Accurate Two-Dimensional Simulation of Advective-Diffusive-Reactive Transport

The present paper presents an accurate numerical algorithm for the simulation of 2D olute/heat transport by unsteady advection-diffusion-reaction. The model was specifically developed for the study of convective exchange processes in a cross section of lakes and ponds, when the currents are predominantly driven by density (temperature) gradients. The numerical scheme is based on the split-operator approach, in which advection and diffusion with chemical/biological kinetic processes are calculated separately at each time step. Special attention is given to the advection operator in order to avoid excessive numerical damping or oscillations, as well as to the source/sink term, which may cause numerical instability and inaccuracy if improperly treated. The model has been verified on standard test problems for a wide range of Courant, Fourier, Péclet, and Thiele numbers, and found to produce stable results of high accuracy.