Abgrall, Rémi; Karni, Smadar Two-layer shallow water system: a relaxation approach. (English) Zbl 1188.76229 SIAM J. Sci. Comput. 31, No. 3, 1603-1627 (2009). Summary: The two-layer shallow water system is an averaged flow model. It forms a nonconservative system which is only conditionally hyperbolic. The coupling between the layers, due to the hydrostatic pressure assumption, does not provide explicit access to the system eigenstructure, which is inconvenient for Riemann solution based numerical schemes. We consider a relaxation approach which offers greater decoupling and accessible eigenstructure. The stability of the model is discussed. Numerical results are shown for unsteady flows as well as for smooth and nonsmooth steady flows. Cited in 1 ReviewCited in 56 Documents MSC: 76M12 Finite volume methods applied to problems in fluid mechanics 35L65 Hyperbolic conservation laws 76N15 Gas dynamics (general theory) 76B70 Stratification effects in inviscid fluids Keywords:hyperbolic conservation laws; balance laws; shallow water equations; relaxation schemes PDFBibTeX XMLCite \textit{R. Abgrall} and \textit{S. Karni}, SIAM J. Sci. Comput. 31, No. 3, 1603--1627 (2009; Zbl 1188.76229) Full Text: DOI