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. Barsukow, Wasilij; Berberich, Jonas P.; Klingenberg, Christian: On the active flux scheme for hyperbolic PDEs with source terms (2021)
  2. Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian: High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws (2021)
  3. Berberich, Jonas P.; Käppeli, Roger; Chandrashekar, Praveen; Klingenberg, Christian: High order discretely well-balanced methods for arbitrary hydrostatic atmospheres (2021)
  4. Bueler, Ed: Conservation laws for free-boundary fluid layers (2021)
  5. Arpaia, Luca; Ricchiuto, Mario: Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes (2020)
  6. Berezovski, Mihhail; Berezovski, Arkadi: Discontinuity-driven mesh alignment for evolving discontinuities in elastic solids (2020)
  7. Charrier, Dominic Etienne; Hazelwood, Benjamin; Weinzierl, Tobias: Enclave tasking for DG methods on dynamically adaptive meshes (2020)
  8. Chertock, Alina; Kurganov, Alexander; Liu, Yongle: Finite-volume-particle methods for the two-component Camassa-Holm system (2020)
  9. de Souza Lourenço, Marcos Antonio; Martínez Padilla, Elie Luis: An octree structured finite volume based solver (2020)
  10. Giles, Daniel; Kashdan, Eugene; Salmanidou, Dimitra M.; Guillas, Serge; Dias, Frédéric: Performance analysis of Volna-OP2 -- massively parallel code for tsunami modelling (2020)
  11. Ginting, Bobby Minola; Ginting, Herli: Extension of artificial viscosity technique for solving 2D non-hydrostatic shallow water equations (2020)
  12. Helzel, Christiane: A third-order accurate wave propagation algorithm for hyperbolic partial differential equations (2020)
  13. Ketcheson, David I.; LeVeque, Randall J.; del Razo, Mauricio J.: Riemann problems and Jupyter solutions (2020)
  14. Kissami, Imad; Seaid, Mohammed; Benkhaldoun, Fayssal: Numerical assessment of criteria for mesh adaptation in the finite volume solution of shallow water equations (2020)
  15. Brus, S. R.; Wirasaet, D.; Kubatko, E. J.; Westerink, J. J.; Dawson, C.: High-order discontinuous Galerkin methods for coastal hydrodynamics applications (2019)
  16. 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)
  17. Wang, Yuepeng; Hu, Kun; Ren, Lanlan; Lin, Guang: Optimal observations-based retrieval of topography in 2D shallow water equations using PC-EnKF (2019)
  18. Wang, Yuepeng; Ren, Lanlan; Zhang, Zongyuan; Lin, Guang; Xu, Chao: Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem (2019)
  19. Didenkulova, I. I.; Pelinovsky, E. N.; Rodin, A. A.: Long wave run-up on plane and “non-reflecting” slopes (2018)
  20. Khakimzyanov, Gayaz; Dutykh, Denys; Gusev, Oleg; Shokina, Nina Yu.: Dispersive shallow water wave modelling. II: Numerical simulation on a globally flat space (2018)

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