Navier-Stokes type model

[Praveen C]

Dear all

I have NS model with some extra terms, see the picture.

The J-phi equations are like Darcy model. B is a given vector field.

Is there any existing example for this model ? If not, can you point some similar examples which can help me couple NS with this extra Darcy-type model ?

Thanks
praveen

[Shyam Sunder Yadav]

Dear sir

These equations look like those from incompressible magnetohydrodynamics.

Are you looking for that phenomenon?

Regards 

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[Praveen C]

Indeed they come from incompressible MHD and is called inductionless model.

The B is fixed in time, which is a strong external field. The induced B is assumed to be small, so ignored, but induced currents are accounted for.

There is full coupling between v-J-phi, otherwise one could have just added the J x B term into the acceleration.

One can solve for phi

Laplace(phi) = div(v x B)

and then get J.

But is there a way to directly solve for J-phi in Basilisk, which is a Darcy-type model ?

best

praveen

[jose.lopez...@gmail.com]

Take a look to electrohydrodynamic libraries. They have many aspects in common.