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A numerical technique for applying time splitting methods in shallow water equations. (English) Zbl 1410.76248
Summary: In this paper, we analyze the use of time splitting techniques for solving shallow water equations. We discuss some properties that these schemes should satisfy so that interactions between the source term and the shock waves are controlled. This work shows that these schemes must be well balanced in the meaning expressed by J. M. Greenberg and A.-Y. Le Roux [SIAM J. Numer. Anal. 33, No. 1, 1–16 (1996; Zbl 0876.65064)]. More specifically, we analyze in what cases it is enough to verify an approximate C-property and in which cases it is required to verify an Exact C-property (see [A. Bermúdez et al., Comput. Methods Appl. Mech. Eng. 155, No. 1–2, 49–72 (1998; Zbl 0961.76047); A. Bermúdez and M. E. Vázquez, Comput. Fluids 23, No. 8, 1049–1071 (1994; Zbl 0816.76052)]). We also discuss this technique in two dimensions and include some numerical tests in order to justify our argument.
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
86A05 Hydrology, hydrography, oceanography
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