Dune::PDELab::TaylorHoodNavierStokes< P > Class Template Reference

A local operator for the Navier-Stokes equations. More...

#include <dune/pdelab/localoperator/taylorhoodnavierstokes.hh>

Public Types
using	BC = StokesBoundaryCondition
	Boundary condition indicator type.
Flags selective assembly
enum
	Whether to do selective assembly on the elements, i.e. whether or not skip_entity() should be called.
enum
	Whether to do selective assembly on the intersections, i.e. whether or not skip_intersection() should be called.
Flags for the sparsity pattern
enum
	Whether to assemble the pattern on the elements, i.e. whether or not pattern_volume() should be called.
enum
	Whether to assemble the pattern on the elements after the skeleton has been handled, i.e. whether or not pattern_volume_post_skeleton() should be called.
enum
	Whether to assemble the pattern on the interior intersections, i.e. whether or not pattern_skeleton() should be called.
enum
	Whether to assemble the pattern on the boundary intersections, i.e. whether or not pattern_boundary() should be called.
Flags for the non-constant part of the residual and the jacobian
enum
	Whether to call the local operator's alpha_volume(), jacobian_apply_volume() and jacobian_volume().
enum
	Whether to call the local operator's alpha_volume_post_skeleton(), jacobian_apply_volume_post_skeleton() and jacobian_volume_post_skeleton().
enum
	Whether to call the local operator's alpha_skeleton(), jacobian_apply_skeleton() and jacobian_skeleton().
enum
	Whether to call the local operator's alpha_boundary(), jacobian_apply_boundary() and jacobian_boundary().
Flags for the constant part of the residual
enum
	Whether to call the local operator's lambda_volume().
enum
	Whether to call the local operator's lambda_volume_post_skeleton().
enum
	Whether to call the local operator's lambda_skeleton().
enum
	Whether to call the local operator's lambda_boundary().
Special flags
enum
	Whether to visit the skeleton methods from both sides.
enum
	Wheter the local operator describes a linear problem.

Public Member Functions
void	setTime (P::Traits::RangeField t_)
	set time for subsequent evaluation More...
P::Traits::RangeField	getTime () const
	get current time More...
void	preStep (RealType time, RealType dt, int stages)
	to be called once before each time step More...
void	postStep ()
	to be called once at the end of each time step More...
void	preStage (RealType time, int r)
	to be called once before each stage More...
int	getStage () const
	get current stage More...
void	postStage ()
	to be called once at the end of each stage
RealType	suggestTimestep (RealType dt) const
	to be called after stage 1 More...

Detailed Description

template<typename P>
class Dune::PDELab::TaylorHoodNavierStokes< P >

A local operator for the Navier-Stokes equations.

This class implements a local operator for conforming finite element discretizations of the Navier-Stokes equations with TaylorHood basis.

\begin{align*} u \cdot \nabla u \cdot v - \nabla \cdot ( \nabla u + (\nabla u)^T + p I) &=& 0 \mbox{ in } \Omega, \\ \nabla \cdot u &=& 0 \mbox{ in } \Omega \\ u &=& g \mbox{ on } \partial\Omega_D \\ -\nu (\nabla u + p I ) \nu &=& j \mbox{ on } \partial\Omega_N \\ \end{align*}

As indicated in the equation above, this implementation utilizes only scalar Neumann conditions.

Template Parameters

P	A suitable parameter class with the interface of TaylorHoodNavierStokesDefaultParameters

Member Function Documentation

getStage()

int Dune::PDELab::InstationaryLocalOperatorDefaultMethods< P::Traits::RangeField >::getStage ( ) const

inlineinherited

get current stage

Returns

The current stage number previously set by preStage().

getTime()

P::Traits::RangeField Dune::PDELab::InstationaryLocalOperatorDefaultMethods< P::Traits::RangeField >::getTime ( ) const

inlineinherited

get current time

Returns

The time previously set by setTime().

postStep()

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< P::Traits::RangeField >::postStep ( )

inlineinherited

to be called once at the end of each time step

Note

With the OneStepMethod and the ExplicitOneStepMetod, for reasons unknown this is only called for temporal but not for spatial local operators. With the MultiStepMethod this is called for all local operators.

preStage()

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< P::Traits::RangeField >::preStage ( RealType  time, int  r  )

inlineinherited

to be called once before each stage

Parameters

time	Time of the stage
r	Number of the stage, r ∈ [1, nstages] inclusive, where nstages is the number of stage in the step given in the previous call to preStep()

Note

For ExplicitOneStepMethod the time given here for stage 1 may be incorrect, since the time step size is only finally determined after the first stage has been assembled.

For the MultiStepMethod, this is called once after preStep() with r=1.

preStep()

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< P::Traits::RangeField >::preStep ( RealType  time, RealType  dt, int  stages  )

inlineinherited

to be called once before each time step

Parameters

time	Time at beginning of the step.
dt	Size of time step.
stages	Number of stages to do in the step. For the MultiStepMethod this is always 1.

Note

For ExplicitOneStepMethod the dt given here may be incorrect, since the time step size is only finally determined after the first stage has been assembled.

For the MultiStepMethod the number of stages is given as

1. Since there are no times of evaluation in the middle of the step, a multi-step method is similar to a one step method with one stage.

setTime()

void Dune::PDELab::InstationaryLocalOperatorDefaultMethods< P::Traits::RangeField >::setTime ( P::Traits::RangeField  t_ )

inlineinherited

set time for subsequent evaluation

This method set the time for subsequent calls to the alpha_*(), lambda_*(), jacobian_*() and jacobian_apply_*() methods.

Note

For ExplicitOneStepMethod the time given here in the first stage may be incorrect, since the time step size is only finally determined after the first stage has been assembled.

suggestTimestep()

RealType Dune::PDELab::InstationaryLocalOperatorDefaultMethods< P::Traits::RangeField >::suggestTimestep ( RealType  dt ) const

inlineinherited

to be called after stage 1

Note

Only used by the ExplicitOneStepMethod.

This may be called on the spatial local operator in the case of an explicit one step scheme. It is called after stage 1 has been assembled (so the time given to preStep() may not apply anymore in this case). All the alpha_*() and lambda_*() methods should have been called, so they are a good place to generate the information returned here.

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

• dune/pdelab/localoperator/taylorhoodnavierstokes.hh