Draft: ENH: relative velocity usage for porosity in MRF regions

Related to #1652 - updates porosity calculation when used with MRF to use relative velocity

Test case from bug report: rotatingCylinders-test.tgz

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• 4ac2b6eb - WIP - relative velocity usage for porosity in MRF regions

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Please note that for the cases where "Using pressure implicit porosity" occurs, this set of commits will have no effect on velocity field. To this end, the formulation should/can be extended in future releases for implicit-porosity applications.

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@andy : Looking into this. I think there is a bit missing in the correction. the expression for drag is: Drag = D (Ua - Umrf) + 0.5Frho* mag(Ua - Umrf) * (Ua - Umrf)

This is for a general the porous media pushing the flow as it moves or slowing the flow with drag.

I think when you subtract :

UEqn.source() -= Udiag*Uref - Usource;

The first term seems correct , but the second is 0.5Frhosqr(Umrf), then the expression for drag is 0.5Frhosqr(Ua) - sqr(Umrf) when it should be sqr(Ua - Umrf) ?.

The final result is actually the same as the converged result is similar as the flow is dragged by the MRF to a final state independently of the model expression. But for transient flow the behavior will be different.

This could be done passing Umrf to apply function:

const tensor Cd = mu[celli]*dZones[j] + (rho[celli]*mag(U[celli]))*fZones[j];

const scalar isoCd = tr(Cd);

const tensor Cd1 = mu[celli]*dZones[j] + (rho[celli]*mag(U[celli]-Umrf[celli]))*fZones[j];

const scalar isoCd1 = tr(Cd1);

Udiag[celli] += V[celli]*isoCd;

Usource[celli] += -V[celli]isoCdUMrf[celli] (<-- this similar) -V[celli]((Cd1 - IisoCd1) & (U[celli]-Umrf[celli]);

The end result is similar.

For the implicit , not sure if we can have the exact expression in place for the second term of the Darcy model.

What I did was similar to your with AU.

tensorField AUmrf = 0 this->correct(UEqn, Umrf, AUmrf);

UEqn.source() -= AUmrf*Uref

The end result is similar. But the second term of the Darcy model is not correct. And i don't think it can be made implicit when solving for Uabs instead of Urel. WE can talk this over.

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The current implementation is wrong for some models - I've tagged as draft (so as not to merge) and will have a play.

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