Navier-Stokes Characteristic Boundary Conditions Using Ghost Cells

Solution methods for the compressible Navier-Stokes equations based on finite volume discretizations often implement boundary conditions using ghost cells outside of the computational domain. Filling the ghost cells using straightforward zeroth- or first-order extrapolation, although computationally expedient, is well known to fail even for some simple flows, especially when turbulent structures interact with the boundaries or if time-varying inflow conditions are imposed. The Navier-Stokes characteristic boundary condition approach provides more accurate boundary conditions, but requires the use of special discretizations at boundaries. The present paper develops a new technique based on the Navier-Stokes characteristic boundary condition approach to derive values for ghost cells that significantly improve the treatment of boundaries over simple extrapolation, but retain the ghost cell approach. It is demonstrated in the context of a Godunov integration procedure that the new method provides accurate results, while allowing the use of the same stencil and numerical methodology near the boundaries as in the interior.