A fully-discrete entropy conserving/stable discretization for inviscid unsteady flows

The aim of this work is to contribute to the development of a high-order accurate discretization that is entropy conserving and entropy stable both in space and in time. To do this, the general framework is based on a high-order accurate discontinuous Galerkin (dG) method in space with entropy working variables, several entropy conservative and stable numerical fluxes and an entropy conserving modified Crank-Nicolson method. We present the first results, obtained with the discretizations here proposed, for two bi-dimensional unsteady viscous test-case: The Taylor-Green vortex and the double shear layer.