An efficient splitting technique for two-layer shallow-water model

Abstract

We consider the numerical approximation of the weak solutions of the two-layer shallow-water equations. The model under consideration is made of two usual one-layer shallow-water model coupled by nonconservative products. Because of the nonconservative products of the system, which couple both one-layer shallow-water subsystems, the usual numerical methods have to consider the full model. Of course, uncoupled numerical techniques, just involving finite volume schemes for the basic shallow-water equations, are very attractive since they are very easy to implement and they are costless. Recently, a stable layer splitting technique was introduced [Bouchut and Morales de Luna, M2AN Math Model Numer Anal 42 (2008), 683–698]. In the same spirit, we exhibit new splitting technique, which is proved to be well balanced and non-negative preserving. The main benefit issuing from the here derived uncoupled method is the ability to correctly approximate the solution of very severe benchmarks. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1396–1423, 2015