2D shallow water model

Two-dimensional shallow water flow (depth-averaged). More...

Description

Two-dimensional shallow water flow (depth-averaged).

\[\frac{\partial \mathbf{U}}{\partial t} + \frac{\partial \mathbf{F}}{\partial x} + \\ \frac{\partial \mathbf{G}}{\partial y} - \mathbf{S_b} - \mathbf{S_f} = 0 \]

with U, F, G are defined as

\[\mathbf{U} = \begin{bmatrix} h \\ uh \\ vh \end{bmatrix}, \mathbf{F} = \begin{bmatrix} hu \\ hu^2 + \frac{1}{2} gh^2 \\ huv \end{bmatrix}, \mathbf{G} = \begin{bmatrix} hv \\ huv \\ hv^2 + \frac{1}{2} gh^2 \end{bmatrix} \]

Z is the bedSurface, h the water depth, u the velocity in x-direction and v the velocity in y-direction, g is the constant of gravity.

The source terms for the bed friction S_b and bed slope S_f are given as

\[\mathbf{S_b} = \begin{bmatrix} 0 \\ -gh \frac{\partial z}{\partial x} \\ -gh \frac{\partial z}{\partial y}\end{bmatrix}, \mathbf{S_f} = \begin{bmatrix} 0 \\ -ghS_{fx} \\ -ghS_{fy}\end{bmatrix}. \]

A cell-centered finte volume method (cctpfa) is applied to solve the SWEs in combination with a fully-implicit time discretization. For large time step sizes (CFL > 1) this can lead to a strong semearing of sharp fronts. This can be seen in the movement of short traveling waves (e.g. dam break waves). Nevertheless the fully implicit time discretization showes often no drawbacks in cases where no short waves are considered. Thus the model can be a good choice for simulating flow in rivers and channels, where the fully-implicit discretization allows large time steps and reduces the overall computation time drastically.

Files
file	boundaryfluxes.hh
	Compute boundary conditions for the Riemann Solver.
file	fluxvariables.hh
	The flux variables class for the shallow water model.
file	indices.hh
	The common indices for the shallow water equations model.
file	iofields.hh
	Add I/O fields specific to shallow water.
file	localresidual.hh
	Element-wise calculation of the residual for the shallow water equations.
file	model.hh
	A two-dimensional shallow water equations model The two-dimensonal shallow water equations (SWEs) can be written as.
file	problem.hh
	Shallow water problem base class.
file	volumevariables.hh
	Volume variables for the shallow water equations model.

Classes
class	Dumux::ShallowWaterFluxVariables< TypeTag >
	The flux variables class for the shallow water model. More...
struct	Dumux::ShallowWaterIndices
	The common indices for the shallow water equations model. More...
class	Dumux::ShallowWaterIOFields
	Adds vtk output fields for the shallow water model. More...
class	Dumux::ShallowWaterResidual< TypeTag >
	Element-wise calculation of the residual for the shallow water equations. More...
struct	Dumux::ShallowWaterModelTraits
	Specifies a number properties of shallow water models. More...
struct	Dumux::ShallowWaterVolumeVariablesTraits< PV, MT >
	Traits class for the volume variables of the shallow water model. More...
class	Dumux::ShallowWaterProblem< TypeTag >
	Shallow water problem base class. More...