Abstract
This paper is concerned with the development of well-balanced high order Roe methods for two-dimensional nonconservative hyperbolic systems. In particular, we are interested in extending the methods introduced in (Castro et al., Math. Comput. 75:1103–1134, 2006) to the two-dimensional case. We also investigate the well-balance properties and the consistency of the resulting schemes. We focus in applications to one and two layer shallow water systems.
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Castro, M.J., Fernández-Nieto, E.D., Ferreiro, A.M. et al. High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems. J Sci Comput 39, 67–114 (2009). https://doi.org/10.1007/s10915-008-9250-4
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DOI: https://doi.org/10.1007/s10915-008-9250-4