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Central-upwind scheme for Savage-Hutter type model of submarine landslides and generated tsunami waves. (English) Zbl 1302.76115

Summary: We develop a new central-upwind scheme for a one-dimensional Savage-Hutter type model of submarine landslides and generated tsunami waves. Our scheme exactly preserves physically relevant steady-states, preserves positivity of water depth, is insensitive to choice of discretization of nonconservative products, and properly incorporates friction inherent in the model. We apply our scheme to a variety of test problems and the numerical results clearly demonstrate a high accuracy and robustness of the proposed method.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
86-08 Computational methods for problems pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
35L65 Hyperbolic conservation laws
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