Is Discontinuous Reconstruction Really a Good Idea?

作者： | Philip Roe |

作者单位： |
^{1}University of Michigan |

刊名： | Journal of Scientific Computing, 2017, Vol.73 (2-3), pp.1094-1114 |

来源数据库： | Springer Journal |

DOI： | 10.1007/s10915-017-0555-z |

关键词： | Hyperbolic conservation laws; Numerical advection; Compressible flow; Wave equations; |

英文摘要： | It has been almost automatically assumed for a quarter century that the numerical solution of hyperbolic conservation laws is best accomplished by making a reconstruction of the initial data that is only piecewise continuous. The effect of the discontinuities is taken into account by means of Riemann solvers. This strategy has enjoyed great practical success but introduces only one-dimensional physics as a guide to the discretization of multidimensional problems. This article points out some of the resulting defects and proposes an alternative viewpoint. The chief novelty of the new “Active Flux” method, apart from the elimination of discontinuities, is the division into advective and acoustic disturbances, with acoustics being handled by exploiting classical solutions to the scalar wave... |

原始语种摘要： | It has been almost automatically assumed for a quarter century that the numerical solution of hyperbolic conservation laws is best accomplished by making a reconstruction of the initial data that is only piecewise continuous. The effect of the discontinuities is taken into account by means of Riemann solvers. This strategy has enjoyed great practical success but introduces only one-dimensional physics as a guide to the discretization of multidimensional problems. This article points out some of the resulting defects and proposes an alternative viewpoint. The chief novelty of the new “Active Flux” method, apart from the elimination of discontinuities, is the division into advective and acoustic disturbances, with acoustics being handled by exploiting classical solutions to the scalar wave... |