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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.

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