New computational methods in tsunami science

Abstract

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 [Formula: see text] to local coastal wave interactions of [Formula: see text] or even [Formula: see text], or from resonating wave phenomena with durations of [Formula: see text] to rupture with time periods of [Formula: see text]. 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.

Tsunamis: bridging science, engineering and society

“…We note that the first tsunami-relevant Large Eddy Simulation (LES) of the Navier-Stokes equations appears to have been that of Liu et al [63] in the context of simulating underwater solid block landslides. Subsequent developments are discussed by Behrens & Dias [64].…”

“…Behrens & Dias [64] present developments in unstructured and adaptive grid techniques to bridge the gap of scales involved in tsunami propagation and inundation simulation. They argue that while computational acceleration by adaptive mesh refinement, hardware acceleration by GPU utilization, and parallelization make even real-time tsunami forecast for certain near-shore tsunamis technically feasible, all communities need to rely on more traditional approaches and a well-educated population.…”

Application of a Combined Finite Element—Finite Volume Method to a 2D Non-hydrostatic Shallow Water Problem

“…The details of the combined method and the treatment of the boundary conditions will be detailed in a forthcoming paper. 4 …”

“…H(x, y,t) a significant impact in the water depth for the propagation of tsunamis [10], [4]. The paper is organized as follows.…”

Risk Assessment and Design of Prevention Structures for Enhanced Tsunami Disaster Resilience (RAPSODI)/Euro-Japan Collaboration

“…The proposed formulas to calculate the forces mainly depend on the accurate predictions of the tsunami flow depth, flow velocity, and flow direction, which are usually obtained from numerical models, see discussion on tsunami numerical models by Behrens and Dias [2015]. Hence, the usage of validated and verified numerical models is essential [Synolakis et al, 2008].…”