Massively parallel computation of conservation laws

Marc Garbey, David Levine

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We 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. We 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. We present timing results for an Alliant FX/8, Connection Machine Model 2, and CRAY X-MP.

Original languageEnglish (US)
Pages (from-to)293-304
Number of pages12
JournalParallel Computing
Issue number2-3
StatePublished - Jan 1 1990


  • Cellular automata
  • Conservation laws
  • Method of characteristics
  • Parallel algorithms
  • Partial differential equations

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computer Graphics and Computer-Aided Design
  • Artificial Intelligence


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