

void	ComputeCurl2D (ParGridFunction &u, ParGridFunction &cu, bool assume_scalar=false)
	Compute \(\nabla \times \nabla \times u\) for \(u \in (H^1)^2\). More...

void	ComputeCurl3D (ParGridFunction &u, ParGridFunction &cu)
	Compute \(\nabla \times \nabla \times u\) for \(u \in (H^1)^3\). More...

void	Orthogonalize (Vector &v)
	Remove mean from a Vector. More...

void	MeanZero (ParGridFunction &v)
	Remove the mean from a ParGridFunction. More...

void	UpdateTimestepHistory (double dt)
	Rotate entries in the time step and solution history arrays. More...

void	SetMaxBDFOrder (int maxbdforder)
	Set the maximum order to use for the BDF method. More...

double	ComputeCFL (ParGridFunction &u, double dt)
	Compute CFL. More...

void	SetCutoffModes (int c)
	Set the number of modes to cut off in the interpolation filter. More...

void	SetFilterAlpha (double a)
	Set the interpolation filter parameter a. More...

Protected Member Functions
void	PrintInfo ()
	Print information about the Navier version. More...

void	SetTimeIntegrationCoefficients (int step)
	Update the EXTk/BDF time integration coefficient. More...

void	EliminateRHS (Operator &A, ConstrainedOperator &constrainedA, const Array< int > &ess_tdof_list, Vector &x, Vector &b, Vector &X, Vector &B, int copy_interior=0)
	Eliminate essential BCs in an Operator and apply to RHS. More...

Protected Attributes
bool	debug = false
	Enable/disable debug output. More...

bool	verbose = true
	Enable/disable verbose output. More...

bool	partial_assembly = false
	Enable/disable partial assembly of forms. More...

bool	numerical_integ = false
	Enable/disable numerical integration rules of forms. More...

ParMesh *	pmesh = nullptr
	The parallel mesh. More...

int	order
	The order of the velocity and pressure space. More...

double	kin_vis
	Kinematic viscosity (dimensionless). More...

FiniteElementCollection *	vfec = nullptr
	Velocity \(H^1\) finite element collection. More...

FiniteElementCollection *	pfec = nullptr
	Pressure \(H^1\) finite element collection. More...

ParFiniteElementSpace *	vfes = nullptr
	Velocity \((H^1)^d\) finite element space. More...

ParFiniteElementSpace *	pfes = nullptr
	Pressure \(H^1\) finite element space. More...

ParNonlinearForm *	N = nullptr

ParBilinearForm *	Mv_form = nullptr

ParBilinearForm *	Sp_form = nullptr

ParMixedBilinearForm *	D_form = nullptr

ParMixedBilinearForm *	G_form = nullptr

ParBilinearForm *	H_form = nullptr

VectorGridFunctionCoefficient *	FText_gfcoeff = nullptr

ParLinearForm *	FText_bdr_form = nullptr

ParLinearForm *	f_form = nullptr

ParLinearForm *	g_bdr_form = nullptr

ParLinearForm *	mass_lf = nullptr
	Linear form to compute the mass matrix in various subroutines. More...

