A Second Order Numerical Scheme for Large-Eddy Simulation of Compressible Flows

In the context of large eddy simulation of turbulent flows, the control of kinetic energy seems to be an essential requirement for a numerical scheme. We propose in this paper a formally second order non-dissipative scheme dedicated to the numerical simulation of the filtered Naviers-Stokes equations for compressible flows. The spatial discretization is staggered and based on the so-called Marker-And-Cell (MAC) scheme. A MUSCL-like technique is used for convection operators of the mass and the internal energy balance equations in order to preserve the positivity of the density and of the internal energy. Time discretization is performed with the Heun scheme. A kinetic energy conservation identity at discrete level is proved. The good behaviour of the scheme is assessed on the simulation of compressible decaying isotropic turbulence.