Finite volume integrated surface‐subsurface flow modeling on nonorthogonal grids

Abstract

In this paper, we present an innovative finite volume surface-subsurface integrated flow model on nonorthogonal grids. The shallow water equation with diffusion wave approximation is used to formulate the surface flow system, while the Richards' equation is used to formulate the saturatedunsaturated subsurface flow system. These two flow systems are discretized using a finite volume method and are then coupled by enforcing the continuity of pressure and flux at the surface-subsurface interface, which does not require unphysical parameters such as the interface permeability and thickness. The numerical instability caused by enforcing the continuity of pressure and flux at the interface is resolved using a cell-centered finite volume discretization. The coupled systems are solved simultaneously by the Newton iterative method. A battery of benchmark analyses and laboratory experiments verify the proposed model's superior performance relative to existing models. Two numerical experiments over irregular terrain show that the nonorthogonal grids and diffusive wave approximation used in the proposed model accurately represent the interaction between surface and subsurface flows for irregular topographies. In particular, they capture the significant topographical effects on runoff discharges, especially where gentle slopes are involved.

New insights into the differences between the dual node approach and the common node approach for coupling surface–subsurface flow

“…This yields a consistent dual node scheme in which the coupling length is defined by the half the thickness of the topmost subsurface cells. The scheme of An and Yu (2014) as well as the scheme of Kumar et al (2009) are essentially very similar to this consistent dual node scheme. In the work of Panday and Huyakorn (2004), one of the suggestions to define the coupling length is to use half the thickness of the topmost subsurface cells, which yields a consistent dual node scheme.…”

“…However, these schemes are not recognized as a dual node scheme. Instead, An and Yu (2014) argue that their scheme is similar to the common node approach of Kollet and Maxwell (2006). Kumar et al (2009) argue that their scheme is similar to the dual node approach if the coupling length goes to zero, which implies that their scheme would be similar to the common node approach.…”

“…However, in their work, the particular advantage of choosing this value (i.e., maintaining a unit gradient in elevation head) is not recognized. The coupling schemes used by An and Yu (2014) and Kumar et al (2009) are also in essence consistent dual node schemes. However, these schemes are not recognized as a dual node scheme.…”

“…Kumar et al (2009) argue that their scheme is similar to the dual node approach if the coupling length goes to zero, which implies that their scheme would be similar to the common node approach. However, contrary to the common node approach the schemes of An and Yu (2014) and Kumar et al (2009) compute exchange fluxes between surface and topmost subsurface nodes, and therefore these schemes are technically dual node schemes. As explained in this study, it is crucial to observe that the schemes of An and Yu (2014) and Kumar et al (2009) are actually quite different from the common node approach.…”

“…However, contrary to the common node approach the schemes of An and Yu (2014) and Kumar et al (2009) compute exchange fluxes between surface and topmost subsurface nodes, and therefore these schemes are technically dual node schemes. As explained in this study, it is crucial to observe that the schemes of An and Yu (2014) and Kumar et al (2009) are actually quite different from the common node approach. As already mentioned, the consistent dual node scheme differs from the common node approach with respect to how the head continuity is formulated at the surface-subsurface interface.…”