Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity
Abstract
A new implementation of the Roe scheme for solving two-layer shallow-water equations is presented in this paper. The proposed A-Roe scheme is based on the analytical solution to the characteristic quartic of the flux matrix, which is an efficient alternative to a numerical eigensolver. Additionally, an accurate method for maintaining the hyperbolic character of the governing system is proposed. The efficiency of the quartic closed-form solver is examined and compared to numerical eigensolvers. Furthermore, the accuracy and computational speed of the A-Roe scheme is compared to the Roe, Lax-Friedrichs, GFORCE, PVM, and IFCP schemes. Finally, numerical tests are presented to evaluate the efficiency of the iterative treatment for the hyperbolicity loss. The proposed A-Roe scheme is as accurate as the Roe scheme, but much faster, with computational speeds closer to the GFORCE and IFCP scheme.
Keywords
Cite
@article{arxiv.1810.11285,
title = {Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity},
author = {Nino Krvavica and Miran Tuhtan and Gordan Jelenić},
journal= {arXiv preprint arXiv:1810.11285},
year = {2018}
}