Flux related to the shallow water model

Flux related to the shallow water model. More...

Description

Files
file	exactriemann.hh
	Function to compute the Riemann flux at the interface.
file	fluxlimiterlet.hh
	Function to limit the fluxes.
file	riemannproblem.hh
	This file includes a function to construct the Riemann problem.

Functions
template<class Scalar >
RiemannSolution< Scalar >	Dumux::ShallowWater::exactRiemann (const Scalar dl, const Scalar dr, const Scalar ul, const Scalar ur, const Scalar vl, const Scalar vr, const Scalar grav, const Scalar s=0.0)
	Exact Riemann solver for the shallow water equations. More...
template<class Scalar >
static Scalar	Dumux::ShallowWater::fluxLimiterLET (const Scalar valueLeft, const Scalar valueRight, const Scalar upperH, const Scalar lowerH)
	Flux limiter function to scale fluxes for small water depths. More...
template<class Scalar , class GlobalPosition >
std::array< Scalar, 3 >	Dumux::ShallowWater::riemannProblem (const Scalar waterDepthLeft, const Scalar waterDepthRight, Scalar velocityXLeft, Scalar velocityXRight, Scalar velocityYLeft, Scalar velocityYRight, const Scalar bedSurfaceLeft, const Scalar bedSurfaceRight, const Scalar gravity, const GlobalPosition &nxy)
	Construct a Riemann problem and solve it. More...

Function Documentation

exactRiemann()

template<class Scalar >

RiemannSolution< Scalar > Dumux::ShallowWater::exactRiemann	(	const Scalar	dl,
		const Scalar	dr,
		const Scalar	ul,
		const Scalar	ur,
		const Scalar	vl,
		const Scalar	vr,
		const Scalar	grav,
		const Scalar	s = 0.0
	)

The flux of the 2D shallow water equations must be rotated to a 1D problem before the Riemann solver can be applied. The computed water flux is given in m^2/s, the momentum fluxes are given in m^3/s^2.

This Riemann solver is described in the book "Shock-capturing methods for free-surface shallow flows" from Toro, 2001. We keep the notation for the variables after Toro.

Parameters

dl	water depth on the left side
dr	water depth on the right side
ul	veloctiyX on the left side
ur	velocityX on the right side
vl	velocityY on the left side
vr	velocityY on the right side
grav	gravity constant
s	sample point (default = 0 since x = 0 for flux computation)

fluxLimiterLET()

template<class Scalar >

static Scalar Dumux::ShallowWater::fluxLimiterLET ( const Scalar  valueLeft, const Scalar  valueRight, const Scalar  upperH, const Scalar  lowerH  )

static

This function acts like a kind of mobility, it limits the water flux for small water depths. The mobility depends on the left and right side state of a variable. The LET-Type function is described at https://en.wikipedia.org/wiki/Relative_permeability The LET-Parameters are fixed. The current parameters are set to a values to get a nice curve. They have no physical meaning.

Template Parameters

Scalar

the scalar type for scalar physical quantities

Parameters

valueLeft	The value on the left side
valueRight	The value on the right side
upperH	Where to start the limit the function (mobility < 1)
lowerH	Where the limit should reach zero (mobility < 0)

riemannProblem()

template<class Scalar , class GlobalPosition >

std::array< Scalar, 3 > Dumux::ShallowWater::riemannProblem	(	const Scalar	waterDepthLeft,
		const Scalar	waterDepthRight,
		Scalar	velocityXLeft,
		Scalar	velocityXRight,
		Scalar	velocityYLeft,
		Scalar	velocityYRight,
		const Scalar	bedSurfaceLeft,
		const Scalar	bedSurfaceRight,
		const Scalar	gravity,
		const GlobalPosition &	nxy
	)

Riemann problem applies the hydrostatic reconstruction, uses the Riemann invariants to transform the two-dimensional problem to a one-dimensional problem, solves this new problem, and rotates the problem back. Further it applies a flux limiter for the water flux to handle drying elements. The correction of the bed slope source term leads to a non-symmetric flux term at the interface for the momentum equations. Since DuMuX computes the fluxes twice from each side this does not matter.

So far this implements the exact Riemann solver (with reconstruction after Audusse).

The computed water flux (localFlux[0]) is given in m^2/s, the momentum fluxes (localFlux[1], localFlux[2]) are given in m^3/s^2. Later this flux will be multiplied by the scvf.area() (given in m for a 2D problem) to get the flux over a face.

Parameters

waterDepthLeft	water depth on the left side
waterDepthRight	water depth on the right side
velocityXLeft	veloctiyX on the left side
velocityXRight	velocityX on the right side
velocityYLeft	velocityY on the left side
velocityYRight	velocityY on the right side
bedSurfaceLeft	surface of the bed on the left side
bedSurfaceRight	surface of the bed on the right side
gravity	gravity constant
nxy	the normal vector