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Abstract
Method of characteristics (MOC) solutions are widely employed in solute transport models of groundwater to estimate tracer concentration. The conventional approach to obtain average tracer concentration for the cell is to arithmetically average the tracer concentration of the moving points within the cell during a particular time step. This requires a large number of moving points and or small cell dimensions to yield satisfactory results.
A weighted average using an 'area of influence' for each moving point to estimate the average cell tracer concentration has been proposed and proven effective for steady, uniform flow fields. However, the calculation of an 'area of influence' is difficult for unsteady, non uniform flow fields. Utilization of a 'distance based' weighting function to estimate the average tracer concentration of a cell is proposed in this study.
Two inverse and two exponential distance based weighting functions were evaluated. All four weighting functions performed similarly. Hence a quasi error analysis was performed and the inverse weighting function which resulted in a minimal absolute error was chosen for further study. The weighting function performed better than, or as well as the traditional arithmetically averaged routine, depending on the nature of the problem studied.
The effect of two forms of moving point introduction, a geometrically uniform pattern and a random pattern on estimation of average tracer concentration of a cell was studied. For uniform, steady flow fields, the geometrically uniform pattern of introducing moving points was found suitable.
The effect of different 'regions of interest' for a particular cell on numerical solutions was studied. In this procedure moving points outside a particular cell were utilized in estimating the average tracer concentration of a cell. This was facilitated by utilizing region size FACTORs ranging from 0.5 to 0.7. However, it was found that utilization of a FACTOR greater than 0.5, which provided for inclusion of moving points outside the cell, resulted in no great improvement in solution accuracy. Hence, a 'region of interest' greater than the cell dimension is not recommended for estimating the average tracer concentration of a cell.