ConstantCoefficient	onecoeff

double	volume = 0.0

ConstantCoefficient	nlcoeff

ConstantCoefficient	Sp_coeff

ConstantCoefficient	H_lincoeff

ConstantCoefficient	H_bdfcoeff

OperatorHandle	Mv

OperatorHandle	Sp

OperatorHandle	D

OperatorHandle	G

OperatorHandle	H

Solver *	MvInvPC = nullptr

CGSolver *	MvInv = nullptr

HypreBoomerAMG *	SpInvPC = nullptr

OrthoSolver *	SpInvOrthoPC = nullptr

CGSolver *	SpInv = nullptr

Solver *	HInvPC = nullptr

CGSolver *	HInv = nullptr

Vector	fn

Vector	un

Vector	un_next

Vector	unm1

Vector	unm2

Vector	Nun

Vector	Nunm1

Vector	Nunm2

Vector	Fext

Vector	FText

Vector	Lext

Vector	resu

Vector	tmp1

Vector	pn

Vector	resp

Vector	FText_bdr

Vector	g_bdr

ParGridFunction	un_gf

ParGridFunction	un_next_gf

ParGridFunction	curlu_gf

ParGridFunction	curlcurlu_gf

ParGridFunction	Lext_gf

ParGridFunction	FText_gf

ParGridFunction	resu_gf

ParGridFunction	pn_gf

ParGridFunction	resp_gf

Array< int >	vel_ess_attr

Array< int >	pres_ess_attr

Array< int >	vel_ess_tdof

Array< int >	pres_ess_tdof

std::vector< VelDirichletBC_T >	vel_dbcs

std::vector< PresDirichletBC_T >	pres_dbcs

std::vector< AccelTerm_T >	accel_terms

int	max_bdf_order = 3

int	cur_step = 0

std::vector< double >	dthist = {0.0, 0.0, 0.0}

double	bd0 = 0.0

double	bd1 = 0.0

double	bd2 = 0.0

double	bd3 = 0.0

double	ab1 = 0.0

double	ab2 = 0.0

double	ab3 = 0.0

StopWatch	sw_setup

StopWatch	sw_step

StopWatch	sw_extrap

StopWatch	sw_curlcurl

StopWatch	sw_spsolve

StopWatch	sw_hsolve

int	pl_mvsolve = 0

int	pl_spsolve = 0

int	pl_hsolve = 0

int	pl_amg = 0

double	rtol_spsolve = 1e-6

double	rtol_hsolve = 1e-8

int	iter_mvsolve = 0

int	iter_spsolve = 0

int	iter_hsolve = 0

double	res_mvsolve = 0.0

double	res_spsolve = 0.0

double	res_hsolve = 0.0

ParMesh *	pmesh_lor = nullptr

FiniteElementCollection *	pfec_lor = nullptr

ParFiniteElementSpace *	pfes_lor = nullptr

InterpolationGridTransfer *	vgt = nullptr

InterpolationGridTransfer *	pgt = nullptr

ParBilinearForm *	Mv_form_lor = nullptr

ParBilinearForm *	Sp_form_lor = nullptr

ParBilinearForm *	H_form_lor = nullptr

OperatorHandle	Mv_lor

OperatorHandle	Sp_lor

OperatorHandle	H_lor

int	filter_cutoff_modes = 1

double	filter_alpha = 0.0

FiniteElementCollection *	vfec_filter = nullptr

ParFiniteElementSpace *	vfes_filter = nullptr

ParGridFunction	un_NM1_gf

ParGridFunction	un_filtered_gf

Detailed Description

Transient incompressible Navier Stokes solver in a split scheme formulation.

This implementation of a transient incompressible Navier Stokes solver uses the non-dimensionalized formulation. The coupled momentum and incompressibility equations are decoupled using the split scheme described in [1]. This leads to three solving steps.

An extrapolation step for all nonlinear terms which are treated explicitly. This step avoids a fully coupled nonlinear solve and only requires a solve of the mass matrix in velocity space \(M_v^{-1}\). On the other hand this introduces a CFL stability condition on the maximum timestep.
A Poisson solve \(S_p^{-1}\).
A Helmholtz like solve \((M_v - \partial t K_v)^{-1}\).

The numerical solver setup for each step are as follows.

\(M_v^{-1}\) is solved using CG with Jacobi as preconditioner.

\(S_p^{-1}\) is solved using CG with AMG applied to the low order refined (LOR) assembled pressure Poisson matrix. To avoid assembling a matrix for preconditioning, one can use p-MG as an alternative (NYI).

\((M_v - \partial t K_v)^{-1}\) due to the CFL condition we expect the time step to be small. Therefore this is solved using CG with Jacobi as preconditioner. For large time steps a preconditioner like AMG or p-MG should be used (NYI).

Statements marked with NYI mean this feature is planned but Not Yet Implemented.

A detailed description is available in [1] section 4.2. The algorithm is originated from [2].

[1] Michael Franco, Jean-Sylvain Camier, Julian Andrej, Will Pazner (2020) High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners (https://arxiv.org/abs/1910.03032)

[2] A. G. Tomboulides, J. C. Y. Lee & S. A. Orszag (1997) Numerical Simulation of Low Mach Number Reactive Flows

Definition at line 142 of file navier_solver.hpp.

Constructor & Destructor Documentation

NavierSolver::NavierSolver	(	ParMesh *	mesh,
		int	order,
		double	kin_vis
	)

Initialize data structures, set FE space order and kinematic viscosity.

