Asymptotically entropy conservative discretization of convective terms in compressible Euler equations

A new class of Asymptotically Entropy Conservative schemes is proposed for the numerical simulation of compressible (shock-free) turbulent flows. These schemes consist of a suitable spatial discretization of the convective terms in the Euler equations, which retains at the discrete level many important properties of the continuous formulation, resulting in enhanced reliability and robustness of the overall numerical method. In addition to the Kinetic Energy Preserving property, the formulation guarantees the preservation of pressure equilibrium in the case of uniform pressure and velocity distributions, and arbitrarily reduces the spurious production of entropy. The main feature of the proposed schemes is that, in contrast to existing Entropy Conservative schemes, which are based on the evaluation of costly transcendental functions, they are based on the specification of numerical fluxes involving only algebraic operations, resulting in an efficient and economical procedure. Numerical tests on a highly controlled one-dimensional problem, as well as on more realistic turbulent three-dimensional cases, are shown, together with a cost-efficiency study.