Premium
A posteriori diffusion analysis of numerical schemes for application to propagating linear waves
Author(s) -
Joshi Subodh M.,
Chatterjee Avijit
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22667
Subject(s) - dissipation , discontinuous galerkin method , mathematics , nonlinear system , computational aeroacoustics , a priori and a posteriori , numerical analysis , energy (signal processing) , algorithm , mathematical analysis , aeroacoustics , finite element method , physics , acoustics , philosophy , epistemology , thermodynamics , statistics , sound pressure , quantum mechanics
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.