A Cell-Averaged Numerical Model for One-Dimensional Subsurface Flow in a Sloping Wetland Bed

Constructed subsurface wetlands are widely used to treat wastewater and diffuse source pollutants. A cell-averaged subsurface flow numerical model has been recently developed to specifically solve water quality problems at scales coarser than the high-resolution point-scale models (e.g., completely-mixed, cell-based). This paper focuses on the hydrologic component. A numerical scheme for cell-averaged water depth was derived for unconfined groundwater flow in a subsurface treatment wetland with a sloping bed and a nonlinear head-flow controlled outflow at the outlet. The governing phreatic aquifer flow equation was integrated over a typical porous cell, and Taylor expansion was implemented to derive an algebraic expression for the interfacial flux. Picard iteration was introduced to linearize a nonlinear system of 2nd-order finite difference equations and to allow for the use of Thomas' algorithm to solve a coupled set of linear equations. The numerical scheme was then modified for potential non-Darcian flow in the highly permeable porous beds (gravel and rock) using the Forchheimer equation. We examined the performance of the numerical scheme with the averaging cell size and the cell size where the numerical solution diverges from actual cell-averaged head values. This was done by comparing the numerical solution with cell-averaged analytical solutions for simple steady-state flow scenarios. It's worth noting that for a very high-resolution discretization, the cell-averaged solution is expected to be equal to that for nodal-based schemes when the node is at the center of the cell. Preliminary results for Darcy flow showed increasingly larger differences with the analytical solutions as the cell size increased and the opposite is true. The non-Darcian flow solution did not show significant differences from the Darcian flow solution for the flow scenarios examined.