Shape grammar for modeling Earth’s bathymetry and performing tsunami simulations

Abstract

AbstractWe present a shape grammar for generating Earth’s bathymetry. The shape grammar uses just two productions to define the Kossaczky mesh-refinement algorithm. The algorithm is then recursively applied to the sphere, starting with a partition into eight elements. As a refinement criterion, we select elements where Earth’s bathymetry needs improvement, based on the Global Multi-Resolution Topography Data Synthesis. Given a computational mesh approximating Earth’s bathymetry, we adopt the long-wave approximation derived from the shallow-water equations under appropriate assumptions to obtain the nonlinear wave equation. The wave equation is subsequently approximated by finite elements in space, and in time, we employ the generalized-α scheme. We present three numerical simulations. The first is the tsunami caused by an asteroid impact in the central North Atlantic Ocean. The second is the tsunami caused by the collapse of a volcano on the Canary Islands. The third is the simulation of the tsunami caused by the earthquake in the Valparaiso region of Chile. We also perform a verification of our shape grammar tsunami simulator.