Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: application to the Malpasset dam-break flood (France, 1959). 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

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  1. Schreiber, Martin; Neckel, Tobias; Bungartz, Hans-Joachim: Evaluation of an efficient stack-RLE clustering concept for dynamically adaptive grids (2016)
  2. Shokin, Yurii I.; Rychkov, Alexander D.; Khakimzyanov, Gayaz S.; Chubarov, Leonid B.: A combined computational algorithm for solving the problem of long surface waves runup on the shore (2016)
  3. Popinet, Stéphane: A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations (2015)
  4. Sætra, Martin L.; Brodtkorb, André R.; Lie, Knut-Andreas: Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations (2015)
  5. Dawson, Clint: A local timestepping Runge-Kutta discontinuous Galerkin method for hurricane storm surge modeling (2014)
  6. Donat, Rosa; Martí, M.Carmen; Martínez-Gavara, Anna; Mulet, Pep: Well-balanced adaptive mesh refinement for shallow water flows (2014)
  7. Dawson, Clint; Trahan, Corey Jason; Kubatko, Ethan J.; Westerink, Joannes J.: A parallel local timestepping Runge-Kutta discontinuous Galerkin method with applications to coastal Ocean modeling (2013)
  8. Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.: ADER-WENO finite volume schemes with space-time adaptive mesh refinement (2013)
  9. Higdon, Robert L.: Pressure forcing and dispersion analysis for discontinuous Galerkin approximations to oceanic fluid flows (2013)
  10. Mishra, Siddhartha; Schwab, Christoph; Šukys, Jonas: Multi-level Monte Carlo finite volume methods for uncertainty quantification in nonlinear systems of balance laws (2013)
  11. Mishra, S.; Schwab, Ch.; Šukys, J.: Multilevel Monte Carlo finite volume methods for shallow water equations with uncertain topography in multi-dimensions (2012)
  12. Trahan, Corey J.; Dawson, Clint: Local time-stepping in Runge-Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations (2012)
  13. George, D.L.: Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: application to the Malpasset dam-break flood (France, 1959) (2011)
  14. LeVeque, Randall J.; George, David L.; Berger, Marsha J.: Tsunami modelling with adaptively refined finite volume methods (2011)