zbMATH — the first resource for mathematics

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.

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
Full Text: DOI