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

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

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

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

Public Member Functions
template<class Entity , class Point >
void	source (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
	The zero-order term as function of local coordinates. More...
template<class Entity , class Point >
void	linearizedSource (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
	The linearized source term as function of local coordinates. More...
void	setEntity (const Entity &entity) const
bool	setIntersection (const Intersection &intersection) const
void	flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
void	linearizedFlux (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
void	robinFlux (const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const
void	linearizedRobinFlux (const RangeType &uBar, const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const
void	fluxDivergence (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, const HessianRangeType &hessian, 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::IncompressibleSelfTransportOperatorParts< FunctionSpace >

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

This fragment models the change in momentum caused by the transport via the velocity field of the fluid on the fluid itself. This forms half of the so called "material derivative" for time-dependent flows and the entire material derivative for stationary flow problems. The "material derivative" of the velocity field of the fluid is the change of the velocity measured by an observier moving with the fluid.

In formulas: this fragment implements the non-linear "source" term

\[ \int_\Omega U_i\,\partial_i U_j\,\phi_j \]

Of course, the formula uses sum-convention. There is also another variant available which move the derivative away from U to the test-function at the cost of introducing a boundary integral.

See also

FluidSelfTransportOperatorParts, DeformationTensorOperatorParts, Transport/Advection Models

Member Enumeration Documentation

ConstituentFlags

enum Dune::ACFem::DefaultOperatorParts::ConstituentFlags

inherited

StructureFlags

enum Dune::ACFem::DefaultOperatorParts::StructureFlags

inherited

Member Function Documentation

flux()

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

inlineinherited

fluxDivergence()

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

inlineinherited

linearizedFlux()

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

inlineinherited

linearizedRobinFlux()

void Dune::ACFem::DefaultOperatorParts< Expression >::linearizedRobinFlux ( const RangeType &  uBar, const Intersection &  intersection, const Point &  x, const DomainType &  unitOuterNormal, const RangeType &  value, RangeType &  result  ) const

inlineinherited

robinFlux()

void Dune::ACFem::DefaultOperatorParts< Expression >::robinFlux ( const Intersection &  intersection, const Point &  x, const DomainType &  unitOuterNormal, const RangeType &  value, RangeType &  result  ) const

inlineinherited

setEntity()

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

inlineinherited

setIntersection()

bool Dune::ACFem::DefaultOperatorParts< Expression >::setIntersection ( const Intersection &  intersection ) const

inlineinherited

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

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