Well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. Application to the dam-break of Aznalcóllar.
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 pro...
| Authors: | , , , , |
|---|---|
| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2008 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/32145 |
| Online Access: | http://hdl.handle.net/11441/32145 https://doi.org/10.1016/j.cma.2008.03.026 |
| Access Level: | Open access |
| Keyword: | Finite volume method Well-balanced Upwinding Shallow water Source terms |
| Summary: | 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. |
|---|