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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, International University, Vietnam National University - Ho Chi Minh City, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam

    Mai Duc Thanh

  2. Department of Mathematics and Computer Science, University of Science, Vietnam National University - Ho Chi Minh City, 227 Nguyen Van Cu str., District 5, Ho Chi Minh City, Vietnam

    Nguyen Xuan Thanh

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  1. Mai Duc Thanh
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Correspondence to Mai Duc Thanh.

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Communicated by Yong Zhou.

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Thanh, M.D., Thanh, N.X. Well-Balanced Numerical Schemes for Shallow Water Equations with Horizontal Temperature Gradient. Bull. Malays. Math. Sci. Soc. 43, 783–807 (2020). https://doi.org/10.1007/s40840-018-00713-5

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  • DOI: https://doi.org/10.1007/s40840-018-00713-5

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