An entropy stable, hybridizable discontinuous galerkin method for the compressible Navier-Stokes equations

This article proves that a particular space-time, hybridizable discontinuous Galerkin method is entropy stable for the compressible Navier- Stokes equations. In order to facilitate the proof, 'entropy variables' are utilized to rewrite the compressible Navier-Stokes equations in a symmetric form. The resulting form of the equations is discretized with a hybridizable discontinuous finite element approach in space, and a classical discontinuous finite element approach in time. Thereafter, the initial solution is shown to continually bound the solutions at later times.