Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method
Open Access
- 1 March 2003
- journal article
- research article
- Published by EDP Sciences in ESAIM: Mathematical Modelling and Numerical Analysis
- Vol. 37 (2), 389-416
- https://doi.org/10.1051/m2an:2003034
Abstract
The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other hand the transport computation ensures the conservation of pollutant mass, a non-negativity property and a maximum principle for the concentration of pollutant and the preservation of discrete steady states associated with the lake at rest equilibrium. The interest of the developed method is to preserve these theoretical properties with a scheme that allows to disconnect the hydrodynamic time step – related to a classical CFL condition – and the transport one – related to a new CFL condition – and further the hydrodynamic calculation and the transport one. The CPU time is very reduced and we can easily solve different transport problems with the same hydrodynamic solution without large storage. Moreover the numerical results exhibit a better accuracy than with a classical method especially when using 1D or 2D regular grids.This publication has 14 references indexed in Scilit:
- Some approximate Godunov schemes to compute shallow-water equations with topographyComputers & Fluids, 2003
- A kinetic scheme for the Saint-Venant system¶with a source termCalcolo, 2001
- A steady-state capturing method for hyperbolic systems with geometrical source termsESAIM: Mathematical Modelling and Numerical Analysis, 2001
- Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validationDiscrete & Continuous Dynamical Systems - B, 2001
- Transport of pollutant in shallow water using kinetic schemesESAIM: Proceedings, 2001
- Finite volume methodsPublished by Elsevier BV ,2000
- Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation AlgorithmJournal of Computational Physics, 1998
- Upwind methods for hyperbolic conservation laws with source termsComputers & Fluids, 1994
- Upwind differencing schemes for hyperbolic conservation laws with source termsLecture Notes in Mathematics, 1987
- The formation of breakers and bores the theory of nonlinear wave propagation in shallow water and open channelsCommunications on Pure and Applied Mathematics, 1948