Evaluation of Kinetic Energy and Entropy Preserving Schemes on the Simulation of Detonation Wave Dynamics

This paper is an update on a work in progress, discussing the motivation for improving the numerical simulation of detonation wave physics for industrially/experimentally relevant configurations. The focus of the work is the accuracy and stability of the discrete, multicomponent, Euler equations. In particular, the non-dissipative convective terms used, in part, with numerical schemes typically utilized for detonation simulations. To this end, a recently developed ``Kinetic Energy and Entropy Preserving'' scheme with desirable accuracy and stability properties is extended to handle multicomponent flows. The proper discretization of the chemical species equations is derived in order to adhere to the original analytical relations of the single component scheme. Three dimensional simulations of a multicomponent Taylor-Green vortex asses the performance of the extended scheme against a standard central differencing scheme. Results show a violation of the theoretical constraints of multicomponent flows, despite the adherence of the analytical relations that should guarantee accurate results. However, the extended scheme is shown to yield physically realistic results as well as better stability properties over the central difference scheme, even if the theoretical results are not obtained. The violation of theoretical results are due to mixing rules used in multicomponent flows, and are related to a classical problem of conservative schemes: the presence of spurious pressure oscillation in multicomponent numerical simulations.