Efficient random walk particle tracking algorithm for advective-dispersive transport in media with discontinuous dispersion coefficients and water contents

摘要

Random walk particle tracking (RWPT) is a well established and efficient alternative to grid-based Eulerian approaches when simulating the advection-dispersion transport problem in highly heterogeneous porous media. However, RWPT methods suffer from a lack of accuracy when the dispersion tensor or the water content is spatially discontinuous. We present improvements to the concept of a partially reflecting barrier used to account for these discontinuities : (1) the nonlinear time splitting with root Delta t = root Delta t(1) vertical bar root Delta t(2) that corrects for the systematic overestimation of the second dispersion displacement across an element interface when linear time splitting is used; (2) the one-sided reflection coefficient that correctly represents the effect of discontinuous dispersion coefficients and water content but eliminates redundant reflections of the two-sided reflection coefficient and limits the error for discrete Delta t; and (3) the transformation of the dispersive displacement across the element interface for complex multidimensional transport problems. The proposed improvements are verified numerically by comparison with an analytical solution and a reference RWPT method. The results indicate an increased efficiency and accuracy of the new RWPT algorithm. Because the new algorithm efficiently simulates both advection- and dispersion-dominated transport conditions, it enhances the applicability of RWPT to scenarios in which both conditions occur, as, for example, in the highly transient unsaturated zone. The algorithm is easily implemented and it is shown that the computational benefit increases with increasing variability of the hydraulic parameter field.