The ParMesh mesh can be a linear or curved parallel mesh. The order of the finite element spaces is this algorithm is of equal order \((P_N)^d P_N\) for velocity and pressure respectively. This means the pressure is in discretized in the same space (just scalar instead of a vector space) as the velocity.

Kinematic viscosity (dimensionless) is set using kin_vis and automatically converted to the Reynolds number. If you want to set the Reynolds number directly, you can provide the inverse.

Definition at line 29 of file navier_solver.cpp.

NavierSolver::~NavierSolver ( )

Definition at line 1125 of file navier_solver.cpp.

Member Function Documentation

void NavierSolver::AddAccelTerm	(	VectorCoefficient *	coeff,
		Array< int > &	attr
	)

Add an acceleration term to the RHS of the equation.

The VecFuncT f is evaluated at the current time t and extrapolated together with the nonlinear parts of the Navier Stokes equation.

Definition at line 999 of file navier_solver.cpp.

void NavierSolver::AddAccelTerm	(	VecFuncT *	f,
		Array< int > &	attr
	)

Definition at line 1017 of file navier_solver.cpp.

void NavierSolver::AddPresDirichletBC	(	Coefficient *	coeff,
		Array< int > &	attr
	)

Add a Dirichlet boundary condition to the pressure field.

Definition at line 966 of file navier_solver.cpp.

void NavierSolver::AddPresDirichletBC	(	ScalarFuncT *	f,
		Array< int > &	attr
	)

Definition at line 994 of file navier_solver.cpp.

void NavierSolver::AddVelDirichletBC	(	VectorCoefficient *	coeff,
		Array< int > &	attr
	)

Add a Dirichlet boundary condition to the velocity field.

Definition at line 933 of file navier_solver.cpp.

void NavierSolver::AddVelDirichletBC	(	VecFuncT *	f,
		Array< int > &	attr
	)

Definition at line 961 of file navier_solver.cpp.

double NavierSolver::ComputeCFL	(	ParGridFunction &	u,
		double	dt
	)

Compute CFL.

Definition at line 852 of file navier_solver.cpp.

void NavierSolver::ComputeCurl2D	(	ParGridFunction &	u,
		ParGridFunction &	cu,
		bool	assume_scalar = `false`
	)

Compute \(\nabla \times \nabla \times u\) for \(u \in (H^1)^2\).

Definition at line 751 of file navier_solver.cpp.

void NavierSolver::ComputeCurl3D	(	ParGridFunction &	u,
		ParGridFunction &	cu
	)

Compute \(\nabla \times \nabla \times u\) for \(u \in (H^1)^3\).

Definition at line 660 of file navier_solver.cpp.

void NavierSolver::EliminateRHS	(	Operator &	A,
		ConstrainedOperator &	constrainedA,
		const Array< int > &	ess_tdof_list,
		Vector &	x,
		Vector &	b,
		Vector &	X,
		Vector &	B,
		int	copy_interior = `0`
	)

protected

Eliminate essential BCs in an Operator and apply to RHS.

Definition at line 627 of file navier_solver.cpp.

void mfem::navier::NavierSolver::EnableNI ( bool ni )

inline

Enable numerical integration rules. This means collocated quadrature at the nodal points.

Definition at line 219 of file navier_solver.hpp.

void mfem::navier::NavierSolver::EnablePA ( bool pa )

inline

Enable partial assembly for every operator.

Definition at line 215 of file navier_solver.hpp.

ParGridFunction* mfem::navier::NavierSolver::GetCurrentPressure ( )

inline

Return a pointer to the current pressure ParGridFunction.

Definition at line 193 of file navier_solver.hpp.

ParGridFunction* mfem::navier::NavierSolver::GetCurrentVelocity ( )

inline

Return a pointer to the current velocity ParGridFunction.

Definition at line 190 of file navier_solver.hpp.

ParGridFunction* mfem::navier::NavierSolver::GetProvisionalVelocity ( )

inline

Return a pointer to the provisional velocity ParGridFunction.

Definition at line 187 of file navier_solver.hpp.

void NavierSolver::MeanZero ( ParGridFunction & v )

Remove the mean from a ParGridFunction.

Modify the ParGridFunction v by subtracting its mean using \( v = v - \int_\Omega \frac{v}{vol(\Omega)} dx \).

