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Adaptive finite volume methods with well‐balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam‐break flood (France, 1959)
Author(s) -
George D. L.
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2298
Subject(s) - riemann solver , finite volume method , terrain , solver , context (archaeology) , shallow water equations , computer science , block (permutation group theory) , quadrilateral , flood myth , adaptive mesh refinement , polygon mesh , mathematics , algorithm , computational science , geology , mathematical optimization , geometry , finite element method , engineering , mechanics , mathematical analysis , computer graphics (images) , geography , physics , paleontology , cartography , structural engineering , archaeology
The simulation of advancing flood waves over rugged topography, by solving the shallow‐water equations with well‐balanced high‐resolution finite volume methods and block‐structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block‐structured AMR makes large‐scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet–dry fronts and non‐stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well‐balanced Riemann solver for inundation and general (non‐stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well‐balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam‐break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in G EO C LAW , a subset of the open‐source CLAWPACK software. All the software is freely available at www.clawpack.org . Published in 2010 by John Wiley & Sons, Ltd.