@Article{IJNAM-20-229,
author = {Nguyen , Thuong},
title = {Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with Variable Density},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2023},
volume = {20},
number = {2},
pages = {229--266},
abstract = {<p style="text-align: justify;">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 &quot;lake-at-rest&quot; 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.</p>},
issn = {2617-8710},
doi = {https://doi.org/ 10.4208/ijnam2023-1010},
url = {http://global-sci.org/intro/article_detail/ijnam/21360.html}
}