Journal of Scientific Computing

, Volume 72, Issue 3, pp 1146–1168 | Cite as

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

  • Xi Deng
  • Ziyao Sun
  • Bin Xie
  • Kensuke Yokoi
  • Chungang ChenEmail author
  • Feng Xiao


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.


Multi-moment method Finite volume method Variation-minimization principle Non-oscillatory scheme High-order scheme Local reconstruction 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Xi Deng
    • 1
  • Ziyao Sun
    • 1
  • Bin Xie
    • 1
  • Kensuke Yokoi
    • 2
  • Chungang Chen
    • 3
    Email author
  • Feng Xiao
    • 1
  1. 1.Department of Mechanical EngineeringTokyo Institute of TechnologyYokohamaJapan
  2. 2.School of EngineeringCardiff UniversityCardiffUK
  3. 3.School of Human Settlement and Civil Engineering & State Key Laboratory for Strength and Vibration of Mechanical StructuresXi’an Jiaotong UniversityXi’anChina

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