Classes
struct	RiemannSolution

Functions
template<class Scalar>
RiemannSolution< Scalar >	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.
template<class Scalar>
static Scalar	fluxLimiterLET (const Scalar valueLeft, const Scalar valueRight, const Scalar upperH, const Scalar lowerH)
	Flux limiter function to scale fluxes for small water depths.
template<class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	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.
template<class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	wallBoundary (const Scalar waterDepthInside, const Scalar velocityXInside, const Scalar velocityYInside, const GlobalPosition &nxy)
	Compute the outer cell state for a slip wall.
template<class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	inflowBoundary (const Scalar waterDepthBoundary, const Scalar speedBoundary, const GlobalPosition &nxy)
	Compute the outer cell state for an inflow with prescribed depth and speed.
template<class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	criticalDepthOutflowBoundary (const Scalar waterDepthInside, const Scalar velocityXInside, const Scalar velocityYInside, const Scalar gravity, const GlobalPosition &nxy)
	Compute the outer cell state for a free overfall (open outflow).
template<class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	fixedWaterDepthBoundary (const Scalar waterDepthBoundary, const Scalar waterDepthInside, const Scalar velocityXInside, const Scalar velocityYInside, const Scalar gravity, const GlobalPosition &nxy)
	Compute the outer cell state for fixed water depth boundary.
template<class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	fixedDischargeBoundary (const Scalar dischargeBoundary, const Scalar waterDepthInside, const Scalar velocityXInside, const Scalar velocityYInside, const Scalar gravity, const GlobalPosition &nxy)
	Compute the outer cell state for a fixed discharge boundary.
template<class PrimaryVariables, class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	noslipWallBoundary (const Scalar alphaWall, const Scalar turbulentViscosity, const PrimaryVariables &state, const GlobalPosition &cellCenterToBoundaryFaceCenter, const GlobalPosition &unitNormal)
	Compute the viscosity/diffusive flux at a rough wall boundary using no-slip formulation.
template<class PrimaryVariables, class Scalar, class GlobalPosition>
std::array< Scalar, 3 >	nikuradseWallBoundary (const Scalar ksWall, const PrimaryVariables &state, const GlobalPosition &cellCenterToBoundaryFaceCenter, const GlobalPosition &unitNormal)
	Compute the viscosity/diffusive flux at a rough wall boundary using Nikuradse formulation.

Function Documentation

◆ criticalDepthOutflowBoundary()

template<class Scalar, class GlobalPosition>

std::array< Scalar, 3 > Dumux::ShallowWater::criticalDepthOutflowBoundary	(	const Scalar	waterDepthInside,
		const Scalar	velocityXInside,
		const Scalar	velocityYInside,
		const Scalar	gravity,
		const GlobalPosition &	nxy )

The boundary characteristics travel with the normal velocity plus or minus the wave celerity. Supercritical outflow carries no characteristic back into the domain, so the outer state is the inner one. Subcritical outflow does carry one; reusing the inner state then imposes a zero gradient, which under-drains and piles water up in the boundary cell, whereas the brink of a free overfall sits at critical depth for the arriving normal discharge. The tangential velocity is kept. Water cannot flow up the brink, so a non-positive normal velocity gives the wall state.

Parameters

waterDepthInside	Water depth in the inner cell [m]
velocityXInside	Velocity in x-direction in the inner cell [m/s]
velocityYInside	Velocity in y-direction in the inner cell [m/s]
gravity	Gravity constant [m/s^2]
nxy	Normal vector of the boundary face

Returns: cellStateOutside The outer cell state

◆ fixedDischargeBoundary()

template<class Scalar, class GlobalPosition>

std::array< Scalar, 3 > Dumux::ShallowWater::fixedDischargeBoundary	(	const Scalar	dischargeBoundary,
		const Scalar	waterDepthInside,
		const Scalar	velocityXInside,
		const Scalar	velocityYInside,
		const Scalar	gravity,
		const GlobalPosition &	nxy )

Parameters

dischargeBoundary	Discharge per meter at the boundary face [m^2/s]
waterDepthInside	Water depth in the inner cell [m]
velocityXInside	Velocity in x-direction in the inner cell [m/s]
velocityYInside	Velocity in y-direction in the inner cell [m/s]
gravity	Gravity constant [m/s^2]
nxy	Normal vector of the boundary face

