High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems

摘要

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.