A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux
Abstract
In this paper, a high order quasi-conservative discontinuous Galerkin (DG) method using the non-oscillatory kinetic flux is proposed for the 5-equation model of compressible multi-component flows with Mie-Gr\"uneisen equation of state. The method mainly consists of three steps: firstly, the DG method with the non-oscillatory kinetic flux is used to solve the conservative equations of the model; secondly, inspired by Abgrall's idea, we derive a DG scheme for the volume fraction equation which can avoid the unphysical oscillations near the material interfaces; finally, a multi-resolution WENO limiter and a maximum-principle-satisfying limiter are employed to ensure oscillation-free near the discontinuities, and preserve the physical bounds for the volume fraction, respectively. Numerical tests show that the method can achieve high order for smooth solutions and keep non-oscillatory at discontinuities. Moreover, the velocity and pressure are oscillation-free at the interface and the volume fraction can stay in the interval [0,1].
Keywords
Cite
@article{arxiv.2007.06014,
title = {A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux},
author = {Dongmi Luo and Jianxian Qiu and Jun Zhu and Yibing Chen},
journal= {arXiv preprint arXiv:2007.06014},
year = {2023}
}
Comments
41 pages, 70 figures