Dispersion and dissipation analysis for unphysical modes of high-order discontinuous galerkin methods

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Dispersion and dissipation of unphysical modes in high-order discontinuous Galerkin (DG) methods are investigated through the Fourier analysis for the one-dimensional scalar advection equation. A combined mode consisting of the physical and unphysical mode is examined. The dispersion and dissipation of the unphysical mode are totally different with those of the physical mode, and the switching between the physical and unphysical modes exists in the combined mode. The unphysical mode is dominant in the combined mode when an input wave number is high. The analysis of the dispersion and dissipation of the combined mode then clarifies that their drastically fluctuations in time when the switching occurs. Through time averaging the dispersion and dissipation of the combined mode, a sudden deviation from exact solutions and the small dissipation for high wave numbers are found. Finally, a simple advection of a sine wave is computed to validate the present Fourier analysis.

Original languageEnglish
Title of host publicationAIAA Scitech 2020 Forum
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
Pages1-9
Number of pages9
ISBN (Print)9781624105951
DOIs
Publication statusPublished - 2020
Externally publishedYes
EventAIAA Scitech Forum, 2020 - Orlando, United States
Duration: 2020 Jan 62020 Jan 10

Publication series

NameAIAA Scitech 2020 Forum
Volume1 PartF

Conference

ConferenceAIAA Scitech Forum, 2020
CountryUnited States
CityOrlando
Period20/1/620/1/10

ASJC Scopus subject areas

  • Aerospace Engineering

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