Definition at line 605 of file navier_solver.cpp.

void NavierSolver::Orthogonalize ( Vector & v )

Remove mean from a Vector.

Modify the Vector v by subtracting its mean using \(v = v - \frac{\sum_i^N v_i}{N} \)

Definition at line 647 of file navier_solver.cpp.

void NavierSolver::PrintInfo ( )

protected

Print information about the Navier version.

Definition at line 1110 of file navier_solver.cpp.

void NavierSolver::PrintTimingData ( )

Print timing summary of the solving routine.

The summary shows the timing in seconds in the first row of

SETUP: Time spent for the setup of all forms, solvers and preconditioners.
STEP: Time spent computing a full time step. It includes all three solves.
EXTRAP: Time spent for extrapolation of all forcing and nonlinear terms.
CURLCURL: Time spent for computing the curl curl term in the pressure Poisson equation (see references for detailed explanation).
PSOLVE: Time spent in the pressure Poisson solve.
HSOLVE: Time spent in the Helmholtz solve.

The second row shows a proportion of a column relative to the whole time step.

Definition at line 1075 of file navier_solver.cpp.

void mfem::navier::NavierSolver::SetCutoffModes ( int c )

inline

Set the number of modes to cut off in the interpolation filter.

Definition at line 275 of file navier_solver.hpp.

void mfem::navier::NavierSolver::SetFilterAlpha ( double a )

inline

Set the interpolation filter parameter a.

If a is > 0, the filtering algorithm for the velocity field after every time step from [1] is used. The parameter should be 0 > >= 1.

[1] Paul Fischer, Julia Mullen (2001) Filter-based stabilization of spectral element methods

Definition at line 285 of file navier_solver.hpp.

void mfem::navier::NavierSolver::SetMaxBDFOrder ( int maxbdforder )

inline

Set the maximum order to use for the BDF method.

Definition at line 269 of file navier_solver.hpp.

void NavierSolver::SetTimeIntegrationCoefficients ( int step )

protected

Update the EXTk/BDF time integration coefficient.

Depending on which time step the computation is in, the EXTk/BDF time integration coefficients have to be set accordingly. This allows bootstrapping with a BDF scheme of order 1 and increasing the order each following time step, up to order 3 (or whichever order is set in SetMaxBDFOrder).

Definition at line 1022 of file navier_solver.cpp.

void NavierSolver::Setup ( double dt )

Initialize forms, solvers and preconditioners.

Definition at line 99 of file navier_solver.cpp.

void NavierSolver::Step	(	double &	time,
		double	dt,
		int	cur_step,
		bool	provisional = `false`
	)

Compute solution at the next time step t+dt.

This method can be called with the default value provisional which always accepts the computed time step by automatically calling UpdateTimestepHistory.

If provisional is set to true, the solution at t+dt is not accepted automatically and the application code has to call UpdateTimestepHistory and update the time variable accordingly.

The application code can check the provisional step by retrieving the GridFunction with the method GetProvisionalVelocity. If the check fails, it is possible to retry the step with a different time step by not calling UpdateTimestepHistory and calling this method with the previous time and cur_step.

The method and parameter choices are based on [1].

[1] D. Wang, S.J. Ruuth (2008) Variable step-size implicit-explicit linear multistep methods for time-dependent partial differential equations

Definition at line 344 of file navier_solver.cpp.

void NavierSolver::UpdateTimestepHistory ( double dt )

Rotate entries in the time step and solution history arrays.

Definition at line 323 of file navier_solver.cpp.

Member Data Documentation

double mfem::navier::NavierSolver::ab1 = 0.0

protected

Definition at line 427 of file navier_solver.hpp.

double mfem::navier::NavierSolver::ab2 = 0.0

protected

Definition at line 428 of file navier_solver.hpp.

double mfem::navier::NavierSolver::ab3 = 0.0

protected

Definition at line 429 of file navier_solver.hpp.

std::vector<AccelTerm_T> mfem::navier::NavierSolver::accel_terms

protected

Definition at line 416 of file navier_solver.hpp.

double mfem::navier::NavierSolver::bd0 = 0.0

protected

Definition at line 423 of file navier_solver.hpp.

double mfem::navier::NavierSolver::bd1 = 0.0

protected

Definition at line 424 of file navier_solver.hpp.

double mfem::navier::NavierSolver::bd2 = 0.0

protected

Definition at line 425 of file navier_solver.hpp.

double mfem::navier::NavierSolver::bd3 = 0.0

protected

Definition at line 426 of file navier_solver.hpp.

int mfem::navier::NavierSolver::cur_step = 0

protected

Definition at line 419 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::curlcurlu_gf

protected

Definition at line 396 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::curlu_gf

protected

Definition at line 396 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::D

protected

Definition at line 376 of file navier_solver.hpp.

