Navier–Stokes characteristic boundary conditions for real fluids with kinetic-energy- and pressure-equilibrium-preserving schemes

Abstract

This study presents Navier–Stokes characteristic boundary conditions (NSCBC) for real fluids in conjunction with kinetic-energy-preserving (KEP) and pressure-equilibrium-preserving (PEP) numerical schemes. The appropriate wave relations are derived for an arbitrary equation of state according to either the locally one-dimensional inviscid (LODI) approximation or its three-dimensional extension. The NSCBC workflow is adapted to the PEP framework, which in this work is based on evolving pressure instead of total energy. A set of canonical tests of increasing complexity demonstrates that the combination of KEP+PEP schemes and 3D-NSCBC is a viable approach to obtain stable numerical results that are free of spurious oscillations/reflections, in the absence of any artificial stabilization mechanism.