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A Non-oscillatory Multi-Moment Finite Volume Scheme with Boundary Gradient Switching

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Abstract

In this work we propose a new formulation for high-order multi-moment constrained finite volume (MCV) method. In the one-dimensional building-block scheme, three local degrees of freedom (DOFs) are equidistantly defined within a grid cell. Two candidate polynomials for spatial reconstruction of third-order are built by adopting one additional constraint condition from the adjacent cells, i.e. the DOF at middle point of left or right neighbour. A boundary gradient switching (BGS) algorithm based on the variation-minimization principle is devised to determine the spatial reconstruction from the two candidates, so as to remove the spurious oscillations around the discontinuities. The resulted non-oscillatory MCV3-BGS scheme is of fourth-order accuracy and completely free of case-dependent ad hoc parameters. The widely used benchmark tests of one- and two-dimensional scalar and Euler hyperbolic conservation laws are solved to verify the performance of the proposed scheme in this paper. The MCV3-BGS scheme is very promising for the practical applications due to its accuracy, non-oscillatory feature and algorithmic simplicity.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 226-8502, Japan

    Xi Deng, Ziyao Sun, Bin Xie & Feng Xiao

  2. School of Engineering, Cardiff University, The Parade, Cardiff, CF24 3AA, UK

    Kensuke Yokoi

  3. School of Human Settlement and Civil Engineering & State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Chungang Chen

Authors
  1. Xi Deng
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  2. Ziyao Sun
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  3. Bin Xie
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  4. Kensuke Yokoi
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  5. Chungang Chen
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  6. Feng Xiao
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Corresponding author

Correspondence to Chungang Chen.

Additional information

This work was supported in part by JSPS KAKENHI (Grant No. 15H03916) and National Natural Science Foundation of China (Grant No. 41522504).

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Deng, X., Sun, Z., Xie, B. et al. A Non-oscillatory Multi-Moment Finite Volume Scheme with Boundary Gradient Switching. J Sci Comput 72, 1146–1168 (2017). https://doi.org/10.1007/s10915-017-0392-0

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  • DOI: https://doi.org/10.1007/s10915-017-0392-0

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