Dumux::FrictionLawViscousNoSlip< VolumeVariables > Class Template Reference

Implementation of a viscous no-slip bottom friction law. More...

#include <dumux/material/fluidmatrixinteractions/frictionlaws/viscousnoslip.hh>

Inheritance diagram for Dumux::FrictionLawViscousNoSlip< VolumeVariables >:

Description

template<typename VolumeVariables>
class Dumux::FrictionLawViscousNoSlip< VolumeVariables >

This assumes thin film flow with a parabolic velocity profile in depth (for the depth-averaged shallow water equations). The velocity profile and associated bottom shear stress can be derived from plane Poiseuille flow with a free surface boundary condition on top and a no-slip boundary condition on the bottom.

Public Member Functions
Dune::FieldVector< Scalar, 2 >	bottomShearStress (const VolumeVariables &volVars) const final
	Compute the bottom shear stress. More...
Scalar	limitRoughH (const Scalar roughnessHeight, const Scalar waterDepth, const Scalar eps=1.0e-12) const
	Limit the friction for small water depth. More...

Member Function Documentation

bottomShearStress()

template<typename VolumeVariables >

Dune::FieldVector< Scalar, 2 > Dumux::FrictionLawViscousNoSlip< VolumeVariables >::bottomShearStress ( const VolumeVariables &  volVars ) const

inlinefinalvirtual

Compute the bottom shear stress due to bottom friction. The bottom shear stress is a projection of the shear stress tensor onto the bottom plane. It can therefore be represented by a (tangent) vector with two entries.

Returns

shear stress in N/m^2. First entry is the x-component, the second the y-component.

Implements Dumux::FrictionLaw< VolumeVariables >.

limitRoughH()

template<typename VolumeVariables >

Scalar Dumux::FrictionLaw< VolumeVariables >::limitRoughH ( const Scalar  roughnessHeight, const Scalar  waterDepth, const Scalar  eps = 1.0e-12  ) const

inlineinherited

Compute a small artificial water depth that is added to the actual water depth to avoid extreme friction values which can occur for small water depths.

The function is called with a roughness height, which can be seen as roughness height of the surface (e.g. grain size). For a zero roughnessHeight the artificial water depth will be zero.

A water depth minUpperH (minUpperH = 2 * roughnessHeight) is defined for the limiting. Limiting is applied between both depths.

----------------------— minUpperH --------—

---------------------—roughnessHeight ------------— /\ /\ roughness /grain\ ----------------------------—bottom ---------------— /////////////////////////////////////////////////

For the limiting the LET model is used, which is usually applied in the porous media flow to limit the permeability due to the saturation. It employs the three empirical parameters L, E and T, which describe the limiting curve (mobility).

auto mobility = (mobility_max * pow(sw,L))/(pow(sw,L) + E * pow(1.0-sw,T));

For the limitation of the roughness height L = 0.0, T = 2.0 and E = 1.0 are chosen. Therefore the calculation of the mobility is simplified significantly.

Parameters

roughnessHeight	roughness height of the representative structure (e.g. largest grain size).
waterDepth	water depth.
eps	If the roughness height falls below this threshold, this function returns zero.

< maximal mobility

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

• viscousnoslip.hh