1 - Introduction

An adaptive mesh refinement algorithm developed for Euler equations and gas dynamics has been extented 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 sources terms or capacity functions, and logically-rectangular curvilinear grids. This framework requires a modified approach to maintaining consistency and conservation at grid interface. The algorithm is implemented in the AMRCLAW package, which is freely available.

AMRCLAW combines the CLAWPACK routines with the Marsha Berger's adaptive mesh refinement ( AMR ) algorithm, which was originally developed for gas dynamics. Once a Riemann solver and boundary conditions have been implemented in CLAWPACK to solve a particular problem, it is quite easy to swith to AMRCLAW and use adaptively refined grids, with the potential for large savings in CPU time for multi-dimentional problems. Berger's original AMR code applies on Cartesian grids; By merging it with CLAWPACK it is now straightforward to apply it on logically-rectangular curvilinear grids as well.