dg::Advection< Geometry, Matrix, Container > Struct Template Reference

Upwind discretization of advection operator \( \vec v\cdot\nabla f\) More...

Public Types
using	geometry_type = Geometry
using	matrix_type = Matrix
using	container_type = Container
using	value_type = get_value_type< Container >

Public Member Functions
	Advection ()=default
	Advection (const Geometry &g)
	Create Arakawa on a grid. More...
	Advection (const Geometry &g, bc bcx, bc bcy)
	Create Advection on a grid using different boundary conditions. More...
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...
template<class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 >
void	upwind (value_type alpha, const ContainerType0 &vx, const ContainerType1 &vy, const ContainerType2 &f, value_type beta, ContainerType3 &result)
	Compute Advection term \( y = \alpha \vec v\cdot\nabla f + \beta y \). More...

Detailed Description

template<class Geometry, class Matrix, class Container>
struct dg::Advection< Geometry, Matrix, Container >

Upwind discretization of advection operator \( \vec v\cdot\nabla f\)

This is the upwind scheme where a backward derivative is used if v is positive and a forward derivative else For example

// v_x  = -dy phi
dg::blas2::symv( -1., dy, phi, 0., vx);
// v_y = dx phi
dg::blas2::symv( 1., dx, phi, 0., vy);
// compute on Cartesian grid in 2d on device
dg::Advection < dg::CartesianGrid2d, dg::DMatrix, dg::DVec> advection(grid);
// df = - v Grad f
advection.upwind( -1., vx, vy, f, 0., df);

Note

This scheme brings its own numerical diffusion and thus does not need any other artificial viscosity mechanisms. The only places where the scheme might run into oscillations is if there is a stagnation point with v==0 at a fixed position

See also

A discussion of this and other advection schemes can be found here https://mwiesenberger.github.io/advection

Template Parameters

Geometry	A type that is or derives from one of the abstract geometry base classes ( aGeometry2d, aGeometry3d, aMPIGeometry2d, ...). Geometry determines which Matrix and Container types can be used:
Matrix	A class for which the dg::blas2::symv functions are callable in connection with the Container class and to which the return type of dg::create::dx() can be converted using dg::blas2::transfer. The Matrix type can be one of: dg::HMatrix with dg::HVec and one of the shared memory geometries dg::DMatrix with dg::DVec and one of the shared memory geometries dg::MHMatrix with dg::MHVec and one of the MPI geometries dg::MDMatrix with dg::MDVec and one of the MPI geometries
Container	A data container class for which the blas1 functionality is overloaded and to which the return type of blas1::subroutine() can be converted using dg::assign. We assume that Container is copyable/assignable and has a swap member function. In connection with Geometry this is one of dg::HVec, dg::DVec when Geometry is a shared memory geometry dg::MHVec or dg::MDVec when Geometry is one of the MPI geometries

Member Typedef Documentation

container_type

template<class Geometry , class Matrix , class Container >

using dg::Advection< Geometry, Matrix, Container >::container_type = Container

geometry_type

template<class Geometry , class Matrix , class Container >

using dg::Advection< Geometry, Matrix, Container >::geometry_type = Geometry

matrix_type

template<class Geometry , class Matrix , class Container >

using dg::Advection< Geometry, Matrix, Container >::matrix_type = Matrix

value_type

template<class Geometry , class Matrix , class Container >

using dg::Advection< Geometry, Matrix, Container >::value_type = get_value_type<Container>

Constructor & Destructor Documentation

Advection() [1/3]

template<class Geometry , class Matrix , class Container >

dg::Advection< Geometry, Matrix, Container >::Advection ( )

default

Advection() [2/3]

template<class Geometry , class Matrix , class Container >

dg::Advection< Geometry, Matrix, Container >::Advection

(

const Geometry &

g

)

Create Arakawa on a grid.

Parameters

g

The grid

Advection() [3/3]

template<class Geometry , class Matrix , class Container >

dg::Advection< Geometry, Matrix, Container >::Advection	(	const Geometry &	g,
		bc	bcx,
		bc	bcy
	)

Create Advection on a grid using different boundary conditions.

Parameters

g	The grid
bcx	The boundary condition in x
bcy	The boundary condition in y

Member Function Documentation

construct()

template<class Geometry , class Matrix , class Container >

template<class ... Params>

void dg::Advection< Geometry, Matrix, Container >::construct ( Params &&...  ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params

deduced by the compiler

Parameters

ps	parameters forwarded to constructors

upwind()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 >

void dg::Advection< Geometry, Matrix, Container >::upwind	(	value_type	alpha,
		const ContainerType0 &	vx,
		const ContainerType1 &	vy,
		const ContainerType2 &	f,
		value_type	beta,
		ContainerType3 &	result
	)

Compute Advection term \( y = \alpha \vec v\cdot\nabla f + \beta y \).

This uses the upwind advection mechanism, i.e. a backward derivative for positive v and a forward derivative else

Parameters

alpha	constant
vx	Velocity in x direction
vy	Velocity in y direction
f	function
beta	constant
result	Result

Template Parameters

ContainerTypes

must be usable with Container in The dg dispatch system

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

• advection.h