New computational methods in tsunami science

Tsunamis are rare events with severe consequences. This generates a high demand on accurate simulation results for planning and risk assessment purposes because of the low availability of actual data from historic events. On the other hand, validation of simulation tools becomes very difficult with such a low amount of real-world data. Tsunami phenomena involve a large span of spatial and temporal scales-from ocean basin scales of O(10(7)) m to local coastal wave interactions of O(10(2)) m or even O(10(1)) m, or from resonating wave phenomena with durations of O(10(5))s to rupture with time periods of O(10(1)) s. The scale gap of five orders of magnitude in each dimension makes accurate modelling very demanding, with a number of approaches being taken to work around the impossibility of direct numerical simulations. Along with the mentioned multi-scale characteristic, the tsunami wave has a multitude of different phases, corresponding to different wave regimes and associated equation sets. While in the deep ocean, wave propagation can be approximated relatively accurately by linear shallow-water theory, the transition to a bore or solitary wave train in shelf areas and then into a breaking wave in coastal regions demands appropriate mathematical and numerical treatments. The short duration and unpredictability of tsunami events pose another challenging requirement to tsunami simulation approaches. An accurate forecast is sought within seconds with very limited data available. Thus, efficiency in numerical solution processes and at the same time the consideration of uncertainty play a big role in tsunami modelling applied for forecasting purposes.