Available online at www.sciencedirect.com Mathematics and Computers in Simulation 79 (2009) 3415–3423 Application of mesh-adaptation for pollutant transport by water flow Fayssal Benkhaldoun a,∗ , Imad Elmahi b , Mohammed Seaïd c a LAGA, Université Paris 13, 99 Av J.B. Clement, 93430 Villetaneuse, France b ENSAO, EMCS Complex Universitaire, B.P. 669, 60000 Oujda, Morocco c School of Engineering, University of Durham, South Road, DH1 3LE, UK Received 1 February 2008; received in revised form 10 December 2008; accepted 9 April 2009 Available online 22 April 2009 Abstract An adaptive finite volume method is proposed for the numerical solution of pollutant transport by water flows. The shallow water equations with eddy viscosity, bottom friction forces and wind shear stresses are used for modelling the water flow whereas, a transport-diffusion equation is used for modelling the advection and dispersion of pollutant concentration. The adaptive finite volume method uses simple centred-type discretization for the source terms, can handle complex topography using unstructured grids and satisfies the conservation property. The adaptation criteria are based on monitoring the pollutant concentration in the computational domain during its dispersion process. The emphasis in this paper is on the application of the proposed method for numerical simulation of pollution dispersion in the Strait of Gibraltar. Results are presented using different tidal conditions and wind-induced flow fields in the Strait. © 2009 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Water flow; Pollutant transport; Adaptive method; Finite volume method; Unstructured grids 1. Introduction During the last decades partial differential equations have been used as practical tools to model many environmental problems from real life. Their have also been used to approximate and predict the dynamics of such problems. The goal of the present work is to provide a simple and practical numerical model able to resolve and correctly capture the transport and dispersion of a pollutant by water flows. The underlying equations describe the free-surface flow and species equations. Here, only water flow and pollutant concentration are coupled and neither chemical reactions nor heat transfer are considered. The flow is governed by the depth-averaged Navier–Stokes equations involving several assumptions including (i) the domain is shallow enough to ignore the vertical effects, (ii) the pressure is hydrostatic, and (iii) viscous dissipation of energy is ignored. A convection–diffusion equation is used to model the distribution of pollutant concentration on the water free-surface. The emphasis of the present work is on the application of the developed methods to a pollution dispersion in the Strait of Gibraltar. The Strait of Gibraltar has been subject of several scientific investigations ranging from meteological studies to geological researches. Its strategical location makes these investigations indispensable for understanding the global oceanography and the climate prediction. The Strait is heavily used by shipping and oil transport, being one ∗ Corresponding author. Tel.: +33 1 49 40 36 15; fax: +33 1 49 40 35 68. E-mail address: fayssal@math.univ-paris13.fr (F. Benkhaldoun). 0378-4754/$36.00 © 2009 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2009.04.007