Entropy–Stable No–Slip Wall Boundary Conditions for the Eulerian Model for Viscous and Heat Conducting Compressible Flows

Abstract

Nonlinear (entropy) stability analysis is used to derive entropy–stable no–slip wall boundary conditions at the continuous and semi–discrete levels for the Eulerian model proposed by Svärd in 2018 (Physica A: Statistical Mechanics and its Applications, 2018). The spatial discretization is based on discontinuous Galerkin summation-by-parts operators of any order for unstructured grids. We provide a set of two–dimensional numerical results for laminar and turbulent flows simulated with both the Eulerian and classical Navier–Stokes models. These results are computed with a high-performance ℎ–entropy–stable solver, that also features explicit and implicit entropy–stable time integration schemes.