ITS 2001 Proceedings, Session 7, Number 7-27 933 A method for numerical modeling of tsunami run-up on the coast of an arbitrary profile Andrei G. Marchuk 1 and Alexandr A. Anisimov 2 1 Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia 2 Novosibirsk State University, Novosibirsk, Russia Abstract. In this paper a new method for numerical simulation of the long wave run-up process is proposed. Nonlinear shallow water equations are used to describe wave propagation up to the water-edge point. Then a special algorithm is used to estimate flow parameters and location of the moving water-edge point. It is based on energy and mass conservation laws. Several series of one-dimensional computations were carried out. A shore profile, which gives the maximum run-up height for the fixed initial wave parameters, has been found. Results of modeling tsunami run-up on the real shore in the Akita prefecture (Japan) are presented. 1. Introduction One of the most important questions in prognostic tsunami modeling is estimation of tsunami run-up heights at different points along the coastline. Methods for numerical simulation of tsunami wave propagation in deep and shallow seas are well developed and are widely used by a great number of scientists. Some of them, in order to find possible submerged areas, use the simplifying assumptions about the ratio between the tsunami wave height near the shore and wave run-up height. But this ratio is heavily dependent on the shore profile above mean sea level. 2. Statement of the Problem In this paper the method for numerical calculation of a tsunami wave run-up on a shore of an arbitrary profile will be described. Numerical modeling of this process was carried out on the basis of the one-dimensional nonlinear shallow-water model u t + uu x + gη x =0, η t +(u(η + H )) x =0. (1) Here u is velocity, η is surface elevation, H is the value of depth, and g is gravity acceleration. The statement of the problem is as follows: there is a one-dimensional nearcostal area with an arbitrary bottom relief. From the left boundary of the computational area the tsunami wave is coming toward the shore. Above the mean sea level the coast is of an arbitrary profile (Fig. 1). In numerical computation, the bottom and coastal relief is given 1 Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division of the Russian Academy of Sciences, Prosp. Lavrentieva, 6, Novosibirsk 630090, Russia (mag@omzg.sscc.ru) 2 Novosibirsk State University, Pirogrov Street, 2, Novosibirsk 630090, Russia (tvist@land3.nsu.ru)