Class for the computation of the standard version ('Voss-Souza-type') of the consistent gravity. More...

#include <consistent_gravity.h>

Inheritance diagram for ug::StdLinConsistentGravity< refDim >:

Public Member Functions
template<int dim>
void	compute (MathVector< dim > &ConsistentGravity, const MathVector< refDim > &LocalCoord, const MathMatrix< dim, refDim > &JTInv, const MathVector< refDim > vLocalGrad, const MathVector< refDim > vConsGravity)
	computation of the consistent gravity at a given point More...

void	prepare (MathVector< 1 > vConsGravity, const int n_co, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	spacialization of the method for edges (reference dimension 1) More...

void	prepare (MathVector< 2 > vConsGravity, const int n_co, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	spacialization of the method for faces (reference dimension 2) More...

void	prepare (MathVector< 3 > vConsGravity, const int n_co, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	spacialization of the method for volumes (reference dimension 3) More...

template<int dim>
void	prepare (MathVector< refDim > vConsGravity, const int n_co, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners, cf. the specializations More...

	StdLinConsistentGravity ()
	constructor (sets the 'not init.' flag) More...

Protected Member Functions
template<int dim>
void	prepare_edge (MathVector< 1 > vConsGravity, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners of an edge More...

template<int dim>
void	prepare_hexahedron (MathVector< 3 > vConsGravity, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners of a hexahedron More...

template<int dim>
void	prepare_prism (MathVector< 3 > vConsGravity, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners of a prism More...

template<int dim>
void	prepare_pyramid (MathVector< 3 > vConsGravity, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners of a pyramid More...

template<int dim>
void	prepare_quadrilateral (MathVector< 2 > vConsGravity, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners of a quadrilateral More...

template<int dim>
void	prepare_tetrahedron (MathVector< 3 > vConsGravity, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners of a tetrahedron More...

template<int dim>
void	prepare_triangle (MathVector< 2 > vConsGravity, const MathVector< dim > vCorners, const number *vDensity, const MathVector< dim > &PhysicalGravity)
	computation of the primary function for the consistent gravity at corners of a triangle More...

Protected Attributes
int	m_nCo
	number of corners of the element for which the object is init. (0 if not init) More...

Static Private Attributes
static const size_t	_X_ = 0

static const size_t	_Y_ = 1

static const size_t	_Z_ = 2

Detailed Description

template<int refDim>
class ug::StdLinConsistentGravity< refDim >

Class for the computation of the standard version ('Voss-Souza-type') of the consistent gravity.

Density driven flow models involve the convection velocity depending on the gradient of the pressure and the density-dependent gravity force, typically of the form \(\mathbf{v} = \mathbf{K} (- \nabla p + \rho \mathbf{g}) / \mu\), where \(\mathbf{K}\) is a matrix, \(\mu\) a scalar, \(\mathbf{g}\) gravity vector (all independent of \(p\) or \(\rho\)), \(p\) is pressure, \(rho\) is density (depending on the concentration, ...). (Both the pressure and the concentration are unknown grid functions in the PDEs.) Treating \(p\) and \(\rho\) as grid functions of the same class (like the piecewise linear/bilinear interpolations of nodal values) leads to oscillatory solutions because \(\nabla p\) and \(\rho \mathbf{g}\) belong to different classes of grid functions. In particular, if \(p\) is a piecewise linear function, \(\nabla p\) can never cancel the of the gravitaty force if \(\rho\) increases linearly from the top down, although this happens in the analytical solution. The idea of the consistent gravity is to consider a vector function \(\mathbf{h} = (h_x, h_y, \dots)\) that is in some sence a primitive function for \(\rho \mathbf{g}\) so that the velocity can be written as \(\mathbf{v} = - \mathbf{K} (p_x - h_x, p_y - h_y, \dots) / \mu\). In the discretization, the function \(\mathbf{h}\) should belong to the same class of the grid functions as \(p\). In the present implementation, \(\mathbf{h}\) is a piecewise linear/bilinear grid function.

