Joint Modeling of Wave Phenomena by Applying the Grid-Characteristic Method and the Discontinuous Galerkin Method

Abstract

Abstract The aim of this work is to develop a hybrid computational method that combines the grid-characteristic method on regular structured grids with the discontinuous Galerkin method on unstructured tetrahedral grids. The proposed method makes it possible to describe integration domains with complex-shaped boundaries and contact boundaries and to calculate seismic fields taking into account the topography of the Earth’s surface, while saving computational resources. This modification of the method in the three-dimensional case has been proposed in this paper for the first time. Examples of using the developed method for calculating elastic wave phenomena arising during seismic prospecting are given. By way of testing, a comparison is made with results produced by the grid-characteristic method on curvilinear structured grids. The proposed hybrid method can be used not only for seismic prospecting, but also for calculating wave phenomena in other objects of complex shape.