Weighted method of characteristics solutions for solute transport models

Abstract

Method of characteristics (MOC) solutions are widely employed in solute transport models to estimate tracer concentration. The conventional approach to obtain average tracer concentration for a particular cell is to arithmetrically average the concentration of moving points within the cell during a particular time step. This results in the prediction of a stepwise or a 'jerky' dispersion front unless a large number of moving points are introduced and/or smaller grid size are used. Criteria proposed in the past to avoid this 'jerky' behaviour are unsuitable if the flow is non-uniform and/or unsteady or if the grid size is large. To overcome this problem, a distance weighted criterion was incorporated in a solute transport model which utilizes the method of characteristics. Results were compared with those from analytical solutions and the conventional arithmetical averaging algorithm. The distance weighting algorithm performed as well as the arithmetic averaging algorithm for small grid sizes. When the grid size was large and/or the seepage velocity was low, the conventional approach resulted in a stepwise dispersion front, whereas the distance weighting approach resulted in a smoother dispersion front, consistent with analytical solution. Application of the proposed method should facilitate the selection of larger grid size for simulating solute transport in porous media.