Moving-mesh methods for one-dimensional hyperbolic problems using CLAWPACK

We develop a one-dimensional moving-mesh method for hyperbolic systems of conservation 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.