Finally, I will show how the scheme can be extended to the two-layer shallow water equations [4] and to the Savage-Hutter type model of submarine landslides and generated tsunami waves [2], 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.

REFERENCES
[1] A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system, M2AN Math. Model. Numer. Anal., 36 (2002), pp. 397425.
[2] A. Kurganov and J. Miller, Central-upwind scheme for Savage-Hutter type model of submarine landslides and generated tsunami waves, submitted.
[3] A. Kurganov and G. Petrova, A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system, Commun. Math. Sci., 5 (2007), pp. 133160.
[4] A. Kurganov and G. Petrova, Central-upwind schemes for two-layer shallow equations, SIAM J. Sci. Comput., 31 (2009), pp. 17421773.