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A Quasi-Conservative Discontinuous Galerkin Method for Multi-component Flows Using the Non-oscillatory Kinetic Flux II: ALE Framework

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Abstract

A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method is a predictor-corrector strategy to define the grid velocity. A Lagrangian mesh is first computed based on the flow velocity and then used as an initial mesh in a moving mesh method (the moving mesh partial differential equation or MMPDE method ) to improve its quality. The fluid dynamic equations are discretized in the direct arbitrary Lagrangian-Eulerian framework using DG elements and the non-oscillatory kinetic flux while the species equation is discretized using a quasi-conservative DG scheme to avoid numerical oscillations near material interfaces. A selection of one- and two-dimensional examples are presented to verify the convergence order and the constant-pressure-velocity preservation property of the method. They also demonstrate that the incorporation of the Lagrangian meshing with the MMPDE moving mesh method works well to concentrate mesh points in regions of shocks and material interfaces.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Dongmi Luo, Shiyi Li & Yibing Chen

  2. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Weizhang Huang

  3. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, China

    Jianxian Qiu

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  1. Dongmi Luo
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The research is supported partly by National Natural Science Foundation of China (Grant Nos. 12101063, 11901044 and 12071392), Science Challenge Project (China), No. TZ2016002, National Key Project (GJXM92579)

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Luo, D., Li, S., Huang, W. et al. A Quasi-Conservative Discontinuous Galerkin Method for Multi-component Flows Using the Non-oscillatory Kinetic Flux II: ALE Framework. J Sci Comput 90, 46 (2022). https://doi.org/10.1007/s10915-021-01732-4

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