Modeling evolving discontinuities with spacetime discontinuous Galerkin methods

Reza Abedi, Shuo Heng Chung, Morgan A. Hawker, Jayandran Palaniappan, Robert B. Haber

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

Abstract

We review recent progress in applying spacetime discontinuous Galerkin (SDG) finite element methods to problems whose solutions exhibit various types of moving discontinuities. SDG models and related solution methods offer a number of attractive features, including element-wise satisfaction of the governing balance laws, linear computational complexity in the number of spacetime elements, and a computational structure that readily supports parallel implementations.We describe the use of new unstructured spacetime meshing procedures ind discretizing evolving discontinuities. Specifically, we show how h-adaptive spacetime meshing can be used to capture weak shocks in linear elastodynamics, how the SDG framework provides a convenient setting for implementing cohesive models for dynamic fracture, and how more advanced spacetime meshing procedures can deliver sharp representations of discontinuous solution features by tracking the trajectories of contact discontinuities in compressible gas dynamics.

Original languageEnglish (US)
Title of host publicationIUTAM Symposium on Discretization Methods for Evolving Discontinuities - Proceedings of the IUTAM Symposium
Pages59-87
Number of pages29
DOIs
StatePublished - Dec 1 2007
EventIUTAM Symposium on Discretization Methods for Evolving Discontinuities - Lyon, France
Duration: Sep 4 2006Sep 7 2006

Publication series

NameSolid Mechanics and its Applications
Volume5
ISSN (Print)1875-3507

Other

OtherIUTAM Symposium on Discretization Methods for Evolving Discontinuities
CountryFrance
CityLyon
Period9/4/069/7/06

Keywords

  • Adaptive analysis
  • Cohesive fracture
  • Discontinuous Galerkin
  • Interface tracking
  • Spacetime

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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