A forward particle tracking Eulerian–Lagrangian Localized Adjoint Method for solution of the contaminant transport equation in three dimensions

The contaminant transport equation is solved in three dimensions using the Eulerian–Lagrangian Localized Adjoint Method (ELLAM). Trilinear and finite volume test functions defined by the characteristics of the governing equation are employed and compared. Integrations are simplified by forward tracking of integration points along the characteristics.

The resulting equations are solved using a preconditioned conjugate gradient method. The algorithm is coupled to a block-centered finite difference approximation of the groundwater flow equation similar to that used in the popular MODFLOW code. The ELLAM is tested by comparison with 1D and 3D analytic solutions.

The method is then applied with random, spatially correlated hydraulic conductivities in a simulation of a tracer experiment performed on Cape Cod, Massachusetts. The linear test function ELLAM was found to perform better than the finite volume ELLAM. Both ELLAM formulations were found to be robust, computationally efficient and relatively straightforward to implement.

When compared to traditional particle tracking and characteristics codes commonly used with MODFLOW, the ELLAM retains the computational advantages of traditional characteristic methods with the added advantage of good mass conservation.