AN ALGORITHM FOR 3-DIMENSIONAL CONVECTION AND DIFFUSION WITH VERY DIFFERENT HORIZONTAL AND VERTICAL LENGTH SCALES

An algorithm is developed and tested for the numerical solution of the three-dimensional convection-diffusion equation appropriate for the marine environment, in which the horizontal and vertical scales differ by one or two orders of magnitude. The algorithm splits the horizontal and vertical parts of the process, treating the horizontal convection and diffusion explicitly and the vertical convection and diffusion by an implicit finite element method that is unconditionally stable. The overall stability conditions on the algorithm are discussed and its accuracy is verified through a number of test problems whose exact solutions are known.