In this paper, we mathematically model contaminant flow in a two-dimensional domain of the Puget Sound using a finite element numerical solution to the advection-diffusion equation coupled with a finite difference numerical solution to the Navier-Stokes equations. We offer two models of contaminant flow in this domain, the first uses a Gaussian point source model of contaminant flow. The second model utilizes a Gaussian point source and a constant boundary source. Figure 1 shows the result of our second model after 560 seconds of run time. In addition to graphically showing our results, we also provide convergence testing of both our numerical results at the final time-step of both our models and find that the numerical results of our models are converging to an analytic solution at that time-step. We also perform a graphical and numerical sensitivity analysis of our models and find that our numerical solutions to both our models are insensitive to small changes in the diffusivity parameter.