An immersed interface method for acoustic wave equations with discontinuous coefficients in complex geometries

Abstract

A new numerical method to solve three-dimensional wave equations in media with arbitrarily-shaped interfaces on a Cartesian grid is proposed. The present method aims to achieve two objectives to simulate wave propagation through realistic geometries: (1) handling wave interaction at the interface with high ratios of acoustic material properties and (2) treating complex geometries involving both smooth and non-smooth interfaces. To achieve the first objective, the present method extends the solution smoothly across the interface in the direction normal to the interface. A cell layer of ghost points on each side of the interface is used to enforce interface conditions, which support not only reflection but also transmission of incident waves. Ghost-point values are determined by applying a local coordinate-transform and a weighted least squares error method, which suppress numerical instabilities. To achieve the second objective, the interface geometry is approximated using an unstructured surface mesh, which does not require analytic information about the interface geometry. Finally, the accuracy and effectiveness of the present method are validated and demonstrated for wave propagation over or through several two-dimensional and three-dimensional obstacles. (C) 2020 Elsevier Inc. All rights reserved.