Moving-Mesh Methods for One-Dimensional Hyperbolic Problems Using CLAWPACK

1. I N T R O D U C T I O N We study high-resolution finite-volume methods for the one-dimensional conservation law qt + f (q ) z = ~ (x ,q ) (1) on a moving grid, where the interface x~ between grid cells varies with time t~. Figure 1 shows a typical moving grid over one time step. We show how the wave-propagation algorithms developed in [1] and implemented in the CLAWPACK software [2] can be modified to handle moving grids. and consider applications to gas dynamics in a tube with moving-piston boundary conditions and also a moving interface between two gases. With a finite volume method, our approximation consists of cell averages 1 f~ x,~+l '~ q(x, t~) dx, The first author would like to express his thanks for the support by a NATO-CNR grant (No. 217.28/01) and the kind hospitality of the Department of Applied Mathematics of the Washington University. The second author has" been supported in part by DOE Grant DE-FG03-96ER25292 and NSF Grants DMS-9505021 and DMS-9626645. 0898-1221/03/$ see front matter (~) 2003 Elsevier Science Ltd. All rights reserved. Typeset by A2~4S-TE X PII: S0898-1221 (02)00339-5