Two-Dimensional Solute Transport
This paper develops approximate solutions to a two-dimensional solute transport problem for either continuous or step inputs. The basic idea is to recognize that solute transport is mainly the result of two processes that can be treated independently, convection with the water flow and mixing by diffusion. Convection is treated exactly using the method of characteristics, and diffusion is accounted for with the method of singular perturbations. The integrals involved are no longer taken along vertical lines, as in one-dimensional problems, but now become contour integrals. This does not change the structure of the solution, it just makes the calculations more elaborate, and in some situations numerical algorithms are required to evaluate these integrals. Nevertheless, this method proves to be faster and less cumbersome than traditional difference and finite element schemes.
KeywordsSolute Transport Singular Perturbation Line Source Perturbation Solution Finite Element Scheme
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