Time-domain parallel simulation of heterogeneous wave propagation on unstructured grids using explicit, nondiffusive, discontinuous Galerkin methods

摘要

A general Discontinuous Calerkin framework is introduced for symmetric systems of conservations laws. It is applied to the three-dimensional electromagnetic wave propagation in heterogeneous media, and to the propagation of aeroacoustic perturbations of either uniform or nonuniform, steady solutions of the three-dimensional Euler equations. In all these linear contexts, the time evolution of some quadratic wave energy is given in a balance equation, with a volumic source term for aeroacoustics in a nonuniform flow. An explicit leap-frog time scheme along with centered numerical fluxes are used in the proposed Discontinuous Galerkin Time Domain (DGTD) method, in order to achieve a discrete equivalent of the balance equation for the wave energy. The scheme introduced is genuinely nondissipative. Numerical first-order boundary conditions are developed to bound the domain and stability is proved on arbitrary unstructured meshes and discontinuous finite elements, under some CFL-like stability condition on the time step. Numerical results obtained with a parallel implementation of the method based on mesh partitioning and message passing are presented to show the potential of the method.