Finally, I will show how the scheme can be extended to the two-layer shallow water equations  and to the Savage-Hutter type model of submarine landslides and generated tsunami waves , which, in addition to the geometric source term, contain nonconservative interlayer exchange terms. It is well-known that such terms, which arise in many dierent multiphase models, are extremely sensitive to a particular choice their numerical discretization. To circumvent this diculty, we rewrite the studied systems in a different way so that the nonconservative terms are multiplied by a quantity, which is, in all practically meaningful cases, very small. We then apply the central- upwind scheme to the rewritten system and demonstrate robustness and superb performance of the proposed method on a number numerical examples.
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