## Adaptive Mesh Refinement - Theory and Applications: Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, Sept. 3-5, 2003Tomasz Plewa, Timur Linde, V. Gregory Weirs Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing. |

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### Contents

3 | |

Adaptive Mesh Refinement on Overlapping Grids | 58 |

A Dynamically Adaptive Arbitrary LagrangianEulerian Method | 73 |

An accuracy study of mesh refinement on mapped grids | 91 |

J Dursi M Zingale 103 | 115 |

Multiresolutionbased adaptive schemes for Hyperbolic Conservation | 137 |

Multiresolution adaptive space refinement in geophysical fluid dynamics | 160 |

A Posteriori Error Estimation and Mesh Adaptivity for Finite Volume | 183 |

Toward Optimizing Enzo an AMR Cosmology Application | 351 |

RalfDeiterding 361 | 373 |

On the efficiency of AMR in NIRVANA3 | 391 |

Recent Advances in the Collapse and Fragmentation of Turbulent | 426 |

3D AMR Simulations of PointSymmetric Nebulae | 443 |

Mesh Refinement Calculations of Gravitational Waves and Black Holes | 453 |

AMR for Astrophysical Applications II Tests | 462 |

Varniere P Poludnenko A Cunningham A Frank A Mitran S 463 | 473 |

AMR for low Mach number reacting flow | 203 |

Simulations of Relativistic Astrophysical Flows | 223 |

A Parallel AMR Implementation of The Discrete Ordinates Method | 255 |

Radiation Transport in | 271 |

Parallel Multidimensional and Multimaterial Eulerian Staggered Mesh | 295 |

AMR for Astrophysical Applications I Methods | 331 |