Ocean Engng, Vol. 25, No. 6, pp. 425–442, 1998  1998 Elsevier Science Ltd. All rights reserved Pergamon Printed in Great Britain 0029–8018/98 $19.00 + 0.00 PII: S0029–8018(97)00008–5 THREE-DIMENSIONAL FINITE DIFFERENCE MODEL FOR TRANSPORT OF CONSERVATIVE POLLUTANTS S. Sankaranarayanan, N. J. Shankar* and H. F. Cheong Department of Civil Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Abstract—A three-dimensional finite difference transport model appropriate for the coastal environment is developed for the solution of the three-dimensional convection–diffusion equation. A higher order upwind scheme is used for the convective terms of the convection–diffusion equation, to minimise the numerical diffusion. The validity of the numerical model is verified through five test problems, whose exact solutions are known.  1998 Elsevier Science Ltd. NOMENCLATURE C(x, y, z, t) pollutant concentration at location (x, y, z) at any time t C 1 , C 2 , C 3 ,  constants C i,j,k concentration at grid location i, j, k G(x, y, z, t) point source or sink K scaling constant K x , K y , K z diffusion coefficients in the x, y and z directions L x , L y , L z length of the basin in x, y and z directions r(t), s(t), f(t) expression [see Equation (26)] T p period of rotation U, V, W flow velocities in the x, y and z directions x 0 , y 0 , z 0 coordinates of the centre of Gaussian pulse  dimensionless parameter t time step x, y, z grid spacing in x, y and z directions  free surface elevation 1. INTRODUCTION Mathematical modelling of the transport of salinity, pollutants and suspended matter in shallow waters involves the numerical solution of a convection–diffusion equation. Many popular finite difference methods, such as the upwind scheme of Spalding (1972) and the flux-corrected scheme (Boris and Book, 1973) are available for the solution of the depth- integrated form of the convection–diffusion equation. Another widely used approach is the split-operator approach (Sobey, 1983; Li and Chen, 1989), in which the convection and diffusion terms are solved by two different numerical methods. Noye and Tan (1988) used a weighted discretisation with the modified equivalent partial differential equation *Author to whom correspondence should be addressed. 425