In the present paper the numerical method for three dimensional run-up, given in Johnsgard and Pedersen, Numerical methods in fluids, 1997, is extended to include wave breaking. In the fundamental problem of run-up of a uniform bore we compare our model to analytical solutions from the literature. The numerical solutions converges, but very slowly. This is not due to the numerical model, but rather to the structure of the solutions themself. Numerical results for two realistic, but simplified Tsunami cases are also presented. In the first case we make two-dimensional simulations concerning the run-up of a Tsunami in Portugal, in the second case we study the three dimensional wave pattern generated after a slide in Tafjord, Norway, in 1931. A discussion of different aspects of the model is summarized at the end of the paper.
The present research has been partially financed by the Commission of the European Communities under the contract ENV4-U96-0297, as part of the international project GITEC-TWO, and by the Norwegian Research Council under contract EMSEFMK.300002. I am also grateful to Professor Geir Pedersen for interesting and fruitful discussions.