A Mathematical Model of the Dispersion of a Concentrated Substance for Use in the Great Salt Lake\u27s South Arm

The ability to predict the dispersion of substances in the Great Salt Lake is a requisite towards making responsible management decisions relating to uses of the lake. The lake is a complex terminal body of water and will require a fairly sophisticated mathematical model to properly simulate the dispersion process in the lake. This finite element convection-dispersion model is a first step towards developing a comprehensive model. The model provides a finite element solution to the two-dimensional convection-dispersion equation and is capable of simulating steady or unsteady-state situations. It utilizes a known velocity field, dispersion coefficients, an introduced substance concentration, substance decay rates, and the region geometry to produce a solution to a given convection-dispersion problem. At the present time, a quantitative verification of the model has not been done, but qualitative use of the model indicates that it yields reasonable solutions satisfying continuity to convection-dispersion problems. Problems tested utilize a uniform flow field and various methods of introducing a substance, such as internal injections, established concentration gradients, and diffusers. This model affords the options in the approximating techniques of linear or quadratic interpolation functions, the Galerkin or upwinding methods of weigh ted residuals, and a linearly or quadratically varying velocity field. The model must use a continuous flow field to produce a credible solution. The model does need improvement in its ability to conserve mass in unsteady-state problems when introducing a substance into the modeled region and allowing dispersive transport at the boundaries. Proper nodal spacing (mesh size) is also important because a relatively coarse mesh size can result in poor approximations in some areas of the region modeled