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Dimensional Splitting Well-Balanced Schemes on Cartesian Mesh for 2D Shallow Water Equations with Variable Topography

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Abstract

We present two types of simple algorithms for numerical approximations of the two-dimensional shallow water equations with variable topography by a dimensional splitting approach. The scheme of the first type has two steps and the the one of the second type has three steps of splitting dimensions in each iteration. In each step, the component computation incorporates a well-balanced method on Cartesian mesh in one-dimensional space. Tests show that these schemes provide us with a reasonable accuracy. Furthermore, we also establish the well-balanced property for both types of schemes.

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Acknowledgements

We would like to thank the Reviewers for their very constructive comments and helpful suggestions. This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under Grant number B2021-28-02.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu Str., District 5, Ho Chi Minh City, Vietnam

    Nguyen Xuan Thanh

  2. Department of Mathematics, International University, Quarter 6, Linh Trung Ward, Thu Duc, Ho Chi Minh City, Vietnam

    Mai Duc Thanh

  3. Department of Mathematics, Ho Chi Minh City University of Education, 280 An Duong Vuong Str., District 5, Ho Chi Minh City, Vietnam

    Dao Huy Cuong

  4. Vietnam National University, Ho Chi Minh City, Vietnam

    Nguyen Xuan Thanh & Mai Duc Thanh

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  1. Nguyen Xuan Thanh
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  2. Mai Duc Thanh
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Correspondence to Mai Duc Thanh.

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Communicated by Davoud Mirzaei.

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Thanh, N.X., Thanh, M.D. & Cuong, D.H. Dimensional Splitting Well-Balanced Schemes on Cartesian Mesh for 2D Shallow Water Equations with Variable Topography. Bull. Iran. Math. Soc. 48, 2321–2348 (2022). https://doi.org/10.1007/s41980-021-00648-x

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  • DOI: https://doi.org/10.1007/s41980-021-00648-x

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