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arXiv · 2411.00285

A Kinetic Scheme Based On Positivity Preservation For Multi-component Euler Equations

Shashi Shekhar Roy·S. V. Raghurama Rao
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Abstract

A kinetic model with flexible velocities is presented for solving the multi-component Euler equations. The model employs a two-velocity formulation in 1D and a three-velocity formulation in 2D. In 2D, the velocities are aligned with the cell-interface to ensure a locally one-dimensional macroscopic normal flux in a finite volume. The velocity magnitudes are defined to satisfy conditions for preservation of positivity of density of each component as well as of overall pressure for first order accuracy under a CFL-like time-step restriction. Additionally, at a stationary contact discontinuity, the velocity definition is modified to achieve exact capture. The basic scheme is extended to third order accuracy using a Chakravarthy-Osher type flux-limited approach along with Strong Stability Preserving Runge-Kutta (SSPRK) method. Benchmark 1D and 2D test cases, including shock-bubble interaction problems, are solved to demonstrate the efficacy of the solver in accurately capturing the relevant flow features.

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Shashi Shekhar Roy, S. V. Raghurama Rao. 2024-11-01. A Kinetic Scheme Based On Positivity Preservation For Multi-component Euler Equations. https://doi.org/10.1016/j.euromechflu.2026.204490

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