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A Two-Dimensional Mesh Refinement Method for Problems with One-Dimensional Singularities

Brown, David L. and Reyna, Luis Guillermo M. (1985) A Two-Dimensional Mesh Refinement Method for Problems with One-Dimensional Singularities. SIAM Journal on Scientific and Statistical Computing, 6 (3). pp. 515-531. ISSN 0196-5204. doi:10.1137/0906036.

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This paper introduces a method for resolving internal layers that can occur in the solutions of time-dependent differential equations in two space dimensions. Singular features in these solutions that are essentially one-dimensional in nature but are not oriented with the computational mesh are resolved using one-dimensional mesh refinement techniques with a procedure that is similar to an ADI method. A careful interpolation procedure assures that the resolution obtained in each ADI step is not lost in the succeeding ADI step.

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Additional Information:© 1985 Society for Industrial and Applied Mathematics. Received by the editors July 14, 1983, and in revised form January 23, 1984. This research was partially supported by the Office of Naval Research under contract N00014-80-CO076. Computer time was provided by the Stanford Exploration Project (Stanford University Department of Geophysics), the National Center for Atmospheric Research, and on the California Institute of Technology Applied Mathematics Department Fluid Dynamics VAX. We would like to thank Michael Naughton for carefully reading the manuscript and making several helpful comments.
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Office of Naval Research (ONR)N00014-80-CO076
Subject Keywords:two-dimensional mesh refinement, internal layers, shock resolution, alternating direction implicit method
Issue or Number:3
Record Number:CaltechAUTHORS:20120629-082824585
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Official Citation:A Two-Dimensional Mesh Refinement Method for Problems with One-Dimensional Singularities David L. Brown, Luis Guillermo M. Reyna SIAM J. Sci. and Stat. Comput. 6-3 (1985), pp. 515-531 (17 pages)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32187
Deposited By: Ruth Sustaita
Deposited On:02 Jul 2012 16:22
Last Modified:09 Nov 2021 21:25

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