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 L2 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.