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Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems. (English) Zbl 0921.65070
The authors present a generalisation of an adaptive mesh refinement algorithm developed for the Euler equations of gas dynamics to employ high-resolution wave-propagation algorithms in a more general framework. This extension can be used on a variety of new problems, including hyperbolic equations, which are not in a conservation form, problems with source terms of capacity functions, and logically rectangular curvilinear grids. The developed framework requires a modified approach to maintaining consistency and conservation at grid interfaces, which is described in detail. The algorithm is implemented in the software package AMRCLAW, which is freely available.

MSC:
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics, general
35L45 Initial value problems for first-order hyperbolic systems
Software:
AMRCLAW; CLAWPACK
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