Two-Dimensional Water Quality Model for Unsteady Advection-Diffusion of Nonconservative Substances

A numerical model for calculation of advective-diffusive transport of nonconservative substances in two-dimensional environments was developed. The numerical method is based on the splitting-operator approach, in which the advection, the diffusion and the chemicallbiological kinetic processes are calculated separately in one time step. Special attention was paid to the advection operator, which introduces essential difficulty in many numerical methods, and to the linearized source term which, in many cases, has proven to cause instability problems. The model calculates pure advection by the explicit Holly-Preissmann method of characteristics, and diffusion plus source/sink terms by an extended implicit alternate-direction (ADI) method. By comparison with analytical results for fronts and discrete mass releases it is established that numerical separation of differential operators does not induce significant errors in the solution or the physical realism of the results. The numerical scheme is accurate, stable and efficient because it eliminates the need to solve a pentadiagonal algebraic systems, replacing it with two tridiagonal ones. The computational method is intended for further use in the, study of a two-dimensional lake hydrodynamic and transport field, driven either by forced (wind induced) or natural (buoyancy induced) convection.