Consistent implementation of characteristic flux-split based finite difference method for compressible multi-material gas flows

Abstract

In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is variable), various non-conservative or quasi-conservative numerical models have been proposed. However, designing a consistent numerical algorithm, especially using the high-order characteristic flux-split based finite-difference method (CFS-FDM),is still an open question. In this study, a systematical analysis of previous algorithms of the consistent implementing the high-order CFS-FDM for such flows is performed, and the reasons of special treatments in these algorithms are revealed. Based on this analysis, a new general numerical methodology that successfully avoids any special treatments as those required in previously reported algorithms, is derived. In this new algorithm, we rewrite the non-conservative term as a conservative term with a source term containing velocity divergence.By consistently treating the advection velocity in the conservative term and velocity divergence in the source term by imposing a new additional criterion, specifically, that a multi-fluid algorithm should have the ability of maintaining a pure single-fluid, we finally derive a new general algorithm that does not need any special treatment, and is very convenient to implement. The results of some * Corresponding author Email address: tian_baolin@iapcm.ac.cn (Baolin Tian)

Consistent high resolution interface-capturing finite volume method for compressible multi-material flows

“…Hence, the artificial diffusion introduced by interface-diffusion capturing methods should be alleviated as much as possible to sharpen the diffusion zones and to increase the resolution of complex structures along the material interface. Several numerical approaches have been developed to minimize the numerical smearing, which attempt to compress the interfaces [28][29][30][31], to sharpen the interfaces [32][33][34], as well as to adopt high-order numerical schemes [21,26,[35][36][37][38][39][40][41][42][43]. Most recent developments tend to apply high-order algorithms to increase the resolution of the diffusive material interfaces.…”

Low-Dissipation Central-Upwind Schemes for Compressible Multifluids

“…We note that both the ghost fluid and interface tracking approaches are very robust in the 1-D case, but their multidimensional extensions are rather cumbersome. For several high-order WENO schemes for compressible multifluids, we refer the reader to [13,19,22,38,39].…”