A posteriori diffusion analysis of numerical schemes for application to propagating linear waves

Abstract

We compare several higher-order accurate numerical schemes based on their dissipation characteristics found out in an a posteriori energy analysis. The diffusion analysis is performed based on correlation between the modal energy as well as the total energy of the broadband signal and the dissipation characteristics of the candidate numerical scheme. This technique is used for analyzing linear as well as nonlinear including space-time coupled numerical schemes used in simulation of propagating linear waves, such as in computational electromagnetics and computational aeroacoustics. It is found that the discontinuous Galerkin scheme best preserves the signal energy over the simulation time among all candidate numerical schemes under consideration.