Direct Numerical Simulation of Supersonic and Transonic Compressible Viscous Flow by Kinetic Energy Preserving Scheme

Viscous and inviscid fluxes must be calculated acrooss a cell face in the finite volume method. In calculaing these fluxes, we can consider some features of the N-S equation like kinetic energy preservation (KEP). Recently, Jameson showed that the interface fluxes of a semi-discrete conservative scheme can be constructed in an alternative way which assures that the global discrete kinetic energy evolves in a manner that exactly corresponds to the true equation for kinetic energy.