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. de Souza Lourenço, Marcos Antonio; Martínez Padilla, Elie Luis: An octree structured finite volume based solver (2020)
  2. Siripatana, A.; Giraldi, L.; Le Maître, O. P.; Knio, O. M.; Hoteit, I.: Combining ensemble Kalman filter and multiresolution analysis for efficient assimilation into adaptive mesh models (2019)
  3. Didenkulova, I. I.; Pelinovsky, E. N.; Rodin, A. A.: Long wave run-up on plane and “non-reflecting” slopes (2018)
  4. Rannabauer, Leonhard; Dumbser, Michael; Bader, Michael: ADER-DG with a-posteriori finite-volume limiting to simulate tsunamis in a parallel adaptive mesh refinement framework (2018)
  5. Giraldi, Loïc; Le Maître, Olivier P.; Mandli, Kyle T.; Dawson, Clint N.; Hoteit, Ibrahim; Knio, Omar M.: Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate (2017)
  6. Vogl, Christopher J.; LeVeque, Randall J.: A high-resolution finite volume seismic model to generate seafloor deformation for tsunami modeling (2017)
  7. Puppo, Gabriella; Semplice, Matteo: Well-balanced high order 1D schemes on non-uniform grids and entropy residuals (2016)
  8. Schreiber, Martin; Neckel, Tobias; Bungartz, Hans-Joachim: Evaluation of an efficient stack-RLE clustering concept for dynamically adaptive grids (2016)
  9. 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)
  10. Neumann, Philipp; Bungartz, Hans-Joachim: Dynamically adaptive lattice Boltzmann simulation of shallow water flows with the Peano framework (2015)
  11. Popinet, Stéphane: A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations (2015)
  12. Sætra, Martin L.; Brodtkorb, André R.; Lie, Knut-Andreas: Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations (2015)
  13. Zanotti, Olindo; Fambri, Francesco; Dumbser, Michael; Hidalgo, Arturo: Space-time adaptive ADER discontinuous Galerkin finite element schemes with \textitaposteriori sub-cell finite volume limiting (2015)
  14. Dawson, Clint: A local timestepping Runge-Kutta discontinuous Galerkin method for hurricane storm surge modeling (2014)
  15. Donat, Rosa; Martí, M. Carmen; Martínez-Gavara, Anna; Mulet, Pep: Well-balanced adaptive mesh refinement for shallow water flows (2014)
  16. George, David L.; Iverson, Richard M.: A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II: Numerical predictions and experimental tests (2014)
  17. 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)
  18. Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.: ADER-WENO finite volume schemes with space-time adaptive mesh refinement (2013)
  19. Higdon, Robert L.: Pressure forcing and dispersion analysis for discontinuous Galerkin approximations to oceanic fluid flows (2013)
  20. Mishra, Siddhartha; Schwab, Christoph; Šukys, Jonas: Multi-level Monte Carlo finite volume methods for uncertainty quantification in nonlinear systems of balance laws (2013)

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