Tsunami run-up modelings with adaptive mesh refinement (AMR) has been carried out to verify applicability and efficacy of the AMR method. A benchmark test for tsunami run-up modeling at Monai Village in Japan due to 1983 Okushiri Tsunami was chosen for validating numerical experiments with various AMR levels and bottom friction coefficients. The results from numerical experiments illustrated that the AMR method is fairly efficient with respects to modeling accuracy and computing load.
Numerical models for tsunami wave propagation are important tools to predict the tsunami heights and tsunami risk in coastal zones. In numerical models for tsunami processes, tsunami run-up is included by taking into account the various assumptions on hydraulic properties (roughness) of the dry land that is important for tsunami risk assessment. Direct calculation of tsunami propagation and run-up from source regions to the coastal zones with a single model domain results in low accuracy. Therefore, various nested methods with different grid intervals in open sea and coastal zone are generally applied. High level accuracy for tsunami run-up in coastal zones requires small grid intervals in the order of 10 meters or even less, resulting in the significant increase of computing times. As a result, such numerical models are difficult to use in operational practice. In this study, we illustrate the efficiency of adaptive mesh refinement method for tsunami run-up modeling through numerical experiments in terms of computational time and accuracy.
Gerris is an open source computational fluid dynamic code that solves non-linear shallow water equations. In this section, Gerris is described briefly in terms of the governing equations, the numerical scheme, and the adaptive mesh refinement method. For full details on Gerris and its various applications, please see Popinet (2003; 2011; 2012) and Lee et al. (2013; 2015).
Tsunamis are most commonly modeled using a long-wave approximation of the mass and momentum conservation equations for a fluid with a free surface. In this approximation, the slopes of both the free surface and the bathymetry are assumed to be negligibly small. However, these assumptions are often violated in the case of tsunamis, particularly those close to shore; somewhat surprisingly, the long-wave approximation still gives reasonable results in practice. Simple scaling arguments show that the vertical velocity of the fluid is also negligibly small in this context. Fluid motion can thus be described by only using the vertically averaged components of the horizontal momentum and the free-surface elevation. The non-linear shallow water equations in conservative form with additional terms for the Coriolis Effect and bottom friction can be described as (equation) where h is the free surface elevation, u=(u, v) is the horizontal velocity vector, g is the acceleration due to gravity, z is the depth of the bathymetry, f is the Coriolis coefficient, and Cf is the friction coefficient.