Class method 'prepare' computes the values of \(h\) at the corners of an element. Using these values, method 'compute' computes the consistent gravity force \(\rho \mathbf{g}\) (not \(\mathbf{h}\)!) at any given point.

Remarks: (Consistent gravity in the computation of the Jacobian) The consistent gravity computed by the implemented methods depends linearly on the density. Thus, to compute the derivative of the consistent gravity w.r.t. the density at one of the corners of the element, set the density to 1 at that corner and to 0 at all other corners, then call the functions. Then 'prepare' prepares the nodal values of the derivatives and 'compute' computes the derivative itself.

Alternatively, you can set the density at that corner to the derivative of the density w.r.t. the concentration (instead of 1). Then you get directly the derivative of the consistent gravity w.r.t. the concentration at that node.

Remarks: There is an enhanced version of the consistent gravity.

See also: StdLinConsistentGravityX

References:

P. Frolkovic, P. Knabner, Consistent Velocity Approximations in Finite Element or Volume Discretizations of Density Driven Flow, In: Computational Methods in WaterResources XI, Vol. 1 (A.A. Aldama et al., eds.), Computational Mechanics Publication, Southhampten, 1996, p. 93-100

Template Parameters

refDim dimensionality of the reference element (e.g. 2 for triangles, 3 for tetrahedra)

Constructor & Destructor Documentation

◆ StdLinConsistentGravity()

template<int refDim>

ug::StdLinConsistentGravity< refDim >::StdLinConsistentGravity ( )

inline

constructor (sets the 'not init.' flag)

Member Function Documentation

◆ compute()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::compute	(	MathVector< dim > &	ConsistentGravity,
		const MathVector< refDim > &	LocalCoord,
		const MathMatrix< dim, refDim > &	JTInv,
		const MathVector< refDim > *	vLocalGrad,
		const MathVector< refDim > *	vConsGravity
	)

inline

computation of the consistent gravity at a given point

Parameters

ConsistentGravity	where to save the vector
LocalCoord	local coordinates of the point
JTInv	inverse transposed Jacobian
vLocalGrad	gradients of the shape functions at the given point
vConsGravity	primary function of the consistent gravity at corners

References ug::StdLinConsistentGravity< refDim >::m_nCo, ug::MatVecMult(), UG_ASSERT, and ug::VecSet().

◆ prepare() [1/4]

void ug::StdLinConsistentGravity< 1 >::prepare	(	MathVector< 1 > *	vConsGravity,
		const int	n_co,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

spacialization of the method for edges (reference dimension 1)

Parameters

vConsGravity	where to save the values (n_co vectors)
n_co	number of corners of the element (should be 2)
vCorners	(global) coordinates of the corners (n_co vectors)
vDensity	corner density (n_co scalar values)
PhysicalGravity	the gravity vector

References UG_ASSERT.

◆ prepare() [2/4]

void ug::StdLinConsistentGravity< 2 >::prepare	(	MathVector< 2 > *	vConsGravity,
		const int	n_co,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

spacialization of the method for faces (reference dimension 2)

Parameters

vConsGravity	where to save the values (n_co vectors)
n_co	number of corners of the element
vCorners	(global) coordinates of the corners (n_co vectors)
vDensity	corner density (n_co scalar values)
PhysicalGravity	the gravity vector

References UG_THROW.

◆ prepare() [3/4]

void ug::StdLinConsistentGravity< 3 >::prepare	(	MathVector< 3 > *	vConsGravity,
		const int	n_co,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

spacialization of the method for volumes (reference dimension 3)

Parameters

vConsGravity	where to save the values (n_co vectors)
n_co	number of corners of the element
vCorners	(global) coordinates of the corners (n_co vectors)
vDensity	corner density (n_co scalar values)
PhysicalGravity	the gravity vector

References UG_THROW.

◆ prepare() [4/4]

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare	(	MathVector< refDim > *	vConsGravity,
		const int	n_co,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inline

computation of the primary function for the consistent gravity at corners, cf. the specializations

Parameters

vConsGravity	where to save the values (n_co vectors)
n_co	number of corners of the element
vCorners	(global) coordinates of the corners (n_co vectors)
vDensity	corner density (n_co scalar values)
PhysicalGravity	the gravity vector

References dim, and UG_THROW.

