A Kinetic Scheme Based On Positivity Preservation For Multi-component Euler Equations
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.
Cite
@article{arxiv.2411.00285,
title = {A Kinetic Scheme Based On Positivity Preservation For Multi-component Euler Equations},
author = {Shashi Shekhar Roy and S. V. Raghurama Rao},
journal= {arXiv preprint arXiv:2411.00285},
year = {2026}
}
Comments
arXiv admin note: text overlap with arXiv:2403.14794