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Standard conservative discretizations of the compressible Euler equations have been shown to admit nonphysical oscillations near some material interfaces. For example, the calorically perfect Euler equations admit these oscillations when both temperature and gamma jump across an interface, but not when either temperature or gamma happen to be constant. These nonphysical oscillations can be alleviated to some degree with a nonconservative modification of the total energy computed by solving a coupled evolution equation for the pressure. In this paper, we develop and illustrate this method for the thermally perfect Euler equations.

A General Technique for Eliminating Spurious Oscillations in Conservative Schemes for Multiphase and Multispecies Euler Equations