Kinetic energy and entropy preserving schemes for compressible flows by split convective forms

This study proposes a kinetic energy and entropy preserving scheme to achieve stable and non-dissipative compressible flow simulations. The proposed scheme is built in such a way that the numerical formulations satisfy the analytical relations among the governing equations at the discrete level. The mass and momentum convective terms are recast into split convective forms. Once the mass and momentum equations are discretized, the constraints given by the analytical relations subsequently determine the formulations of the numerical fluxes solved in the total energy equation. An analysis reveals that satisfying the analytical relations at the discrete level is essential for solving the energy exchange between the kinetic energy and internal energy correctly in the total energy equation, and therefore important for entropy conservation. Taylor–Green vortex and Euler isotropic turbulence simulations at infinite Reynolds number are conducted to verify the analysis given in this paper. The proposed scheme achieves both kinetic energy conservation in the incompressible limit and entropy conservation as well as convergences of thermodynamic variable fluctuations, whereas existing kinetic energy preserving schemes fail entropy conservation and the thermodynamic variable fluctuations diverge.