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. We offer a graphical presentation of both models and we also provide convergence testing of our numerical results at the final time-step. When we test for convergence of our numerical results, we find that our models are converging to an analytic solution at the final 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.
This paper is the Senior Thesis of Jordan Trinka, Class of 2017, from Carroll College, Helena MT USA, under the supervision of Dr. Eric Sullivan, Faculty of the College.
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