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.
@article{arxiv.2011.06143,
title = {Adaptive Central-Upwind Scheme on Triangular Grids for the Saint-Venant System},
author = {Yekaterina Epshteyn and Thuong Nguyen},
journal= {arXiv preprint arXiv:2011.06143},
year = {2021}
}