Treatment of internal sources in the finite-volume ELLAM

The finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) is a mass-conservative approach for solving the advection-dispersion equation. The method has been shown to be accurate and efficient for solving advection-dominated problems of solute transport in ground water in 1, 2, and 3 dimensions. Previous implementations of FVELLAM have had difficulty in representing internal sources because the standard assumption of lowest order Raviart-Thomas velocity field does not hold for source cells. Therefore, tracking of particles within source cells is problematic. A new approach has been developed to account for internal sources in FVELLAM. It is assumed that the source is uniformly distributed across a grid cell and that instantaneous mixing takes place within the cell, such that concentration is uniform across the cell at any time. Sub-time steps are used in the time-integration scheme to track mass outflow from the edges of the source cell. This avoids the need for tracking within the source cell. We describe the new method and compare results for a test problem with a wide range of cell Peclet numbers.