Burgers operator assembly class. More...

#include <burgers_assembler_carreau.hpp>

Public Types
typedef DataType_	DataType
	the datatype we use here More...

Public Member Functions
	BurgersAssemblerCarreau ()
	default constructor More...

template<typename Space_ , typename CubatureFactory_ >
void	assemble_matrix (LAFEM::SparseMatrixBCSR< DataType_, IndexType_, dim_, dim_ > &matrix, const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &convect, const Space_ &space, const CubatureFactory_ &cubature_factory, const DataType_ scale=DataType_(1)) const
	Assembles the Burgers operator into a matrix. More...

template<typename Space_ , typename CubatureFactory_ >
void	assemble_vector (LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &vector, const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &convect, const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &primal, const Space_ &space, const CubatureFactory_ &cubature_factory, const DataType_ scale=DataType_(1)) const
	Assembles the Burgers operator into a vector. More...

template<typename LocalVector_ , typename Mirror_ >
void	set_sd_v_norm (const Global::Vector< LocalVector_, Mirror_ > &convect)
	Sets the convection field norm \(\\|v\\|_\Omega\) for the streamline diffusion parameter delta_T. More...

void	set_sd_v_norm (const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &convect)
	Sets the convection field norm \(\\|v\\|_\Omega\) for the local streamline diffusion parameter delta_T. More...

Public Attributes
DataType_	a

DataType_	beta
	scaling parameter for convective operator K More...

bool	deformation
	specifies whether to use the deformation tensor More...

bool	diff

DataType_	frechet_beta
	scaling parameter for Frechet derivative of convective operator K' More...

bool	frechet_diff

DataType_	lambda

DataType_	mu_0

DataType_	mu_inf
	Carreau Data Parameter. More...

DataType_	n

DataType_	reg_eps

DataType_	sd_delta
	scaling parameter for streamline diffusion stabilization operator S More...

DataType_	sd_nu
	viscosity parameter nu_S for streamline diffusion (usually equal to nu) More...

DataType_	sd_v_norm
	velocity norm for streamline diffusion More...

DataType_	theta
	scaling parameter for diffusive operator L (aka viscosity) More...

Detailed Description

template<typename DataType_, typename IndexType_, int dim_>
class FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >

Burgers operator assembly class.

This class is responsible for assembling the scalar and vector-valued Burgers operators:

\[\mathbf{N}(v,u,\psi) := \nu \mathbf{L}(u,\psi) + \theta \mathbf{M}(u,\psi) + \beta \mathbf{K}(v,u,\psi) + \beta' \mathbf{K'(v,u,\psi)} + \delta \mathbf{S}(v,u,\psi)\]

where

L is the diffusive operator, which is either
- the gradient tensor:
  \[\mathbf{L}(u,\psi) := \int_\Omega \nabla u \cdot \nabla \psi \]
- or the deformation tensor:
  \[\mathbf{L}(u,\psi) := \frac{1}{4} \int_\Omega (\nabla+\nabla^\top) u : (\nabla+\nabla^\top) \psi\]
M is the reactive operator:
\[\mathbf{M}(u,\psi) := \int_\Omega u\psi\]
K is the convective operator:
\[\mathbf{K}(v,u,\psi) := \int_\Omega v\cdot \nabla u \psi\]
K' is the Frechet derivative of the convective operator:
\[\mathbf{K'}(v,u,\psi) := \int_\Omega \nabla v u \psi\]
S is the Samarskij-style streamline-diffusion stabilization operator:
\[\mathbf{S}(v,u,\psi) := \sum_{T\in\mathcal{T}_h}\delta_{T}\int_T (v\cdot\nabla u)\cdot(v\cdot\nabla\psi)\]
where
\[\delta_T := \frac{h_T}{\|v\|_\Omega}\cdot\frac{2Re_T}{1+Re_T}\qquad\textnormal{and}\qquad Re_T := \frac{\|v\|_T\cdot h_T}{\nu_\mathbf{S}}\]

Notes on Streamline Diffusion Stabilization:
The implementation of the streamline diffusion stabilization is based on Turek's CFD book (see [TurekCFD], pages 119 – 123), however, in the formula above, the local stabilization parameter \(\delta_T\) is not pre- multiplied by the global parameter \(\delta^*\), compare eq. (3.75) in the book, as we use delta as a scaling parameter for the whole operator S in the definition of the full operator N, see above. To enable streamline diffusion stabilization, you have to perform several tasks:

Set the global stabilization parameter sd_delta, which corresponds to the delta* parameter in the CFD book. According to the book (and previous FEAT versions), the value should be in range [0.1, 2], but according to my personal experience, even smaller values may be a good choice (e.g. 0.02).
Set the viscosity parameter sd_nu, which is usually set equal to nu. The only reason for this extra parameter is so that you can use this assembler class to assemble the stabilization without necessarily also assembling the diffusion operator, which is what would happen if you set nu to a non-zero value.
Set the (maximum) velocity norm sd_v_norm of the convection field, which corresponds to \(\|v\|_\Omega\) and is required for the computation of the local delta_T parameters. You can do this by either specifying the value directly or, more conveniently, use one of this class's set_sd_v_norm() functions to compute this norm from a (local or global) convection field vector.

