A moving mesh method for one-dimensional hyperbolic conservation laws

John M. Stockie, John A. MacKenzie, Robert D. Russell

Research output: Contribution to journalArticlepeer-review

89 Citations (Scopus)
23 Downloads (Pure)


We develop an adaptive method for solving one-dimensional systems of hyperbolic conservation laws that employs a high resolution Godunov-type scheme for the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods developed to solve hyperbolic problems use a fully implicit discretization for the coupled solution-mesh equations, and so suffer from a significant degree of numerical stiffness. We employ a semi-implicit approach that couples the moving mesh equation to an efficient, explicit solver for the physical PDE, with the resulting scheme behaving in practice as a two-step predictor-corrector method. In comparison with computations on a fixed, uniform mesh, our method exhibits more accurate resolution of discontinuities for a similar level of computational work.
Original languageEnglish
Pages (from-to)1791-1813
Number of pages23
JournalSIAM Journal on Scientific Computing
Issue number5
Publication statusPublished - 2001


  • moving mesh
  • adaptivity
  • equidistribution
  • shock capturing
  • hyperbolic conservation laws
  • finite volume methods
  • numerical mathematics


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