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A general technique for assessing the numerical accuracy of solute transport models
Author(s) -
Ruan Feng,
McLaughlin Dennis,
Li Shuguang
Publication year - 1999
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/1999wr900244
Subject(s) - solver , forcing (mathematics) , interpolation (computer graphics) , mathematics , grid , variable (mathematics) , test case , numerical analysis , computer simulation , mathematical optimization , computer science , mathematical analysis , simulation , frame (networking) , statistics , telecommunications , geometry , regression analysis
This note describes a procedure for evaluating the accuracy of numerical solute transport models in situations where exact closed‐form solutions are difficult or even impossible to obtain. The procedure attempts to match a specified closed‐form “test solution” by adding forcing terms to the original equation, which is solved numerically. The quality of the match provides valuable information about the performance of the numerical algorithm. We illustrate this “prescribed forcing method” with an example which simulates solute transport in a heterogeneous velocity field. The numerical solver considered in the example is based on the Eulerian‐Lagrangian method with linear velocity and concentration interpolation. Two test solutions of different degrees of difficulty are considered. Differences between the exact and numerical test solutions for the example clearly reveal the influence of grid resolution on model accuracy. The example demonstrates that the prescribed forcing method can be used to assess numerical accuracy in practical situations where model inputs are highly variable and the true solution is unknown.