Implementing MHD with Incompressible Flow

[Siddhant Ranka]

Hello,

My name is Siddhant Ranka and I am a new dedalus user. I have previously sent a post about using the MHD model to simulate the merging of two Taylor states and I had run into an error implementing the MHD continuity equation. I still have been unable to implement the MHD continuity equation, so I have been trying to implement MHD with incompressible flow by keeping the density constant. I am using an IVP with 2 by 2 mesh, cartesian coordinates in 3 dimensions, and the RealFourier basis for the x, y, and z bases. I am using div(v) = 0 to represent incompressible flow. However, I keep getting RuntimeError: Factor is exactly singular as my error. I have attached the code for this problem below. My problem is set up as SSX = d3.IVP([v, A, lnrho, T, phi, tau_A], time=t, namespace=locals()). I have also attached a screenshot showing the rest of the simulation equations.

Thank you,

Siddhant

[Daniel Lecoanet]

Hi Siddhant,

You’ve missing a pressure gauge. See for example this script:

https://dedalus-project.readthedocs.io/en/latest/pages/examples/ivp_2d_shear_flow.html

Daniel

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<IVP_SSX.py><Screenshot 2024-07-01 at 5.09.35 PM.png>

[Siddhant Ranka]

Thank you Daniel. I implemented the pressure gauge by adding integ(p)  = 0 and by adding div(v) + tau_p = 0, but I still keep getting the same error. I created a scalar pressure field p as well by writing p = dist.Field(name='p', bases=(xbasis, ybasis, zbasis)). I have attached my new screenshots of the code below. 

Sincerely,

Siddhant

[Siddhant Ranka]

It works now - I forgot to add grad(p) to the momentum equation.

Thank you,

Siddhant