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Distributed Octree Data Structures and Local Refinement Method for the Parallel Solution of Three-Dimensional Conservation Laws

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Grid Generation and Adaptive Algorithms

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 113))

Abstract

Conservation laws are solved by a local Galerkin finite element procedure with adaptive space-time mesh refinement and explicit time integration. A distributed octree structure representing a spatial decomposition of the domain is used for mesh generation, and later may be used to correct for processor load imbalances introduced at adaptive enrichment steps. A Courant stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size. Computational results are presented for the three-dimensional Euler equations of compressible flow solved on an IBM SP2 computer. The problem examined is the flow inside a perforated shock tube.

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Authors and Affiliations

  1. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, New York, 12180-3590, USA

    J. E. Flaherty, R. M. Loy, M. S. Shephard, M. L. Simone, B. K. Szymanski, J. D. Teresco & L. H. Ziantz

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  1. J. E. Flaherty
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  2. R. M. Loy
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  3. M. S. Shephard
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  4. M. L. Simone
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  5. B. K. Szymanski
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  6. J. D. Teresco
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Editor information

Editors and Affiliations

  1. Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA, 94304-1314, USA

    Marshall W. Bern

  2. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, New York, 12180-3590, USA

    Joseph E. Flaherty

  3. School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN, 55455, USA

    Mitchell Luskin

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Flaherty, J.E. et al. (1999). Distributed Octree Data Structures and Local Refinement Method for the Parallel Solution of Three-Dimensional Conservation Laws. In: Bern, M.W., Flaherty, J.E., Luskin, M. (eds) Grid Generation and Adaptive Algorithms. The IMA Volumes in Mathematics and its Applications, vol 113. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1556-1_7

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  • DOI: https://doi.org/10.1007/978-1-4612-1556-1_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7191-8

  • Online ISBN: 978-1-4612-1556-1

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