Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with Variable Density
Year: 2023
Author: Thuong Nguyen
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 2 : pp. 229–266
Abstract
In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is well-balanced, positivity-preserving, and oscillation free at the curve where two types of fluid merge. The proposed approach is an extension of the adaptive well-balanced, positivity-preserving scheme developed in Epshteyn and Nguyen (arXiv preprint arXiv:2011.06143, 2020). In particular, to preserve "lake-at-rest" steady states, we utilize the Riemann Solver with appropriately rotated coordinates to obtain the point values in neighborhood of the fluid interface. In addition, to improve the efficiency of an adaptive method in the multi-fluid flow, the curve of density discontinuity is reconstructed by using the level set method and volume fraction method. To demonstrate the accuracy, high-resolution, and efficiency of the new adaptive central-upwind scheme, several challenging tests for Shallow water models with variable density are performed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1010
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 2 : pp. 229–266
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Shallow water equations with variable density central-upwind scheme well-balanced and positivity-preserving scheme adaptive algorithm interface tracking Riemann solver weak local residual error estimator unstructured triangular grid.