Well-Balanced Numerical Schemes for Shallow Water Equations with Horizontal Temperature Gradient

  • Mai Duc ThanhEmail author
  • Nguyen Xuan Thanh


A class of well-balanced numerical schemes for the one-dimensional shallow water equations with temperature gradient is constructed. The construction of the schemes is based on two steps: the first step to absorb the nonconservative term and the second step to deal with the evolution of the system. Algorithms for computing contact waves which absorb the nonconservative term are developed. Furthermore, to improve the accuracy, the underlying numerical fluxes can be formed as convex combinations of a pair of numerical fluxes of a low and stable scheme and a higher and fast scheme. The schemes are well balanced and can retain the positivity of the water height and the water temperature. Numerical tests show that the schemes are stable and have a good accuracy.


Shallow water equations Ripa system Conservation law Well-balanced scheme Convergence Accuracy 

Mathematics Subject Classification

35L65 65M08 76B15 



The authors would like to thank the reviewers for their very valuable comments and suggestions. This research is funded by the Vietnam National University HoChiMinh City (VNU-HCM) under Grant No. B2018-28-01.


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.Department of Mathematics, International UniversityVietnam National University - Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.Department of Mathematics and Computer Science, University of ScienceVietnam National University - Ho Chi Minh CityHo Chi Minh CityVietnam

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