A conservative semi-Lagrangian numerical method for solute transport in steady nonuniform flows is presented. The method is an extension of earlier work on the authors' DISCUS method. Numerical results are compared against an exact solution for solute transport in a nonuniform flow with a linearly varying velocity coefficient and a quadratically varying dispersion coefficient. The method is stable and fully conservative at large Courant and grid Péclet numbers. Accuracy is also good and appears to be primarily related to spatial resolution and grid Péclet number. The method is significantly more computationally efficient than Eulerian numerical methods.
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Manson et al. (1999) studied this question.
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