A general technique for assessing the numerical accuracy of solute transport models

This note describes a procedure for evaluating the accuracy of numerical so lute transport models in situations where exact closed-form solutions are d ifficult or even impossible to obtain. The procedure attempts to match a sp ecified closed-form "test solution" by adding forcing terms to the original equation, which is solved numerically. The quality of the match provides v aluable information about the performance of the numerical algorithm. We il lustrate this "prescribed forcing method" with an example which simulates s olute transport in a heterogeneous velocity field. The numerical solver con sidered in the example is based on the Eulerian-Lagrangian method with line ar velocity and concentration interpolation. Two test solutions of differen t degrees of difficulty are considered. Differences between the exact and n umerical test solutions for the example clearly reveal the influence of gri d resolution on model accuracy. The example demonstrates that the prescribe d forcing method can be used to assess numerical accuracy in practical situ ations where model inputs are highly variable and the true solution is unkn own.