An automatic approach for the acoustic analysis of three-dimensional bounded and unbounded domains by scaled boundary finite element method

Abstract

An automatic approach for modeling acoustic responses of 3D bounded and unbounded domains is proposed based on the scaled boundary finite element method (SBFEM). The bounded acoustic near field is modeled by SBFEM. Due to the fact that SBFEM only requires boundary discretizations, the meshing process in this approach is automatically accomplished by introducing an octree-based meshing technique and boundary trimming. Therefore, models with very complex geometries can be analyzed automatically, i.e. no human input/intervention is needed/required. For modeling the unbounded acoustic far field, a spherical high-order doubly-asymptotic open boundary is developed for modeling scalar wave propagation in 3D unbounded domain. This doubly-asymptotic open boundary is able to represent the unbounded domain accurately and efficiently as it includes recursive continued-fraction expansions in both high and low frequency limits. The continued-fraction solutions are expressed in the time-domain by introducing auxiliary variables. The bounded and unbounded domains are coupled via the nodal fluxes on the near/far field interface. The final coupled ordinary differential equations can be solve using standard time-stepping methods directly for obtaining transient acoustic responses. Various numerical examples are presented in this paper for demonstrating the accuracy, efficiency and capability of this approach for analyzing acoustic problems with complex geometries.