Fully Discrete Entropy Conserving/Stable Discontinuous Galerkin Discretization of the Euler Equations in Entropy Variables

A fully discrete entropy conserving and entropy stable discretization of the Euler equations is here presented. The discretization in space is performed with a discontinuous Galerkin (dG) method with entropy working variables and several entropy conserving and entropy stable numerical fluxes. The discretization in time is performed with an entropy conserving generalized Crank-Nicolson scheme. The numerical results, obtained for the isentropic convecting vortex and the double shear layer, will show the order of accuracy and the conservation properties of both the time and the spatial discretization schemes.