Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SPLITTING TECHNIQUE AND GODUNOV-TYPE SCHEMES FOR 2D SHALLOW WATER EQUATIONS WITH VARIABLE TOPOGRAPHY

  • Dao Huy Cuong (Department of Mathematics Ho Chi Minh City University of Education) ;
  • Mai Duc Thanh (Department of Mathematics International University and Vietnam National University)
  • Received : 2023.09.21
  • Accepted : 2024.03.25
  • Published : 2024.07.31
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Abstract

We present numerical schemes to deal with nonconservative terms in the two-dimensional shallow water equations with variable topography. Relying on the dimensional splitting technique, we construct Godunov-type schemes. Such schemes can be categorized into two classes, namely the partly and fully splitting ones, depending on how deeply the scheme employs the splitting method. An upwind scheme technique is employed for the evolution of the velocity component for the partly splitting scheme. These schemes are shown to possess interesting properties: They can preserve the positivity of the water height, and they are well-balanced.

Keywords

Acknowledgement

We are very grateful to the reviewer for his/her very constructive comments and helpful suggestions. This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number B2023-28-07.

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