Boundary conditions
 

Hello,

I'm probably asking seemingly very basic questions, and I know there are a lot of threads on this matter (I have looked at them already), nevertheless I'd like to exchange a bit on the topic of boundary conditions since they are most likely giving me lots of trouble.

I'm trying to simulate a 2D atmosphere, using compressible euler hydrodynamic equations. For now my model only accounts for advection and gravity. I'm working in spherical polar coordinates such that a curvilinear source term appear in the equations.

Since I assume axisymmetry around the equator (make the 2D semi-circle "rotate" around phi [0,2pi]), I'd like to apply reflecting boundary conditions at "angular" edges (left/right).
As for the outer radial edge, I'd like to assume open boundaries where the information can only vanish ("outflow").
Inner edge should be fixed conditions for scalars, which should physically always go "upwards" (it's the idea of a planetary solid core surrounded by ideal gas).

Also, I'm working with a structured collocated grid with two ghost cells on each sides. The ghost cells possess their own "realistic" spatial coordinates but fictitious values to implement BCs.

Could someone give me some insight on how to properly implement those three types of boundary conditions ?

So far how I understood it:

-Axisymmetric/reflective: mirror scalar values at ghost cells, angular speed should be inverted while radial speed mirrored using two nearest "real" cells

-Free/outflow: ghost cells scalar values should copy the nearest "real" cell, radial speed should only be positive (if negative set to zero) in ghost cells, angular speed should be copied like for scalars

-Fixed: set scalar values for ghost cells at desired values, angular speed set to zero, radial speed set to zero or upward thermal wind (which instead yields some inflow)

This is a pretty interesting topic. I will continue to follow this article
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First of all, the type of BCs strongly depends on the mathematical character of the equations.
Before addressing any hint for your case, could you add some sketch of your 2d model to help a reader?
Take into account that you are working in a low-Mach flow. Density variations are due to gravity effects that can be modelled in an incompressible flow model.