Abstract
Abstract. The common node approach and the dual node approach are two widely applied approaches to coupling surface–subsurface flow. In this study both approaches are analyzed for cell-centered as well as vertex-centered finite difference schemes. It is shown that the dual node approach should be conceptualized and implemented as a one-sided first-order finite difference to approximate the vertical subsurface hydraulic gradient at the land surface. This results in a consistent dual node approach in which the coupling length is related to grid topology. In this coupling approach the coupling length is not to be interpreted as a nonphysical model parameter. Although this particular coupling approach is technically not new, the differences between this consistent dual node approach and the common node approach have not been studied in detail. In fact, this coupling scheme is often believed to be similar to the common node approach. In this study it is illustrated that in comparison to the common node approach, the head continuity at the surface–subsurface interface is formulated more correctly in the consistent dual node approach. Numerical experiments indicate that the consistent dual node approach is less sensitive to the vertical discretization when simulating excess infiltration. It is also found that the consistent dual node approach can be advantageous in terms of numerical efficiency.
Highlights
There is a variety of hydrogeological problems, such as the hydrologic response of hillslopes and river catchments, which requires an integrated analysis of surface and subsurface flows
The finding of this study show that the consistent dual node approach compares more positively with respect to the common node approach than other dual node approaches
Considering that nodal values ideally represent the mean values within discrete control volumes, as described in Sect. 2, it can be argued that the head continuity as implemented in the common node approach is not in agreement with the physical principle of head continuity at the land surface
Summary
There is a variety of hydrogeological problems, such as the hydrologic response of hillslopes and river catchments, which requires an integrated analysis of surface and subsurface flows. It is shown that the dual node approach should be interpreted and implemented as a one-sided finite difference approximation of the vertical hydraulic gradient at the land surface This yields a consistent dual node scheme in which the coupling length is defined by the half the thickness of the topmost subsurface cells. A correct interpretation of nodal values is crucial for understanding the dual and common node approach for coupling surface–subsurface flow Both coupling approaches depend on the configuration of surface and topmost subsurface nodes near the land surface. Considering that nodal values ideally represent the mean values within discrete control volumes, as described, it can be argued that the head continuity as implemented in the common node approach is not in agreement with the physical principle of head continuity at the land surface. The common node approach is only numerically correct if the topmost subsurface cells are very thin
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
