Axisymmetric Cylindrical MMS Testing for Zapdos

[csde...@ncsu.edu]

Good afternoon,

I am doing some MMS testing for Zapdos and I notice something for 2D axisymmetric cylindrical coordinates. My process for the axisymmetric cylindrical MMS testing is as follows:

- Define a density as n(r,z)

- Derive the source term using the differential operators in cylindrical coordinates

- Plug in the source term and BCs into Zapdos and check the solution

The Zapdos solutions and the manufactured solutions are off, even for a basic diffusion problem. I went looking for MOOSE tests of cylindrical types and notice that the Navier Stokes module has kernels that account for cylindrical coordinates (like INSMass vs INSMassRZ). My understanding was that MOOSE takes care the the conversion between cartesian and cylindrical coordinates in the Problem block. I know that the MOOSE test "/coord_type/coord_type_rz.i" just uses the diffusion kernel with no correction terms. Should the plasma fluid equations also have defined RZ kernels in MOOSE or I am missing something? Also, if this is more of the MOOSE question, please let me know and I can also post it on the MOOSE google group.

Thanks,

Corey DeChant

[Alexander Lindsay]

Diffusion should be fine since it is integrated by parts. The only del operator remaining is the gradient operator, and that only has extra "stuff" for the phi coordinate which doesn't exist for axisymmetric

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[Alexander Lindsay]

In Navier-Stokes for the mass equation, we actually apply the divergence operator so we get additional terms there.

For the momentum equation we get a few more terms because of the tensor and vector math. That should not happen for the scalar transport. I've attached a PDF for the navier-stokes axisymmetric derivation.