Validity of a moving boundary finite element model for salt intrusion in a branching estuary D.B. Das a, * , V. Nassehi b a Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK b Chemical Engineering Department, Loughborough University, Loughborough LE11 3TU, UK Received 20 June 2003; received in revised form 24 March 2004; accepted 5 April 2004 Available online 5 June 2004 Abstract A previously developed scheme for modelling of salt intrusion in estuaries with significant flow channel boundary variations during tidal cycles has been applied to a narrow branching estuary. It is shown that realistic simulations for complex tidal water systems can be obtained with this scheme provided that a suitable modification to the solution algorithm is implemented. The required modification is explained in detail and the model is applied to simulate salt intrusion in the Upper Milford Haven estuary in Wales, UK. Essentially, this moving boundary scheme introduces a distinct procedure for transient mass balance to ensure logical division of flow at an estuary junction and tracking of fluid particle trajectories along various branches of the estuary. Compu- tational results and available field survey data for depth-averaged salinities are compared to determine the accuracy of the developed model. It is shown that the numerical results converge closer to field values than those previously reported. The method promises to provide new insights for environmental assessment, such as the determination of more accurate effluent discharge policies for estuaries. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Moving boundary domain; Finite element method; Lagrange–Galerkin scheme; Tracking of fluid particle trajectories; The Upper Milford Haven estuary 1. Introduction During the past three decades many algorithms have been proposed for the solution of moving boundary flow problems encountered in natural water systems [1–9]. These problems include, for example, flow in estuaries, river channels and flood plains and, rise and fall of ground water table. The flow geometry in these pro- cesses is not known a priori and some sections of the domain boundary vary with flow (both spatially and temporally). Although the above algorithms for variable boundary domains have been implemented in a variety of water management problems, due to the wide range of conditions under which moving boundary flow may occur none of these schemes can be said to have uni- versal applicability. Accordingly, models representing specific types of moving boundary problems are usually reported [7]. Despite the proven accuracy and robust- ness of many moving boundary schemes, the modelling of a branch situation still remains to be too complex for most methods. The main focus of the present paper is to develop and test the validity of a finite element based Galerkin–Lagrangian variable boundary model for branching estuaries. The core of the methodology in- volves tracking of fluid particle trajectories in the flow domains. The technique eliminates a number of limita- tions of the existing schemes for moving boundary problems and is capable of generating computationally efficient results, as demonstrated later. One important practical application of the inclusion of the moving variable domains in the simulation tools for the estua- rine transport processes [10–12] is that they allow more accurate design of effluent discharge policies for estu- aries. The validity of the present scheme is tested against field measurements for salinity levels in the Upper Mil- ford Haven estuary, a branching estuary in Wales, UK. The enhanced accuracy of the simulated results due to the incorporation of moving boundary schemes is * Corresponding author. Tel.: +44-1865-283454; fax: +44-1865- 283273. E-mail address: diganta.das@eng.ox.ac.uk (D.B. Das). 0309-1708/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2004.04.001 Advances in Water Resources 27 (2004) 725–735 www.elsevier.com/locate/advwatres