ParMixedBilinearForm* mfem::navier::NavierSolver::D_form = nullptr

protected

Definition at line 350 of file navier_solver.hpp.

bool mfem::navier::NavierSolver::debug = false

protected

Enable/disable debug output.

Definition at line 312 of file navier_solver.hpp.

std::vector<double> mfem::navier::NavierSolver::dthist = {0.0, 0.0, 0.0}

protected

Definition at line 420 of file navier_solver.hpp.

ParLinearForm* mfem::navier::NavierSolver::f_form = nullptr

protected

Definition at line 360 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::Fext

protected

Definition at line 390 of file navier_solver.hpp.

double mfem::navier::NavierSolver::filter_alpha = 0.0

protected

Definition at line 466 of file navier_solver.hpp.

int mfem::navier::NavierSolver::filter_cutoff_modes = 1

protected

Definition at line 465 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::fn

protected

Definition at line 390 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::FText

protected

Definition at line 390 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::FText_bdr

protected

Definition at line 394 of file navier_solver.hpp.

ParLinearForm* mfem::navier::NavierSolver::FText_bdr_form = nullptr

protected

Definition at line 358 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::FText_gf

protected

Definition at line 396 of file navier_solver.hpp.

VectorGridFunctionCoefficient* mfem::navier::NavierSolver::FText_gfcoeff = nullptr

protected

Definition at line 356 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::G

protected

Definition at line 377 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::g_bdr

protected

Definition at line 394 of file navier_solver.hpp.

ParLinearForm* mfem::navier::NavierSolver::g_bdr_form = nullptr

protected

Definition at line 362 of file navier_solver.hpp.

ParMixedBilinearForm* mfem::navier::NavierSolver::G_form = nullptr

protected

Definition at line 352 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::H

protected

Definition at line 378 of file navier_solver.hpp.

ConstantCoefficient mfem::navier::NavierSolver::H_bdfcoeff

protected

Definition at line 372 of file navier_solver.hpp.

ParBilinearForm* mfem::navier::NavierSolver::H_form = nullptr

protected

Definition at line 354 of file navier_solver.hpp.

ParBilinearForm* mfem::navier::NavierSolver::H_form_lor = nullptr

protected

Definition at line 458 of file navier_solver.hpp.

ConstantCoefficient mfem::navier::NavierSolver::H_lincoeff

protected

Definition at line 371 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::H_lor

protected

Definition at line 462 of file navier_solver.hpp.

CGSolver* mfem::navier::NavierSolver::HInv = nullptr

protected

Definition at line 388 of file navier_solver.hpp.

Solver* mfem::navier::NavierSolver::HInvPC = nullptr

protected

Definition at line 387 of file navier_solver.hpp.

int mfem::navier::NavierSolver::iter_hsolve = 0

protected

Definition at line 445 of file navier_solver.hpp.

int mfem::navier::NavierSolver::iter_mvsolve = 0

protected

Definition at line 445 of file navier_solver.hpp.

int mfem::navier::NavierSolver::iter_spsolve = 0

protected

Definition at line 445 of file navier_solver.hpp.

double mfem::navier::NavierSolver::kin_vis

protected

Kinematic viscosity (dimensionless).

Definition at line 330 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::Lext

protected

Definition at line 390 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::Lext_gf

protected

Definition at line 396 of file navier_solver.hpp.

ParLinearForm* mfem::navier::NavierSolver::mass_lf = nullptr

protected

Linear form to compute the mass matrix in various subroutines.

Definition at line 365 of file navier_solver.hpp.

int mfem::navier::NavierSolver::max_bdf_order = 3

protected

Definition at line 418 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::Mv

protected

Definition at line 374 of file navier_solver.hpp.

