Communications in Mathematical Sciences
Volume 21 (2023)
Adaptive central-upwind scheme on triangular grids for the Saint–Venant system
Pages: 671 – 708
In this work, we develop a robust adaptive well-balanced and positivity-preserving centralupwind scheme on unstructured triangular grids for shallow water equations. The numerical method is an extension of the scheme from [Liu et al., J. Comput. Phys., 374:213–236, 2018]. As a part of the adaptive central-upwind algorithm, we obtain a local a posterior error estimator for the efficient mesh refinement strategy. The accuracy, high-resolution and efficiency of new adaptive central-upwind scheme are demonstrated on a number of challenging tests for shallow water models.
Saint–Venant system of shallow water equations, central-upwind scheme, well-balanced and positivity-preserving scheme, adaptive algorithm, weak local residual error estimator, unstructured triangular grid
2010 Mathematics Subject Classification
35L65, 65M08, 76M12, 86-08, 86A05
The work of Yekaterina Epshteyn was partially supported by NSF DMS-2207207.
Received 25 June 2021
Received revised 1 June 2022
Accepted 8 July 2022
Published 27 February 2023