◆ prepare_edge()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare_edge	(	MathVector< 1 > *	vConsGravity,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inlineprotected

computation of the primary function for the consistent gravity at corners of an edge

Parameters

vConsGravity	where to save the values (2 vectors)
vCorners	(global) coordinates of the corners (2 vectors)
vDensity	corner density (2 scalar values)
PhysicalGravity	the gravity vector

References ug::StdLinConsistentGravity< refDim >::_X_, ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed(), ug::MatVecMult(), ug::ReferenceMapping< TRefElem, TWorldDim >::update(), and ug::VecSet().

◆ prepare_hexahedron()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare_hexahedron	(	MathVector< 3 > *	vConsGravity,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inlineprotected

computation of the primary function for the consistent gravity at corners of a hexahedron

Parameters

vConsGravity	where to save the values (8 vectors)
vCorners	(global) coordinates of the corners (8 vectors)
vDensity	corner density (8 scalar values)
PhysicalGravity	the gravity vector

References ug::StdLinConsistentGravity< refDim >::_X_, ug::StdLinConsistentGravity< refDim >::_Y_, ug::StdLinConsistentGravity< refDim >::_Z_, ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed(), ug::MatVecMult(), and ug::ReferenceMapping< TRefElem, TWorldDim >::update().

◆ prepare_prism()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare_prism	(	MathVector< 3 > *	vConsGravity,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inlineprotected

computation of the primary function for the consistent gravity at corners of a prism

Parameters

vConsGravity	where to save the values (6 vectors)
vCorners	(global) coordinates of the corners (6 vectors)
vDensity	corner density (6 scalar values)
PhysicalGravity	the gravity vector

References ug::StdLinConsistentGravity< refDim >::_X_, ug::StdLinConsistentGravity< refDim >::_Y_, ug::StdLinConsistentGravity< refDim >::_Z_, ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed(), ug::MatVecMult(), and ug::ReferenceMapping< TRefElem, TWorldDim >::update().

◆ prepare_pyramid()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare_pyramid	(	MathVector< 3 > *	vConsGravity,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inlineprotected

computation of the primary function for the consistent gravity at corners of a pyramid

TODO: Verify this implementation! Cf. UG3.

Parameters

vConsGravity	where to save the values (5 vectors)
vCorners	(global) coordinates of the corners (5 vectors)
vDensity	corner density (5 scalar values)
PhysicalGravity	the gravity vector

References ug::StdLinConsistentGravity< refDim >::_X_, ug::StdLinConsistentGravity< refDim >::_Y_, ug::StdLinConsistentGravity< refDim >::_Z_, ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed(), ug::MatVecMult(), and ug::ReferenceMapping< TRefElem, TWorldDim >::update().

◆ prepare_quadrilateral()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare_quadrilateral	(	MathVector< 2 > *	vConsGravity,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inlineprotected

computation of the primary function for the consistent gravity at corners of a quadrilateral

Parameters

vConsGravity	where to save the values (4 vectors)
vCorners	(global) coordinates of the corners (4 vectors)
vDensity	corner density (4 scalar values)
PhysicalGravity	the gravity vector

References ug::StdLinConsistentGravity< refDim >::_X_, ug::StdLinConsistentGravity< refDim >::_Y_, ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed(), ug::MatVecMult(), ug::ReferenceMapping< TRefElem, TWorldDim >::update(), and ug::VecSet().

◆ prepare_tetrahedron()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare_tetrahedron	(	MathVector< 3 > *	vConsGravity,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inlineprotected

computation of the primary function for the consistent gravity at corners of a tetrahedron

Parameters

vConsGravity	where to save the values (4 vectors)
vCorners	(global) coordinates of the corners (4 vectors)
vDensity	corner density (4 scalar values)
PhysicalGravity	the gravity vector

References ug::StdLinConsistentGravity< refDim >::_X_, ug::StdLinConsistentGravity< refDim >::_Y_, ug::StdLinConsistentGravity< refDim >::_Z_, ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed(), ug::MatVecMult(), and ug::ReferenceMapping< TRefElem, TWorldDim >::update().

