### Abstract

Language | English |
---|---|

Pages | 1791-1813 |

Number of pages | 23 |

Journal | SIAM Journal on Scientific Computing |

Volume | 22 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

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

### Cite this

*SIAM Journal on Scientific Computing*,

*22*(5), 1791-1813. https://doi.org/10.1137/S1064827599364428

}

*SIAM Journal on Scientific Computing*, vol. 22, no. 5, pp. 1791-1813. https://doi.org/10.1137/S1064827599364428

**A moving mesh method for one-dimensional hyperbolic conservation laws.** / Stockie, John M.; MacKenzie, John A.; Russell, Robert D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A moving mesh method for one-dimensional hyperbolic conservation laws

AU - Stockie, John M.

AU - MacKenzie, John A.

AU - Russell, Robert D.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - moving mesh

KW - adaptivity

KW - equidistribution

KW - shock capturing

KW - hyperbolic conservation laws

KW - finite volume methods

KW - numerical mathematics

U2 - 10.1137/S1064827599364428

DO - 10.1137/S1064827599364428

M3 - Article

VL - 22

SP - 1791

EP - 1813

JO - SIAM Journal on Scientific Computing

T2 - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 5

ER -