Particle tracking in transient groundwater flow fields with the Laplace transform analytic element method

The Laplace transform analytic element method (LT-AEM) has been shown to be a viable extension of the 2D analytic element method (AEM) to transient porous media flow problems. Furman and Neuman (2003) and Kuhlman (2008) illustrate the use of eigenfunction expansion to develop point, circular, elliptical, and line elements to solve the Laplace-transformed governing equation for 2D transient groundwater flow. A numerical inverse Laplace transform (de Hoog et al, 1982) is used to compute the solution in the time domain. We utilize these methods to perform particle tracking in transient flow fields, integrating the computed velocity field using an adaptive fourth-order Runge-Kutta algorithm. While transient particle tracking has previously been performed in steady-state flow fields computed from AEM solutions, most modeling situations a transient flow solution is more appropriate. We illustrate several characteristic transient LT-AEM pathlines computed from LT-AEM flow fields and compare one result to a gridded MODFLOW + MODPATH solution.