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United States Department of Agriculture

Agricultural Research Service


Location: Watershed Physical Processes Research Unit

Title: A Coupled Finite-Volume Model for 2-D Surface and 3-D Subsurface Flows

item He, Zhiguo -
item Wu, Weiming -
item Wang, Sam -

Submitted to: Journal Hydrologic Engineering
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: October 17, 2007
Publication Date: September 1, 2008
Citation: He, Z., Wu, W., Wang, S.S.Y. 2008. A Coupled Finite-Volume Model for 2-D Surface and 3-D Subsurface Flows. Journal Hydrologic Engineering (ASCE) 13(9), 835-845.

Interpretive Summary: A physically based coupled numerical model for 2D surface and 3D subsurface flows has been presented in this study. Based on the continuity conditions of pressure head and exchange flux at the ground surface, a general framework for coupling the surface and subsurface flows has been adopted. A new form of surface flow equation based on the diffusion wave approach has been developed. It is intrinsically coupled with the subsurface flow equation in the integrated surface-subsurface model. The system of flow equations is discretized using the finite-volume method in space and the implicit scheme in time. The modified Picard procedure with under-relaxation is used to linearize the surface and subsurface flow equations. In the discretized surface equation, the diffusion coefficients at the interface of control volumes are evaluated using an upwind scheme to ensure solution monotonicity. The time derivative term for the volumetric soil water content in the nonlinear Richards equation is discretized using the method of Celia et al. (1990) to efficiently yield robust numerical solutions and maintain mass balance for unsaturated flow problems. The system of nonlinear flow equations is solved using Stone’s Strongly Implicit Procedure. The coupled surface-subsurface flow model developed has been tested and verified by comparing the numerical solutions with analytical solutions and experimental data. The surface and subsurface flow components are first tested separately by comparing numerical solutions from the present model with the data published by Gottardi and Venutelli (1993), Di Giammarco et al. (1996), and Panday and Huyakorn (2004) for surface flow, and the results presented in Zhang and Ewen (2000) for subsurface flow. Then, the integrated flow model is verified using a set of experimental and numerical data presented in Smith and Woolhiser (1971) and shows a good agreement. Applications of the integrated flow model to the field-scale experiment of Abdul (1985) and the Deep Hollow Lake watershed, Mississippi indicate its ability to simulate, with relative errors less than 18%, shallow water surface flow and subsurface flow at the field scale.

Technical Abstract: Surface-subsurface interactions are an intrinsic component of the hydrologic response within a watershed; therefore, hydrologic modeling tools should consider these interactions to provide reliable predictions, especially during rainfall-runoff processes. This paper presents a fully implicit coupled model designed for hydrologic evaluation in wetlands, agricultural fields, etc. The model uses the depth-averaged two-dimensional diffusion wave equation for shallow surface water flow and the three-dimensional mixed-form Richards equation for variably saturated subsurface flow. The interactions between surface and subsurface flows are considered via infiltration in dynamic equilibrium. A general framework for coupling the surface and subsurface flow equations is adopted, based on the continuity conditions of pressure head and exchange flux rather than the traditional conductance concept. The diffusion wave surface water equation is used as an upper boundary condition for the initial-boundary value problem of variably saturated subsurface flow. The coupled system of equations governing surface and subsurface flows is discretized using the finite-volume method in space and an implicit scheme in time. Component modules and the coupled flow model have been tested by comparing numerical results with published experimental data and analytical solutions. The verified integrated flow model has been applied to simulate the rainfall-runoff processes in a published field-scale experiment and the Deep Hollow Lake watershed, Mississippi. The results have demonstrated that the established numerical model is capable of simulating 3D subsurface flow and 2D surface shallow water flow as well as predicting the interactions between them.

Last Modified: 9/21/2014
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