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An Oscillation-Free Bound-Preserving Discontinuous Galerkin Method for Multi-component Chemically Reacting Flows

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Abstract

This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving the multi-component chemically reacting flows. Two common governing equations are considered: reactive Euler equations and Navier–Stokes equations. Based on our recently developed high-order bound-preserving discontinuous Galerkin method in Du and Yang (J Comput Phys 469:111548, 2022), we add an extra damping term into this scheme to control the spurious oscillations. With the careful construction of the damping term, the proposed method not only achieves non-oscillatory property without sacrificing any order of accuracy but also preserves the conservative property which is the key ingredient of the bound-preserving technique developed in Du and Yang (2022). Therefore, the proposed OFDG method is well-compatible with the bound-preserving limiter in Du and Yang (2022). Similar to Liu et al. (SIAM J Sci Comput 44:A230–A259, 2022), the conservative modified exponential Runge–Kutta method is used to relax the restriction of time step sizes and preserve the conservative property of the fully discrete schemes. Numerical experiments, including one- and two-dimensional space, demonstrate the proposed method has desired properties.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Funding

J. Du: Research is partially supported by National Key R &D Program of China (Grant No. 2021YFA0719200). Y. Liu: Research is partially supported by NSFC Grants 12201621 and Youth Innovation Promotion Association CAS. Y. Yang: Research is partially supported by Simons Foundation 961585.

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Authors and Affiliations

  1. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, People’s Republic of China

    Jie Du

  2. Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408, People’s Republic of China

    Jie Du

  3. LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Yong Liu

  4. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Yang Yang

Authors
  1. Jie Du
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  2. Yong Liu
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  3. Yang Yang
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Correspondence to Yong Liu.

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The original version of the article was revised: Grant No. for Dr. Du was incorrect. It has been corrected.

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Du, J., Liu, Y. & Yang, Y. An Oscillation-Free Bound-Preserving Discontinuous Galerkin Method for Multi-component Chemically Reacting Flows. J Sci Comput 95, 90 (2023). https://doi.org/10.1007/s10915-023-02217-2

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  • DOI: https://doi.org/10.1007/s10915-023-02217-2

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