A spacetime finite element method for coupled acoustic fluid-structure interactions

Abstract

The spacetime discontinuous Galerkin (SDG) finite element method is applied to problems of acoustic propagation. The spacetime discontinuous Galerkin are a family of discontinuous finite element methods for hyperbolic systems of equations. They utilize an advancing front mesh generation procedure that allows local “patches” of elements to become decoupled from the global solution domain through causality. Causal space-time meshes enable a locally implicit solution procedure with provably linear computational complexity. Mesh adaptivity is shown to effectively resolve propagating waves and minimize dispersion error. Numerical results demonstrate the effectiveness of the proposed solution method, including achieving optimal convergence rates. Time domain simulations of several canonical acoustic problems are presented.