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An Entropy-Stable Residual Distribution Scheme for the System of Two-Dimensional Inviscid Shallow Water Equations

  • Wei Shyang Chang
  • Farzad Ismail
  • Hossain Chizari
Article
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Abstract

An entropy-stable residual distribution (RD) method is developed for the systems of two-dimensional shallow water equations (SWE). The construction of entropy stability for the residual distribution method is derived from finite volume method principles, albeit using a multidimensional approach. The paper delves into in-depth discussions on how finite volume methods achieve entropy stability in a “one-dimensional” sense for two-dimensional systems of SWE unlike the residual distribution methods. Results herein demonstrate the superiority of the entropy-stable RD methods relative to their finite volume counterparts, especially on highly irregular triangular grids. The comparative results with other established RD methods are also included, depicting similar performances with the Lax–Wendroff method for unsteady smooth flows but more accurate than the multidimensional upwind approaches (N, LDA) on both smooth and discontinuous test cases.

Keywords

Entropy-stable Residual distribution Semi-discrete Shallow water Flux function 

Mathematics Subject Classification

65N08 

Notes

Acknowledgements

We would like to thank Universiti Sains Malaysia for financially supporting this research work under the Academic Staff Training Scheme (ASTS) and the USM Research University Grant (No: 1001/PAERO/8014091).

Supplementary material

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  • Wei Shyang Chang
    • 1
  • Farzad Ismail
    • 1
  • Hossain Chizari
    • 2
  1. 1.School of Aerospace Engineering, Engineering CampusUniversiti Sains MalaysiaPulau PinangMalaysia
  2. 2.International Center for Applied Mechanics (ICAM), State Key Laboratory for Strength and Vibration of Mechanical StructuresXi’an Jiaotong University (XJTU)Xi’anPeople’s Republic of China

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