Stable Interface Conditions for Discontinuous Galerkin Approximations of Navier-Stokes Equations

A study of boundary and interface conditions for Discontinuous Galerkin approximations of fluid flow equations is undertaken in this paper. While the interface flux for the inviscid case is usually computed by approximate Riemann solvers, most discretizations of the Navier-Stokes equations use an average of the viscous fluxes from neighboring elements. The paper presents a methodology for constructing a set of stable boundary/interface conditions that can be thought of as “viscous” Riemann solvers and are compatible with the inviscid limit.