A coupled surface‐subsurface model for hydrostatic flows under saturated and variably saturated conditions |
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| Authors: | Vincenzo Casulli |
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| Affiliation: | Laboratory of Applied Mathematics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy |
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| Abstract: | In this paper, the governing differential equations for hydrostatic surface‐subsurface flows are derived from the Richards and from the Navier‐Stokes equations. A vertically integrated continuity equation is formulated to account for both surface and subsurface flows under saturated and variable saturated conditions. Numerically, the horizontal domain is covered by an unstructured orthogonal grid that may include subgrid specifications. Along the vertical direction, a simple z‐layer discretization is adopted. Semi‐implicit finite difference equations for velocities, and a finite volume approximation for the vertically integrated continuity equation, are derived in such a fashion that, after simple manipulation, the resulting discrete pressure equation can be assembled into a single, two‐dimensional, mildly nonlinear system. This system is solved by a nested Newton‐type method, which yields simultaneously the (hydrostatic) pressure and a nonnegative fluid volume throughout the computational grid. The resulting algorithm is relatively simple, extremely efficient, and very accurate. Stability, convergence, and exact mass conservation are assured throughout also in presence of wetting and drying, in variable saturated conditions, and during flow transition through the soil interface. A few examples illustrate the model applicability and demonstrate the effectiveness of the proposed algorithm. |
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| Keywords: | free‐surface flow mildly nonlinear system surface‐subsurface flow semi‐implicit method subgrid resolution variable saturated soil |
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