| Warlord |
December 8, 2017 13:14 |
EulerD2dt2Scheme
Hello folks,
Does anyone know how to derive the formulas implemented for the EulerD2dt2Scheme::fvmD2dt2? Specially for the first one, applied when the mesh is moving. Any reference?
Code:
template<class Type>
tmp<fvMatrix<Type> >
EulerD2dt2Scheme<Type>::fvmD2dt2
(
const dimensionedScalar& rho,
GeometricField<Type, fvPatchField, volMesh>& vf
)
{
tmp<fvMatrix<Type> > tfvm
(
new fvMatrix<Type>
(
vf,
rho.dimensions()*vf.dimensions()*dimVol
/dimTime/dimTime
)
);
fvMatrix<Type>& fvm = tfvm();
scalar deltaT = mesh().time().deltaT().value();
scalar deltaT0 = mesh().time().deltaT0().value();
scalar coefft = (deltaT + deltaT0)/(2*deltaT);
scalar coefft00 = (deltaT + deltaT0)/(2*deltaT0);
scalar rDeltaT2 = 4.0/sqr(deltaT + deltaT0);
if (mesh().moving())
{
scalar halfRdeltaT2 = 0.5*rDeltaT2;
scalarField VV0 = mesh().V() + mesh().V0();
scalarField V0V00 = mesh().V0() + mesh().V00();
fvm.diag() = rho.value()*(coefft*halfRdeltaT2)*VV0;
fvm.source() = halfRdeltaT2*rho.value()*
(
(coefft*VV0 + coefft00*V0V00)
*vf.oldTime().internalField()
- (coefft00*V0V00)*vf.oldTime().oldTime().internalField()
);
}
else
{
fvm.diag() = (coefft*rDeltaT2)*mesh().V()*rho.value();
fvm.source() = rDeltaT2*mesh().V()*rho.value()*
(
(coefft + coefft00)*vf.oldTime().internalField()
- coefft00*vf.oldTime().oldTime().internalField()
);
}
return tfvm;
}
Thank you |
