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Physics > Computational Physics

arXiv:2007.06014 (physics)
[Submitted on 12 Jul 2020]

Title:A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux

Authors:Dongmi Luo, Jianxian Qiu, Jun Zhu, Yibing Chen
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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-Grüneisen 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].
Comments: 41 pages, 70 figures
Subjects: Computational Physics (physics.comp-ph); Numerical Analysis (math.NA)
Cite as: arXiv:2007.06014 [physics.comp-ph]
  (or arXiv:2007.06014v1 [physics.comp-ph] for this version)
  https://doi.org/10.48550/arXiv.2007.06014
Related DOI: https://doi.org/10.1007/s10915-021-01494-z

Submission history

From: Dongmi Luo [view email]
[v1] Sun, 12 Jul 2020 15:17:17 UTC (4,312 KB)
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