Author: Jonas Dünnebacke (based on Peter Zajacs BurgersAssembler)

Definition at line 63 of file burgers_assembler_carreau.hpp.

Member Typedef Documentation

◆ DataType

template<typename DataType_ , typename IndexType_ , int dim_>

typedef DataType_ FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::DataType

the datatype we use here

Definition at line 67 of file burgers_assembler_carreau.hpp.

Constructor & Destructor Documentation

◆ BurgersAssemblerCarreau()

template<typename DataType_ , typename IndexType_ , int dim_>

FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::BurgersAssemblerCarreau ( )

inline

default constructor

Definition at line 102 of file burgers_assembler_carreau.hpp.

Member Function Documentation

◆ assemble_matrix()

template<typename DataType_ , typename IndexType_ , int dim_>

template<typename Space_ , typename CubatureFactory_ >

void FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_matrix	(	LAFEM::SparseMatrixBCSR< DataType_, IndexType_, dim_, dim_ > &	matrix,
		const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &	convect,
		const Space_ &	space,
		const CubatureFactory_ &	cubature_factory,
		const DataType_	scale = `DataType_(1)`
	)		const

inline

Assembles the Burgers operator into a matrix.

Parameters

[in,out]	matrix	The transient matrix to be assembled.
[in]	convect	The transient transport vector for the convection.
[in]	space	The transient velocity space.
[in]	cubature_factory	The transient cubature factory to be used for integration.
[in]	scale	A scaling factor for the matrix to be assembled.

Definition at line 140 of file burgers_assembler_carreau.hpp.

References FEAT::Math::abs(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::beta, FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::columns(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::deformation, FEAT::Tiny::dot(), FEAT::Tiny::Vector< T_, n_, s_ >::format(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::frechet_beta, FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::mu_inf, FEAT::Math::pow(), FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::rows(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::sd_delta, FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::sd_v_norm, FEAT::LAFEM::DenseVectorBlocked< DT_, IT_, BlockSize_ >::size(), FEAT::Math::sqrt(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::theta, FEAT::value, XASSERT, and XASSERTM.

◆ assemble_vector()

template<typename DataType_ , typename IndexType_ , int dim_>

template<typename Space_ , typename CubatureFactory_ >

void FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_vector	(	LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &	vector,
		const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &	convect,
		const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > &	primal,
		const Space_ &	space,
		const CubatureFactory_ &	cubature_factory,
		const DataType_	scale = `DataType_(1)`
	)		const

inline

Assembles the Burgers operator into a vector.

Parameters

[in,out]	vector	The transient vector to be assembled.
[in]	convect	The transient transport vector for the convection.
[in]	primal	The transient primal vector, usually a solution vector.
[in]	space	The transient velocity space.
[in]	cubature_factory	The transient cubature factory to be used for integration.
[in]	scale	A scaling factor the vector to be assembled.

Definition at line 516 of file burgers_assembler_carreau.hpp.

References FEAT::Math::abs(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::add_outer_product(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::axpy(), FEAT::Tiny::Vector< T_, n_, s_ >::axpy(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::beta, FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::deformation, FEAT::Tiny::dot(), FEAT::Tiny::Vector< T_, n_, s_ >::format(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::format(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::mu_inf, FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_frobenius(), FEAT::Math::pow(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_transpose(), FEAT::LAFEM::DenseVectorBlocked< DT_, IT_, BlockSize_ >::size(), FEAT::Math::sqrt(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::theta, FEAT::value, and XASSERTM.

◆ set_sd_v_norm() [1/2]

template<typename DataType_ , typename IndexType_ , int dim_>

template<typename LocalVector_ , typename Mirror_ >

void FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::set_sd_v_norm ( const Global::Vector< LocalVector_, Mirror_ > & convect )

inline

Sets the convection field norm \(\|v\|_\Omega\) for the streamline diffusion parameter delta_T.

Note: This function automatically syncs the norm over all processes by using the vector's gate.

Parameters

[in] convect The transient (global) convection field vector.

Definition at line 788 of file burgers_assembler_carreau.hpp.

References FEAT::Global::Vector< LocalVector_, Mirror_ >::get_gate(), FEAT::Global::Vector< LocalVector_, Mirror_ >::local(), FEAT::Global::Gate< LocalVector_, Mirror_ >::max(), and FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::set_sd_v_norm().

◆ set_sd_v_norm() [2/2]

template<typename DataType_ , typename IndexType_ , int dim_>

void FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::set_sd_v_norm ( const LAFEM::DenseVectorBlocked< DataType_, IndexType_, dim_ > & convect )

inline

Sets the convection field norm \(\|v\|_\Omega\) for the local streamline diffusion parameter delta_T.

Parameters

[in] convect The transient (local) convection field vector.

Definition at line 769 of file burgers_assembler_carreau.hpp.

References FEAT::LAFEM::DenseVectorBlocked< DT_, IT_, BlockSize_ >::elements(), FEAT::Math::max(), and FEAT::LAFEM::DenseVectorBlocked< DT_, IT_, BlockSize_ >::size().

Referenced by FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::set_sd_v_norm().