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Discontinuous Solutions to Hyperbolic Systems Under Operator Splitting

  • P. L. Roe

Abstract

Two-dimensional systems of linear hyperbolic equations are studied with regard to their behavior under a solution strategy that in alternate time-steps exactly solves the component one-dimensional operators. The initial data is a step function across an oblique discontinuity. The manner in which this discontinuity breaks up under repeated applications of the split operator is analyzed, and it is shown that the split solution will fail to match the true solution in any case where the two operators do not share all their eigenvectors. The special case of the fluid flow equations is analyzed in more detail, and it is shown that arbitrary initial data gives rise to “pseudo acoustic waves” and a nonphysical stationary wave. The implications of these find-ings for the design of high-resolution computing schemes are discussed.

Keywords

Hyperbolic System Split Operator Discontinuous Solution Generalize Hypergeometric Function Initial Discontinuity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • P. L. Roe
    • 1
  1. 1.Cranfield Institute of TechnologyCranfieldUK

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