Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
by Marsha J. Berger and Randall J. LeVeque SIAM J. Numer. Anal., 35(1998), pp. 2298-2316.

Abstract. An adaptive mesh refinement algorithm developed for the Euler equations of gas dynamics has been extended to employ high-resolution wave-propagation algorithms in a more general framework. This allows its use on a variety of new problems, including hyperbolic equations not in conservation form, problems with source terms or capacity functions, and logically rectangular curvilinear grids. This framework requires a modified approach to maintaining consistency and conservation at grid interfaces, which is described in detail. The algorithm is implemented in the AMRCLAW package, which is freely available.

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bibtex entry:
@Article{mjb-rjl:amrclaw,
author = "M. J. Berger and R. J. LeVeque",
title = "Adaptive Mesh Refinement using Wave-Propagation Algorithms for Hyperbolic Systems",
journal = "SIAM J. Numer. Anal.",
volume = "35",
year = "1998",
pages = "2298--2316",
}