197(45):3932–3950.

Paper abstract bibtex

Paper abstract bibtex

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 that happened in the province of Seville, Spain in 1998

@article{castro_diaz_well-balanced_2008, title = {Well-balanced finite volume schemes for 2d non-homogeneous hyperboli systems. Application to the dam break of Aznalcóllar}, volume = {197}, url = {http://www.sciencedirect.com/science/article/pii/S0045782508001394}, abstract = {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 that happened in the province of Seville, Spain in 1998}, pages = {3932--3950}, number = {45}, journaltitle = {Comput. Methods Appl. Mech. Engrg.}, author = {Castro Díaz, Manuel J. and Chacón-Rebollo, T. and Fernández Nieto, E. D. and González-Vida, J.-M. and Parés, Carlos}, date = {2008}, }

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