Coupling of the time domain random walk method with the finite fragment method to simulate flow and transport in 1-D heterogeneous media

Abstract

A new method to simulate flow and solute transport in 1-D heterogeneous media is presented. This method integrates the time domain random walk method (TDRW) and the finite fragment method (FFM). The TDRW, similar in concept to the classical random walk method, calculates the arrival time of a particle cloud at a given location and provides the solute breakthrough curve. The FFM, which can be seen as an enhancement of the finite difference scheme, allows a heterogenous media to be divided into homogeneous zones to which the TDRW can be applied. The main advantage of the resulting coupling is that the restrictions can be avoided on the space increments and the time steps which exist with the classical methods of finite differences and random walk. In a homogeneous zone of soil, the breakthrough curve can be calculated directly at a given distance with a reasonable number of particles. A 1-D heterogeneous domain to be simulated is then split into homogeneous zones in which the hydraulic heads and the velocities are calculated by the FFM and at the end of which the temporal solute distributions are calculated by the TDRW. A few hundred particles are generally sufficient to clearly define the breakthrough curve. Comparisons with analytical and numerical solutions and experimental data shows the reliability and advantages of this new method.