Graph-grammar based algorithm for asteroid tsunami simulations

Abstract

Around 1 million kilometers from Earth, five times the distance from Earth to the Moon, a large asteroid passed without harm to the Earth. Theoretically, however, the event of the asteroid falling into Earth, causing the tsunami, is possible since there are over 27,000 near-Earth asteroids [1], and the Earth's surface is covered in 71 percent by water. We introduce a novel graph-grammar-based framework for asteroid tsunami simulations. Our framework adaptively generates the computational mesh of the Earth model. It is built from triangular elements representing the seashore and the seabed. The computational mesh is represented as a graph, with graph vertices representing the computational mesh element's interiors and edges. Mesh refinements are often performed by the longest-edge refinement algorithm. We have expressed this algorithm by only two graph-grammar productions. The resulting graph represents the terrain approximating the topography with a prescribed accuracy. We generalize the graph-grammar mesh refinement algorithm to work on the entire Earth model, allowing the generation of the terrain topography, including the seabed. Having the seashore and the seabed represented by a graph, we introduce the finite element method simulations of the tsunami wave propagation. We illustrate the framework with simulations of the disastrous asteroid falling into the Baltic sea.