This article is a U.S. Government work and is in the public domain in the U.S.A.
Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam-break flood (France, 1959)†
Article first published online: 4 MAR 2010
This article is a U.S. Government work and is in the public domain in the U.S.A. Published in 2010 by John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 66, Issue 8, pages 1000–1018, 20 July 2011
How to Cite
George, D. L. (2011), Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam-break flood (France, 1959). Int. J. Numer. Meth. Fluids, 66: 1000–1018. doi: 10.1002/fld.2298
- Issue published online: 4 MAR 2010
- Article first published online: 4 MAR 2010
- Manuscript Accepted: 9 JAN 2010
- Manuscript Revised: 7 JAN 2010
- Manuscript Received: 11 SEP 2009
- shallow water;
- finite volume methods;
- mesh adaptation;
- hyperbolic PDE;
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 GEOCLAW, 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.