ParBilinearForm* mfem::navier::NavierSolver::Mv_form = nullptr

protected

Definition at line 346 of file navier_solver.hpp.

ParBilinearForm* mfem::navier::NavierSolver::Mv_form_lor = nullptr

protected

Definition at line 456 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::Mv_lor

protected

Definition at line 460 of file navier_solver.hpp.

CGSolver* mfem::navier::NavierSolver::MvInv = nullptr

protected

Definition at line 381 of file navier_solver.hpp.

Solver* mfem::navier::NavierSolver::MvInvPC = nullptr

protected

Definition at line 380 of file navier_solver.hpp.

ParNonlinearForm* mfem::navier::NavierSolver::N = nullptr

protected

Definition at line 344 of file navier_solver.hpp.

ConstantCoefficient mfem::navier::NavierSolver::nlcoeff

protected

Definition at line 369 of file navier_solver.hpp.

bool mfem::navier::NavierSolver::numerical_integ = false

protected

Enable/disable numerical integration rules of forms.

Definition at line 321 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::Nun

protected

Definition at line 390 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::Nunm1

protected

Definition at line 390 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::Nunm2

protected

Definition at line 390 of file navier_solver.hpp.

ConstantCoefficient mfem::navier::NavierSolver::onecoeff

protected

Definition at line 366 of file navier_solver.hpp.

int mfem::navier::NavierSolver::order

protected

The order of the velocity and pressure space.

Definition at line 327 of file navier_solver.hpp.

bool mfem::navier::NavierSolver::partial_assembly = false

protected

Enable/disable partial assembly of forms.

Definition at line 318 of file navier_solver.hpp.

FiniteElementCollection* mfem::navier::NavierSolver::pfec = nullptr

protected

Pressure \(H^1\) finite element collection.

Definition at line 336 of file navier_solver.hpp.

FiniteElementCollection* mfem::navier::NavierSolver::pfec_lor = nullptr

protected

Definition at line 452 of file navier_solver.hpp.

ParFiniteElementSpace* mfem::navier::NavierSolver::pfes = nullptr

protected

Pressure \(H^1\) finite element space.

Definition at line 342 of file navier_solver.hpp.

ParFiniteElementSpace* mfem::navier::NavierSolver::pfes_lor = nullptr

protected

Definition at line 453 of file navier_solver.hpp.

InterpolationGridTransfer * mfem::navier::NavierSolver::pgt = nullptr

protected

Definition at line 454 of file navier_solver.hpp.

int mfem::navier::NavierSolver::pl_amg = 0

protected

Definition at line 438 of file navier_solver.hpp.

int mfem::navier::NavierSolver::pl_hsolve = 0

protected

Definition at line 437 of file navier_solver.hpp.

int mfem::navier::NavierSolver::pl_mvsolve = 0

protected

Definition at line 435 of file navier_solver.hpp.

int mfem::navier::NavierSolver::pl_spsolve = 0

protected

Definition at line 436 of file navier_solver.hpp.

ParMesh* mfem::navier::NavierSolver::pmesh = nullptr

protected

The parallel mesh.

Definition at line 324 of file navier_solver.hpp.

ParMesh* mfem::navier::NavierSolver::pmesh_lor = nullptr

protected

Definition at line 451 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::pn

protected

Definition at line 394 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::pn_gf

protected

Definition at line 399 of file navier_solver.hpp.

std::vector<PresDirichletBC_T> mfem::navier::NavierSolver::pres_dbcs

protected

Definition at line 413 of file navier_solver.hpp.

Array<int> mfem::navier::NavierSolver::pres_ess_attr

protected

Definition at line 403 of file navier_solver.hpp.

Array<int> mfem::navier::NavierSolver::pres_ess_tdof

protected

Definition at line 407 of file navier_solver.hpp.

double mfem::navier::NavierSolver::res_hsolve = 0.0

protected

Definition at line 448 of file navier_solver.hpp.

double mfem::navier::NavierSolver::res_mvsolve = 0.0

protected

Definition at line 448 of file navier_solver.hpp.

double mfem::navier::NavierSolver::res_spsolve = 0.0

protected

Definition at line 448 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::resp

protected

Definition at line 394 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::resp_gf

protected

Definition at line 399 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::resu

protected

Definition at line 390 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::resu_gf

protected

Definition at line 396 of file navier_solver.hpp.

double mfem::navier::NavierSolver::rtol_hsolve = 1e-8

protected

Definition at line 442 of file navier_solver.hpp.

double mfem::navier::NavierSolver::rtol_spsolve = 1e-6

protected

Definition at line 441 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::Sp

protected

Definition at line 375 of file navier_solver.hpp.

