Entropy Stability and the No-Slip Wall Boundary Condition

Abstract

We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an $L^2$ bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.