Stockie, J.M. and MacKenzie, J.A. and Russell, R.D. (2001) *A moving mesh method for one-dimensional hyperbolic conservation laws.* SIAM Journal on Scientific Computing, 22 (5). pp. 1791-1813. ISSN 1064-8275

## 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.

Item type: | Article |

ID code: | 4705 |

Keywords: | moving mesh, adaptivity, equidistribution, shock capturing, hyperbolic conservation laws, finite volume methods, numerical mathematics, Mathematics, Physics, Computational Mathematics, Applied Mathematics |

Subjects: | Science > Mathematics Science > Physics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 12 Nov 2007 |

Last modified: | 05 Sep 2014 13:19 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4705 |
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