ConstantCoefficient mfem::navier::NavierSolver::Sp_coeff

protected

Definition at line 370 of file navier_solver.hpp.

ParBilinearForm* mfem::navier::NavierSolver::Sp_form = nullptr

protected

Definition at line 348 of file navier_solver.hpp.

ParBilinearForm* mfem::navier::NavierSolver::Sp_form_lor = nullptr

protected

Definition at line 457 of file navier_solver.hpp.

OperatorHandle mfem::navier::NavierSolver::Sp_lor

protected

Definition at line 461 of file navier_solver.hpp.

CGSolver* mfem::navier::NavierSolver::SpInv = nullptr

protected

Definition at line 385 of file navier_solver.hpp.

OrthoSolver* mfem::navier::NavierSolver::SpInvOrthoPC = nullptr

protected

Definition at line 384 of file navier_solver.hpp.

HypreBoomerAMG* mfem::navier::NavierSolver::SpInvPC = nullptr

protected

Definition at line 383 of file navier_solver.hpp.

StopWatch mfem::navier::NavierSolver::sw_curlcurl

protected

Definition at line 432 of file navier_solver.hpp.

StopWatch mfem::navier::NavierSolver::sw_extrap

protected

Definition at line 432 of file navier_solver.hpp.

StopWatch mfem::navier::NavierSolver::sw_hsolve

protected

Definition at line 432 of file navier_solver.hpp.

StopWatch mfem::navier::NavierSolver::sw_setup

protected

Definition at line 432 of file navier_solver.hpp.

StopWatch mfem::navier::NavierSolver::sw_spsolve

protected

Definition at line 432 of file navier_solver.hpp.

StopWatch mfem::navier::NavierSolver::sw_step

protected

Definition at line 432 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::tmp1

protected

Definition at line 392 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::un

protected

Definition at line 390 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::un_filtered_gf

protected

Definition at line 470 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::un_gf

protected

Definition at line 396 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::un_next

protected

Definition at line 390 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::un_next_gf

protected

Definition at line 396 of file navier_solver.hpp.

ParGridFunction mfem::navier::NavierSolver::un_NM1_gf

protected

Definition at line 469 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::unm1

protected

Definition at line 390 of file navier_solver.hpp.

Vector mfem::navier::NavierSolver::unm2

protected

Definition at line 390 of file navier_solver.hpp.

std::vector<VelDirichletBC_T> mfem::navier::NavierSolver::vel_dbcs

protected

Definition at line 410 of file navier_solver.hpp.

Array<int> mfem::navier::NavierSolver::vel_ess_attr

protected

Definition at line 402 of file navier_solver.hpp.

Array<int> mfem::navier::NavierSolver::vel_ess_tdof

protected

Definition at line 406 of file navier_solver.hpp.

bool mfem::navier::NavierSolver::verbose = true

protected

Enable/disable verbose output.

Definition at line 315 of file navier_solver.hpp.

FiniteElementCollection* mfem::navier::NavierSolver::vfec = nullptr

protected

Velocity \(H^1\) finite element collection.

Definition at line 333 of file navier_solver.hpp.

FiniteElementCollection* mfem::navier::NavierSolver::vfec_filter = nullptr

protected

Definition at line 467 of file navier_solver.hpp.

ParFiniteElementSpace* mfem::navier::NavierSolver::vfes = nullptr

protected

Velocity \((H^1)^d\) finite element space.

Definition at line 339 of file navier_solver.hpp.

ParFiniteElementSpace* mfem::navier::NavierSolver::vfes_filter = nullptr

protected

Definition at line 468 of file navier_solver.hpp.

InterpolationGridTransfer* mfem::navier::NavierSolver::vgt = nullptr

protected

Definition at line 454 of file navier_solver.hpp.

double mfem::navier::NavierSolver::volume = 0.0

protected

Definition at line 367 of file navier_solver.hpp.

The documentation for this class was generated from the following files:

miniapps/navier/navier_solver.hpp
miniapps/navier/navier_solver.cpp

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