An arbitrary high-order discontinuous Galerkin method with local time-stepping for linear acoustic wave propagation

This paper presents a numerical scheme of arbitrary order accuracy in both space and time, based on the high-order derivatives methodology, for transient acoustic simulations. The combines nodal discontinuous Galerkin method spatial discretization Taylor series integrator (TSI) time integration. main idea TSI is temporal expansion all unknown variables which are replaced by via Cauchy-Kovalewski procedure. computational cost integration linearly proportional to accuracy. To increase efficiency simulations involving strongly varying mesh sizes or material properties, local time-stepping (LTS) algorithm accompanying (ADER-DG) scheme, ensures correct communications between domains with different step sizes, proposed. A stability analysis terms maximum allowable performed. Based convergence analysis, we demonstrate that nonuniform meshes, consistent achieved using ADER-DG LTS. An application sound propagation across transmissive noise barrier validates potential proposed practical problems demanding high