Propagation of large destructive waves

In this paper, we discuss some critical aspects of standard numerical models for tsunami simulation. We evaluate the importance of dispersion in open sea and demonstrate that the Boussinesq equations offer a surprisingly good balance between accuracy and mathematical simplicity for tsunami problems. Numerical artifacts of wave propagation in discrete media, with emphasis on effects of staircase boundaries commonly used in finite difference models, are also exemplified. Our conclusion is that tsunami simulation needs different partial differential equations, treated by different numerical techniques and implementations, in different parts of the domain. This calls for a domain decomposition approach.