Adaptive Central-Upwind Scheme on Triangular Grids for the Saint-Venant System

2020/11/12 by Epshteyn, Yekaterina, Nguyen, Thuong
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2011.06143

Abstract

In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical method is an extension of the scheme from [\sc Liu \em et al.,J. of Comp. Phys, 374 (2018), pp. 213 - 236]. As a part of the adaptive central-upwind algorithm, we obtain local a posteriori error estimator for the efficient mesh refinement strategy. The accuracy, high-resolution, and efficiency of the new adaptive central-upwind scheme are demonstrated on a number of challenging tests for shallow water models.

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