A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws

  • Authors:

  • John M. Stockie;John A. Mackenzie;Robert D. Russell

  • Affiliations:

  • -;-;-

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 2000

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Abstract

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.