Returns: cellStateOutside The outer cell state

◆ fixedWaterDepthBoundary()

template<class Scalar, class GlobalPosition>

std::array< Scalar, 3 > Dumux::ShallowWater::fixedWaterDepthBoundary	(	const Scalar	waterDepthBoundary,
		const Scalar	waterDepthInside,
		const Scalar	velocityXInside,
		const Scalar	velocityYInside,
		const Scalar	gravity,
		const GlobalPosition &	nxy )

Parameters

waterDepthBoundary	Water depth at the boundary face [m^2/s]
waterDepthInside	Water depth in the inner cell [m]
velocityXInside	Velocity in x-direction in the inner cell [m/s]
velocityYInside	Velocity in y-direction in the inner cell [m/s]
gravity	Gravity constant [m/s^2]
nxy	Normal vector of the boundary face

Returns: cellStateOutside The outer cell state

◆ inflowBoundary()

template<class Scalar, class GlobalPosition>

std::array< Scalar, 3 > Dumux::ShallowWater::inflowBoundary	(	const Scalar	waterDepthBoundary,
		const Scalar	speedBoundary,
		const GlobalPosition &	nxy )

Both characteristics enter the domain when the inflow is supercritical, so depth and velocity have to be imposed together. For subcritical inflow one of them is determined by the interior, see fixedDischargeBoundary and fixedWaterDepthBoundary.

Parameters

waterDepthBoundary	Water depth at the boundary face [m]
speedBoundary	Speed of the inflowing water, positive into the domain [m/s]
nxy	Normal vector of the boundary face

Returns: cellStateOutside The outer cell state

◆ nikuradseWallBoundary()

template<class PrimaryVariables, class Scalar, class GlobalPosition>

std::array< Scalar, 3 > Dumux::ShallowWater::nikuradseWallBoundary	(	const Scalar	ksWall,
		const PrimaryVariables &	state,
		const GlobalPosition &	cellCenterToBoundaryFaceCenter,
		const GlobalPosition &	unitNormal )

Parameters

ksWall	Nikuradse roughness height for the wall [m]
state	the primary variable state (water depth, velocities)
cellCenterToBoundaryFaceCenter	Cell-center to boundary distance
unitNormal	Normal vector of the boundary face

◆ noslipWallBoundary()

template<class PrimaryVariables, class Scalar, class GlobalPosition>

std::array< Scalar, 3 > Dumux::ShallowWater::noslipWallBoundary	(	const Scalar	alphaWall,
		const Scalar	turbulentViscosity,
		const PrimaryVariables &	state,
		const GlobalPosition &	cellCenterToBoundaryFaceCenter,
		const GlobalPosition &	unitNormal )

Parameters

alphaWall	Roughness parameter: alphaWall=0.0 means full slip, alphaWall=1.0 means no slip, \(0.0<\text{alphaWall}<1.0\) means partial slip [-]
turbulentViscosity	Turbulent viscosity [m^2/s]
state	Primary variables (water depth, velocities)
cellCenterToBoundaryFaceCenter	Cell-center to boundary distance
unitNormal	Normal vector of the boundary face

◆ wallBoundary()

template<class Scalar, class GlobalPosition>

std::array< Scalar, 3 > Dumux::ShallowWater::wallBoundary	(	const Scalar	waterDepthInside,
		const Scalar	velocityXInside,
		const Scalar	velocityYInside,
		const GlobalPosition &	nxy )

The normal velocity is mirrored and the tangential velocity kept, so the Riemann problem across the face carries no mass flux and the hydrostatic pressure force.

Parameters

waterDepthInside	Water depth in the inner cell [m]
velocityXInside	Velocity in x-direction in the inner cell [m/s]
velocityYInside	Velocity in y-direction in the inner cell [m/s]
nxy	Normal vector of the boundary face

Returns: cellStateOutside The outer cell state

Classes

Functions

Function Documentation

◆ criticalDepthOutflowBoundary()

◆ fixedDischargeBoundary()

◆ fixedWaterDepthBoundary()

◆ inflowBoundary()

◆ nikuradseWallBoundary()

◆ noslipWallBoundary()

◆ wallBoundary()