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

Authors:
M. J. Castro;E. D. Fernández-Nieto;A. M. Ferreiro;J. A. García-Rodríguez;C. Parés
Affiliations:
Dpto. de Análisis Matemático, Universidad de Málaga, Málaga, Spain 29080;Dpto. de Matemática Aplicada I, Universidad de Sevilla, Sevilla, Spain 41012;Dpto. de Matemáticas, Universidad de A Coruña, A Coruña, Spain 15071;Dpto. de Matemáticas, Universidad de A Coruña, A Coruña, Spain 15071;Dpto. de Análisis Matemático, Universidad de Málaga, Málaga, Spain 29080
Venue:
Journal of Scientific Computing
Year:
2009

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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.