Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows

TL;DR

This paper develops entropy stable no-slip wall boundary conditions for the Eulerian model of viscous, heat-conducting compressible flows, ensuring numerical stability and accuracy on unstructured grids.

Contribution

It introduces a nonlinear entropy stability analysis to derive boundary conditions compatible with entropy stable discretizations for the Eulerian model.

Findings

Entropy stable boundary conditions are successfully derived.

Numerical comparisons show similarities and differences between Eulerian and Navier-Stokes models.

The approach enhances stability for simulations on unstructured grids.

Abstract

Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Sv\"{a}rd (Physica A: Statistical Mechanics and its Applications, 2018). and its spatial discretization based on entropy stable collocated discontinuous Galerkin operators with the summation-by-parts property for unstructured grids. A set of viscous test cases of increasing complexity are simulated using both the Eulerian and the classic compressible Navier-Stokes models. The numerical results obtained with the two models are compared, and differences and similarities are then highlighted.