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Massively parallel computation of conservation laws

Abstract

The authors present a new method for computing solutions of conservation laws based on the use of cellular automata with the method of characteristics. The method exploits the high degree of parallelism available with cellular automata and retains important features of the method of characteristics. It yields high numerical accuracy and extends naturally to adaptive meshes and domain decomposition methods for perturbed conservation laws. They describe the method and its implementation for a Dirichlet problem with a single conservation law for the one-dimensional case. Numerical results for the one-dimensional law with the classical Burgers nonlinearity or the Buckley-Leverett equation show good numerical accuracy outside the neighborhood of the shocks. The error in the area of the shocks is of the order of the mesh size. The algorithm is well suited for execution on both massively parallel computers and vector machines. They present timing results for an Alliant FX/8, Connection Machine Model 2, and CRAY X-MP.
Authors:
Garbey, M; [1]  Levine, D [2] 
  1. Univ. Claude Bernard, Villeurbanne (France)
  2. Argonne National Lab., IL (United States)
Publication Date:
Jan 01, 1990
Product Type:
Journal Article
Reference Number:
EDB-93-010610
Resource Relation:
Journal Name: Parallel Computing; (Netherlands); Journal Volume: 16
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CONSERVATION LAWS; ALGORITHMS; NUMERICAL SOLUTION; ACCURACY; CALCULATION METHODS; ERRORS; NONLINEAR PROBLEMS; PARALLEL PROCESSING; PARTIAL DIFFERENTIAL EQUATIONS; PERFORMANCE; PERTURBATION THEORY; SUPERCOMPUTERS; VECTOR PROCESSING; COMPUTERS; DIFFERENTIAL EQUATIONS; DIGITAL COMPUTERS; EQUATIONS; MATHEMATICAL LOGIC; PROGRAMMING; 662120* - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-); 990200 - Mathematics & Computers
OSTI ID:
6892716
Country of Origin:
Netherlands
Language:
English
Contract Number:
W-31109-ENG-38
Other Identifying Numbers:
Journal ID: ISSN 0167-8191; CODEN: PACOEJ
Submitting Site:
JMT
Size:
Pages: 293-304
Announcement Date:

Citation Formats

Garbey, M, and Levine, D. Massively parallel computation of conservation laws. Netherlands: N. p., 1990. Web. doi:10.1016/0167-8191(90)90067-J.
Garbey, M, & Levine, D. Massively parallel computation of conservation laws. Netherlands. doi:10.1016/0167-8191(90)90067-J.
Garbey, M, and Levine, D. 1990. "Massively parallel computation of conservation laws." Netherlands. doi:10.1016/0167-8191(90)90067-J. https://www.osti.gov/servlets/purl/10.1016/0167-8191(90)90067-J.
@misc{etde_6892716,
title = {Massively parallel computation of conservation laws}
author = {Garbey, M, and Levine, D}
abstractNote = {The authors present a new method for computing solutions of conservation laws based on the use of cellular automata with the method of characteristics. The method exploits the high degree of parallelism available with cellular automata and retains important features of the method of characteristics. It yields high numerical accuracy and extends naturally to adaptive meshes and domain decomposition methods for perturbed conservation laws. They describe the method and its implementation for a Dirichlet problem with a single conservation law for the one-dimensional case. Numerical results for the one-dimensional law with the classical Burgers nonlinearity or the Buckley-Leverett equation show good numerical accuracy outside the neighborhood of the shocks. The error in the area of the shocks is of the order of the mesh size. The algorithm is well suited for execution on both massively parallel computers and vector machines. They present timing results for an Alliant FX/8, Connection Machine Model 2, and CRAY X-MP.}
doi = {10.1016/0167-8191(90)90067-J}
journal = {Parallel Computing; (Netherlands)}
volume = {16}
journal type = {AC}
place = {Netherlands}
year = {1990}
month = {Jan}
}