Supra-Conservative Finite-Volume Methods for the Simulation of Subsonic Flow

Abstract

It is demonstrated how finite-volume methods can be designed such that, next to the primary invariants (mass, momentum and internal energy), they also conserve secondary invariants (kinetic energy), i.e., they are supra-conservative. Key ingredient is a consistency between the discrete divergence terms in the constituting equations and the discrete pressure gradient. The requirements hold for any discretization method with a volume-consistent scaling.

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