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

作者：Berthon Christophe^*; Foucher Francoise; Morales Tomas

来源：Numerical Methods for Partial Differential Equations, 2015, 31(5): 1396-1423.

DOI：10.1002/num.21949

• two-layer shallow-water model
• finite volume schemes
• source term approximations
• splitting schemes
• well-balanced schemes
• non-negative preserving schemes

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.

• 出版日期2015-9