| Abstract: | The objective of this research is to develop a model that will adequately simulate the dynamics of tsunami propagating across the continental shelf. In practical terms, a large spatial domain with high resolution is required so that source areas and runup areas are adequately resolved. Hence efficiency of the model is a major issue. The three‐dimensional Reynolds averaged Navier–Stokes equations are depth‐averaged to yield a set of equations that are similar to the shallow water equations but retain the non‐hydrostatic pressure terms. This approach differs from the development of the Boussinesq equations where pressure is eliminated in favour of high‐order velocity and geometry terms. The model gives good results for several test problems including an oscillating basin, propagation of a solitary wave, and a wave transformation over a bar. The hydrostatic and non‐hydrostatic versions of the model are compared for a large‐scale problem where a fault rupture generates a tsunami on the New Zealand continental shelf. The model efficiency is also very good and execution times are about a factor of 1.8 to 5 slower than the standard shallow water model, depending on problem size. Moreover, there are at least two methods to increase model accuracy when warranted: choosing a more optimal vertical interpolation function, and dividing the problem into layers. Copyright © 2005 John Wiley & Sons, Ltd. |
