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Compressible Navier-Stokes with embedded boundaries has several important computational challenges.
- Diffusion should be treated implicitly.
- The interaction of viscosity with energy equation (viscous dissipation) is challenging to discretize in a stable way in the presence of small cells.
- Refluxing must be done implicitly.
- Diffusive operators have variable coefficients.
Viscosity can significantly change the results of even simple 2D problems.
This 8-level calculation shows substantial changes from the inviscid case including
- Boundary layer separation.
- Substantially reduced Mach stem due to boundary layer effects.