Anistropic Viscosity in Dedalus 3

[Marty Hewitt]

I am trying to solve for motion in an incompressible fluid in Dedalus 3, the setup is very similar to the Rayleigh Benard example given on the website. I have attached a screenshot with my equations of motion. The fluid is simulated on a 2D plane, here u is a 2D vector giving velocity in the plane and v is a scalar field representing velocity into and out of the plane.

I am trying to go from an isotropic viscosity, as in the term "nu*div(grad_u)", to an anistropic viscosity, in which the diffusion along the x direction is subjected to a different viscosity than the diffusion along the z direction. 

I have tried a few different ways to implement this but my ideas have not worked. Is there a way to implement anistropic viscosity in the vector equations of Dedalus 3? I imagine this is not an uncommon thing to do, but I don't know how to implement it while still using the symbolic vector equations. Thanks for the help!

[Keaton Burns]

Hi Marty,

The easiest approach is probably to just enter the equations componentwise with partial derivatives, but it should still be possible in the vectorial interface if you define a (spatially constant, so no bases) diffusivity tensor K encoding the different diffusivities, and contract with it like div(K@grad_u). 

Best,

-Keaton

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[Marty Hewitt]

Hello Keaton,

Thanks for the quick reply! 

I had ended up figuring out the issue a little while after I submitted the ticket, I did end up using a tensor formed from an outer product of the basis vectors. I appreciate that you included the functionality for an outer product operation like this in Dedalus, it’s very intuitive.

Regards,

Marty

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