Problems with compressible NS in a ball

[Lautaro Alvear]

Hello Dedalus experts.

I am trying to solve the compressible Navier-Stokes equations with an ideal-gas equation of state in a ball domain with entropy and density as the independent variables, such that the equations to be solved are

I've built the code that tries to solve these equations and I have tried with many values for the parameters of the simulations but I haven't been able to have success with it, since in the second or third iteration all the variables have values nan.

I've tried solving for \ln rho and rho, multiple choices for the parameters, random initial conditions and a set initial condition for rho and s (included in the script below) without any success.

I was wondering if someone else has tried solving a similar set of equations in a ball basis and if they've ran into similar problems or if someone has any insight on why my code is failing.

Regards,
Lautaro.

[Keaton Burns]

Hi Lautaro,

It’s important to implicitly integrate the stiff terms, meaning you should put a linearized version of the viscous term on the LHS and subtract the same from the RHS. Typically you also only want to impose boundary conditions and have tau terms for the fields that are being diffused, so just velocity and entropy (if you add thermal diffusion), but not density.

Best,

-Keaton

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[Lautaro Alvear]

Thanks Keaton for your help.

Best Regards,
Lautaro.

[Ben Brown]

Lautaro,

      Depending on the speed of your flows (u) vs sound waves in your system (sqrt(gamma*P/rho), you may also have substantial stiffness in your grad(P)/rho term in the momentum equation.

Various of us have been interested in approaches to those for years, and we've had success solving them in Dedalus, which may give you some hints on how to proceed.

Some starting points (direct journal links, as these are open access):

• Anders & Brown 2017: https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.2.083501
  
  
• Anders et al 2019: https://iopscience.iop.org/article/10.3847/1538-4357/aaff61/meta
  
  
• Anders et al 2023: https://www.nature.com/articles/s41550-023-02040-7
  
  
• Powers et al 2024: https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.043501

--Ben

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