Grid-Characteristic Method on Joint Structured Regular and Curved Grids for Modeling Coupled Elastic and Acoustic Wave Phenomena in Objects of Complex Shape

This work is devoted to the modification of the grid-characteristic numerical method. We propose using joint structured regular and curved computational grids to describe the complex geometric shape of objects and save computing resources. In subdomains, where possible, we propose use structured regular computational grids conformal with structured curved grids. Moreover, we use different calculation algorithms in subdomains with structured regular grids and with curved grids. The elastic and acoustic wave equations are also jointly solved in various subdomains of the integration domain for a more accurate description of the simulated model. We use the corresponding contact conditions at the boundaries between subdomains with different types of computational grids, different solved systems of equations, and different elastic and acoustic parameters of the media. We have proved in this paper the equivalence of using the contact condition of complete adhesion with the absence of an interface in the case of the same elastic and acoustic properties. The proposed modification of the grid-characteristic method was tested on the problems of studying the earthquake resistance of a bridge over a river and a bridge over a highway.