On unstructured collocated meshes the Reynolds stress tends to decouple from the
velocity creating pronounced staggering patterns in the solution. This effect
is reduced or eliminated by a special coupling algorithm which replaces the
gradient diffusion component of the Reynolds stress with the equivalent compact
representation on the mesh, i.e. div-grad with Laplacian in the DivDevRhoReff function:
template<class BasicMomentumTransportModel>
template<class RhoFieldType>
Foam::tmp<Foam::fvVectorMatrix>
Foam::ReynoldsStress<BasicMomentumTransportModel>::DivDevRhoReff
(
const RhoFieldType& rho,
volVectorField& U
) const
{
tmp<volTensorField> tgradU = fvc::grad(U);
const volTensorField& gradU = tgradU();
const surfaceTensorField gradUf(fvc::interpolate(gradU));
// Interpolate Reynolds stress to the faces
// with either a stress or velocity coupling correction
const surfaceVectorField Refff
(
(this->mesh().Sf() & fvc::interpolate(R_))
// Stress coupling
+ couplingFactor_
*(this->mesh().Sf() & fvc::interpolate(this->nut()*gradU))
// or velocity gradient coupling
// + couplingFactor_
// *fvc::interpolate(this->nut())*(this->mesh().Sf() & gradUf)
- fvc::interpolate(couplingFactor_*this->nut() + this->nu())
*this->mesh().magSf()*fvc::snGrad(U)
- fvc::interpolate(this->nu())*(this->mesh().Sf() & dev2(gradUf.T()))
);
return
(
fvc::div(fvc::interpolate(this->alpha_*rho)*Refff)
- correction(fvm::laplacian(this->alpha_*rho*this->nuEff(), U))
);
}
In the above two options for the coupling term are provided, one based on the
stress correction (un-commented) and an alternative based an the velocity
gradient correction (commented). Tests run so far indicate that the stress
correction provides better coupling while minimising the error introduced.
A new tutorial case ductSecondaryFlow is provided which demonstrates the updated
coupling algorithm on the simulation of the classic secondary flow generated in
rectangular ducts.
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