Well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. Application to the dam break of Aznalcóllar

• Published in: Computer methods in applied mechanics and engineering Vol. 197; no. 45; pp. 3932 - 3950
• Main Authors: Díaz, M.J. Castro, Rebollo, T. Chacón, Fernández-Nieto, E.D., Vida, J.M. González, Parés, C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.08.2008; Elsevier
• Subjects: Applied fluid mechanics; Applied sciences; Buildings. Public works; Computational techniques; Dams and subsidiary installations; Exact sciences and technology; Finite volume method; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Hydraulic constructions; Hydrodynamics, hydraulics, hydrostatics; Mathematical methods in physics; Physics; Shallow water; Source terms; Upwinding; Well-balanced; Source terms; Finite volume method; Upwinding; Shallow water; Well-balanced; Dam; Open channel flow; Hyperbolic equation; Aqueous solution; Hydraulic jump; Finite volume method;Well-balanced;Upwinding;Shallow water;Source terms; Drop
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2008.03.026

In this paper, we introduce a class of well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. We extend the derivation of standard finite volume solvers for homogeneous systems to non-homogeneous ones using the method of lines. We study conservation and some well-balanced properties of the numerical scheme. We apply our solvers to shallow water equations: we prove that these exactly compute the water at rest solutions. We also perform some numerical tests, by comparing with 1D solutions, simulating the formation of a hydraulic drop and a hydraulic jump, and studying a real dam break: Aznalcóllar, an ecological disaster happened in the province of Seville, Spain in 1998.