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Moving-mesh methods for one-dimensional hyperbolic problems using CLAWPACK. (English) Zbl 1035.65094

Summary: 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.

65M06Finite difference methods (IVP of PDE)
35L65Conservation laws
76L05Shock waves; blast waves (fluid mechanics)
76M20Finite difference methods (fluid mechanics)