Dune::ACFem::FluidSelfTransportOperatorParts< FunctionSpace > Class Template Reference

Define a model for the "Navier-Stokes" non-lineariry. More...

#include <dune/acfem/models/modules/fluidselftransportmodel.hh>

Public Types
enum	StructureFlags
enum	ConstituentFlags
typedef Expression	ExpressionType
	The type of the underlying expression.

Public Member Functions
template<class Intersection >
bool	setIntersection (const Intersection &intersection) const
	Per-intersection initialization for the boundary contributions. More...
template<class Entity , class Point >
void	flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
	Evaluate \(A(x, u)\nabla u(x)\) in local coordinates. More...
template<class Entity , class Point >
void	linearizedFlux (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
	Evaluate the linearized flux in local coordinates. More...
template<class Entity , class Point >
void	fluxDivergence (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, const HessianRangeType &hessian, RangeType &result) const
	Compute the point-wise value of the flux-part of the operator, meaning the part of the differential operator which is multiplied by the derivative of the test function. More...
void	setEntity (const Entity &entity) const
void	source (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
void	linearizedSource (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
const ExpressionType &	expression () const
	Return a const reference to the underlying expression.
ExpressionType &	expression ()
	Return a mutable reference to the underlying expression.
ExpressionType	operator* () const
	Return a copy from of the underlying expression.

Detailed Description

template<class FunctionSpace>
class Dune::ACFem::FluidSelfTransportOperatorParts< FunctionSpace >

Define a model for the "Navier-Stokes" non-lineariry.

An alternate formulation of the the Navier-Stokes non-linearity obtained by integration by parts, at the cost of introducting a boundary integral for non-Dirichlet boundaries

In formulas: this fragment implements the right-hand-side of the following equation (where the equality only holds for \(\nabla\cdot U = 0\)):

\[ \int_\Omega U_i\,\partial_i U_j\,\phi_j = - \int_\Omega U_i\,U_j\,\partial_i\phi_j + \int_{\partial\Omega} U\cdot\nu\,U\cdot\phi \]

Of course, the formula uses sum-convention. The left-hand-side is implemented by IncompressibleSelfTransportModel.

See also

IncompressibleSelfTransportModel, DeformationTensorModel, Transport/Advection Models

Parameters

GridPart

The grid-part we live on.

Member Enumeration Documentation

ConstituentFlags

enum Dune::ACFem::DefaultOperatorParts::ConstituentFlags

inherited

StructureFlags

enum Dune::ACFem::DefaultOperatorParts::StructureFlags

inherited

Member Function Documentation

linearizedSource()

void Dune::ACFem::DefaultOperatorParts< Expression >::linearizedSource ( const RangeType &  uBar, const JacobianRangeType &  DuBar, const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, RangeType &  result  ) const

inlineinherited

setEntity()

void Dune::ACFem::DefaultOperatorParts< Expression >::setEntity ( const Entity &  entity ) const

inlineinherited

source()

void Dune::ACFem::DefaultOperatorParts< Expression >::source ( const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, RangeType &  result  ) const

inlineinherited

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

• dune/acfem/models/modules/fluidselftransportmodel.hh