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-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].
- Publication:
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arXiv e-prints
- Pub Date:
- July 2020
- DOI:
- 10.48550/arXiv.2007.06014
- arXiv:
- arXiv:2007.06014
- Bibcode:
- 2020arXiv200706014L
- Keywords:
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- Physics - Computational Physics;
- Mathematics - Numerical Analysis
- E-Print:
- 41 pages, 70 figures