A hybrid PSTD/DG method to solve the linearized Euler equations

The Fourier Pseudospectral Time Domain (Fourier-PSTD) method was shown to be an effective way of modelling wave propagation. Fourier-PSTD is based on Fourier analysis and synthesis to compute the spatial derivatives of the governing wave equation. Therefore, the method suffers from the well-known Gibbs phenomenon when computing a non-smooth or discontinuous function. This limits its possibilities to compute arbitrary boundary conditions. Furthermore, the method needs to be computed on a regular mesh. Although some developments have been presented to locally refine the grid using multidomain implementations, its performance is limited when computing complex geometries. This paper presents a hybrid approach to solve the linearized Euler equations, coupling the Fourier-PSTD method with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of arbitrary boundary conditions and complex geometries by using the benefits of the DG method while keeping Fourier-PSTD in the bulk of the domain. In this paper, a coupling algorithm is presented together with an analysis of the precision of the hybrid approach