Well - Balanced Finite Volume schemes for 2 D non - homogeneous hyperbolic systems . Application to the Dam - break of Aznalcóllar . ∗
نویسندگان
چکیده
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. Short title : 2D Asymptotically balanced schemes.
منابع مشابه
A New Approach of High OrderWell-Balanced Finite Volume WENO Schemes and Discontinuous Galerkin Methods for a Class of Hyperbolic Systems with Source Terms†
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms. In our earlier work [31–33], we designed high order well-balanced schemes to a class of hyperbolic systems with separable source terms. In this paper, we present a different approach to the same purpose: designing high order well-balanced finite volume weight...
متن کامل1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method
The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative fini...
متن کاملNoelle , Xing , Shu . Well - balanced schemes for moving water . 1 High Order Well - balanced Finite Volume WENO Schemes for Shallow Water Equation with Moving Water
A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Recently a number of so-called well-balanced schemes were developed which satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. In most cases, applications t...
متن کاملThe comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws
This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...
متن کاملHigh-order well-balanced finite volume WENO schemes for shallow water equation with moving water
A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Recently a number of so-called well-balanced schemes were developed which satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. In most cases, applications t...
متن کامل