A Dynamic Programming Solution to Solute Transport and Dispersion Equations in Groundwater

Abstract

The partial differential equations for water flow and solute transport in a twodimensional saturated domain are rendered discrete using the finite difference technique; the resulting system of algebraic equations is solved using a dynamic programming (DP) method. The advantage of the DP algorithm is that the problem is converted from solving an algebraic system of order NC(NL-1) ×NC(NL-1) into one of solving a difference equation of order NC×NC over NL-1 steps and involving NL-1 matrix inversions of order NC×NC. The accuracy and precision of the solutions are shown by comparing the results with an analytical solution and calculation of mass the balance. In addition, the performance of the DP model was compared with the results of the MOC model developed by US Geological Survey. In all cases, the DP model showed good results with sufficient accuracy.