Formulation of Kinetic Energy Preserving Conservative Schemes for Gas Dynamics and Direct Numerical Simulation of One-Dimensional Viscous Compressible Flow in a Shock Tube Using Entropy and Kinetic Energy Preserving Schemes

Abstract This paper follows up on the author’s recent paper “The Construction of Discretely Conservative Finite Volume Schemes that also Globally Conserve Energy or Enthalpy”. In the case of the gas dynamics equations the previous formulation leads to an entropy preserving (EP) scheme. It is shown in the present paper that it is also possible to construct the flux of a conservative finite volume scheme to produce a kinetic energy preserving (KEP) scheme which exactly satisfies the global conservation law for kinetic energy. A proof is presented for three dimensional discretization on arbitrary grids. Both the EP and KEP schemes have been applied to the direct numerical simulation of one-dimensional viscous flow in a shock tube. The computations verify that both schemes can be used to simulate flows with shock waves and contact discontinuities without the introduction of any artificial diffusion. The KEP scheme performed better in the tests.

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