◆ prepare_triangle()

template<int refDim>

template<int dim>

void ug::StdLinConsistentGravity< refDim >::prepare_triangle	(	MathVector< 2 > *	vConsGravity,
		const MathVector< dim > *	vCorners,
		const number *	vDensity,
		const MathVector< dim > &	PhysicalGravity
	)

inlineprotected

computation of the primary function for the consistent gravity at corners of a triangle

Parameters

vConsGravity	where to save the values (3 vectors)
vCorners	(global) coordinates of the corners (3 vectors)
vDensity	corner density (3 scalar values)
PhysicalGravity	the gravity vector

References ug::StdLinConsistentGravity< refDim >::_X_, ug::StdLinConsistentGravity< refDim >::_Y_, ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed(), ug::MatVecMult(), ug::ReferenceMapping< TRefElem, TWorldDim >::update(), and ug::VecSet().

Member Data Documentation

◆ _X_

template<int refDim>

const size_t ug::StdLinConsistentGravity< refDim >::_X_ = 0

staticprivate

Referenced by ug::StdLinConsistentGravity< refDim >::prepare_edge(), ug::StdLinConsistentGravity< refDim >::prepare_hexahedron(), ug::StdLinConsistentGravity< refDim >::prepare_prism(), ug::StdLinConsistentGravity< refDim >::prepare_pyramid(), ug::StdLinConsistentGravity< refDim >::prepare_quadrilateral(), ug::StdLinConsistentGravity< refDim >::prepare_tetrahedron(), and ug::StdLinConsistentGravity< refDim >::prepare_triangle().

◆ _Y_

template<int refDim>

const size_t ug::StdLinConsistentGravity< refDim >::_Y_ = 1

staticprivate

Referenced by ug::StdLinConsistentGravity< refDim >::prepare_hexahedron(), ug::StdLinConsistentGravity< refDim >::prepare_prism(), ug::StdLinConsistentGravity< refDim >::prepare_pyramid(), ug::StdLinConsistentGravity< refDim >::prepare_quadrilateral(), ug::StdLinConsistentGravity< refDim >::prepare_tetrahedron(), and ug::StdLinConsistentGravity< refDim >::prepare_triangle().

◆ _Z_

template<int refDim>

const size_t ug::StdLinConsistentGravity< refDim >::_Z_ = 2

staticprivate

Referenced by ug::StdLinConsistentGravity< refDim >::prepare_hexahedron(), ug::StdLinConsistentGravity< refDim >::prepare_prism(), ug::StdLinConsistentGravity< refDim >::prepare_pyramid(), and ug::StdLinConsistentGravity< refDim >::prepare_tetrahedron().

◆ m_nCo

template<int refDim>

int ug::StdLinConsistentGravity< refDim >::m_nCo

protected

number of corners of the element for which the object is init. (0 if not init)

Referenced by ug::StdLinConsistentGravity< refDim >::compute().

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

ugbase/lib_disc/spatial_disc/disc_util/consistent_gravity.h

Public Member Functions

Protected Member Functions

Protected Attributes

Static Private Attributes

Detailed Description

template<int refDim> class ug::StdLinConsistentGravity< refDim >

Constructor & Destructor Documentation

◆ StdLinConsistentGravity()

Member Function Documentation

◆ compute()

◆ prepare() [1/4]

◆ prepare() [2/4]

◆ prepare() [3/4]

◆ prepare() [4/4]

◆ prepare_edge()

◆ prepare_hexahedron()

◆ prepare_prism()

◆ prepare_pyramid()

◆ prepare_quadrilateral()

◆ prepare_tetrahedron()

◆ prepare_triangle()

Member Data Documentation

◆ _X_

◆ _Y_

◆ _Z_

◆ m_nCo

template<int refDim>
class ug::StdLinConsistentGravity< refDim >