Discontinuous Galerkin for Stiff Hyperbolic Systems

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A Discontinuous Galerkin (DG) method is applied to hyperbolic systems that contain stiff relaxation terms. We demonstrate that when the relaxation time is under-resolved, DG is accurate in the sense that the method accurately represents the system's Chapman-Enskog (or ''diffusion'') approximation. Moreover, we demonstrate that a high-resolution, finite-volume method using the same time-integration method as DG is very inaccurate in the diffusion limit. Results for DG are presented for the hyperbolic heat equation, the Broadwell model of gas kinetics, and coupled radiation-hydrodynamics.

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10 p.

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Lowrie, R.B. & Morel, J.E. June 27, 1999.

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Description

A Discontinuous Galerkin (DG) method is applied to hyperbolic systems that contain stiff relaxation terms. We demonstrate that when the relaxation time is under-resolved, DG is accurate in the sense that the method accurately represents the system's Chapman-Enskog (or ''diffusion'') approximation. Moreover, we demonstrate that a high-resolution, finite-volume method using the same time-integration method as DG is very inaccurate in the diffusion limit. Results for DG are presented for the hyperbolic heat equation, the Broadwell model of gas kinetics, and coupled radiation-hydrodynamics.

Physical Description

10 p.

Notes

OSTI as DE00761235

Medium: P; Size: 10 pages

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  • American Institute of Aeronautics and Astronautics, Norfolk, VA (US), 06/27/1999--07/01/1999

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  • Report No.: LA-UR-99-2097
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 761235
  • Archival Resource Key: ark:/67531/metadc723239

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  • June 27, 1999

Added to The UNT Digital Library

  • Sept. 29, 2015, 5:31 a.m.

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  • April 6, 2017, 6:42 p.m.

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Lowrie, R.B. & Morel, J.E. Discontinuous Galerkin for Stiff Hyperbolic Systems, article, June 27, 1999; New Mexico. (digital.library.unt.edu/ark:/67531/metadc723239/: accessed October 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.