TY - GEN
T1 - Modeling evolving discontinuities with spacetime discontinuous Galerkin methods
AU - Abedi, Reza
AU - Chung, Shuo Heng
AU - Hawker, Morgan A.
AU - Palaniappan, Jayandran
AU - Haber, Robert B.
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
KW - Adaptive analysis
KW - Cohesive fracture
KW - Discontinuous Galerkin
KW - Interface tracking
KW - Spacetime
UR - http://www.scopus.com/inward/record.url?scp=84861158841&partnerID=8YFLogxK
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U2 - 10.1007/978-1-4020-6530-9_4
DO - 10.1007/978-1-4020-6530-9_4
M3 - Conference contribution
AN - SCOPUS:84861158841
SN - 9781402065293
T3 - Solid Mechanics and its Applications
SP - 59
EP - 87
BT - IUTAM Symposium on Discretization Methods for Evolving Discontinuities - Proceedings of the IUTAM Symposium
T2 - IUTAM Symposium on Discretization Methods for Evolving Discontinuities
Y2 - 4 September 2006 through 7 September 2006
ER -