Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems

1998/12/01 by Marsha J. Berger, Marsha Berger, Randall J. LeVeque · 279 citations
Earth and Planetary Sciences · Engineering · Mathematics · #Adaptive mesh refinement #Algorithm #Applied mathematics #Computational Fluid Dynamics and Aerodynamics #Computational science #Computer science #Conservation law #Consistency (knowledge bases) #Curvilinear coordinates #Euler equations #Gas Dynamics and Kinetic Theory #Geometry #Grid #Hyperbolic partial differential equation #Mathematical analysis #Mathematics #Meteorological Phenomena and Simulations #Partial differential equation #Variety (cybernetics) #Wave propagation

paper · doi:10.1137/s0036142997315974

published in SIAM Journal on Numerical Analysis 35(6), 2298-2316 (Society for Industrial and Applied Mathematics)

openalex publication_date 1998/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

An adaptive mesh refinement algorithm developed for the Euler equations of gas dynamics has been extended to employ high-resolution wave-propagation algorithms in a more general framework. This allows its use on a variety of new problems, including hyperbolic equations not in conservation form, problems with source terms or capacity functions, and logically rectangular curvilinear grids. This framework requires a modified approach to maintaining consistency and conservation at grid interfaces, which is described in detail. The algorithm is implemented in the AMRCLAW package, which is freely available.

Citations

• High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws

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