Physically consistent formulations for kinetic energy preservation by quasi-skew-symmetric forms

Kinetic energy preserving schemes for non-dissipative and stable flow simulations are proposed. The schemes are designed such that numerical fluxes are physically “consistent” to the analytical relation among the governing equations; especially, the kinetic energy numerical fluxes are consistent to the mass and momentum numerical fluxes. In a numerical experiment, the consistent schemes proposed show good numerical stability with preserving the kinetic energy. Enthalpy numerical fluxes are solved in the total energy equation in some existing kinetic energy preserving schemes, whereas internal energy and pressure numerical fluxes are solved instead here. Although both the existing and proposed kinetic energy preserving schemes successfully preserve the kinetic energy, some different characteristics are highlighted in the result of the density variation. More detailed analyses will be presented in the conference and a paper in preparation [1].