Abstract. We develop a one-dimensional moving-mesh method for hyperbolic systems of conser- vation laws. This method is based on the high-resolution finite-volume "wave-propagation method", implemented in the CLAWPACK software package. A modified system of conservation laws is solved on a fixed, uniform computational grid, with a grid mapping function computed simultaneously in such a way that in physical space certain features are tracked by cell interfaces. The method is tested on a shock-tube problem with multiple reflections where the contact discontinuity is tracked, and also on two multifluid problems where the interface between two distinct gases is tracked. One is a standard test problem and the other also involves a moving piston whose motion is also tracked by the moving mesh.
Keywords. Moving-mesh methods, Finite-volume methods, Hyperbolic conservation laws, Inter- face problems.
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bibtex entry:
@Article{fazio-rjl,
author = "R. Fazio and R. J. LeVeque",
title = "Moving Mesh Methods for One-Dimensional Conservation
Laws Using {\sc clawpack}",
journal = "Comp. Math. Appl.",
volume = "45",
year = "2003",
pages = "273--298",
}