Gasto et al., 2002) have also been implemented successfully. Despite the promising results reported by the differ-Water flow in unsaturated porous media is usually simulated using ent authors, these schemes have not been widely adopted the Richards equation in combination with some numerical method for spatial and temporal discretization. In this study we implement a because of the additional complexity and/or computamixed hybrid finite element solution with different formulations for tional effort involved. Moreover, little information exists the equivalent hydraulic conductivity in an attempt to more accurately about the treatment of interblock conductivities when simulate variably saturated flow. The advantages of a quadrature rule the two neighboring nodes are located in soil layers with are demonstrated for simulations of sharp infiltration fronts. Results contrasting hydraulic properties (Zaidel and Russo, 1992; show the importance of selecting an appropriate equivalent conductiv-Brunone et al., 2003), a situation which is commonly ity. Geometric, weighted and integrated formulations produced better encountered in the field. The accuracy of unsaturated solutions than a traditional scheme using a mean conductivity calculated flow predictions may then very much depend on how with a mean pressure head. Two illustrative test cases are considered interlayer conductivities are evaluated. for infiltration in initially dry homogeneous and heterogeneous soils This study is focused principally on an alternatively subject to both Dirichlet and variable Neumann boundary conditions. The accuracy and computational efficiency of the proposed algorithm numerical approach referred to in the literature as the with the different conductivity formulations is demonstrated by means mixed hybrid finite element (MHFE) method (Chavent of comparisons with a finite difference approach using various inter-
352P of accurate fl uid movement in porous media is an important issue for scientists and engineers who are interested in the management of water resources. Computational simulations have received much attention to achieve this predictive role. Even if its validity is still discussed, the Richards equation (RE) is a valuable model to predict water movement and solute transport in variably saturated media (Simunek and Bradford, 2008).From a mathematical point of view, the RE can be a highly nonlinear parabolic equation under unsaturated conditions, or a partial diff erential equation (PDE) of elliptic type for a fl uid-saturated incompressible porous media. Among the various numerical schemes that can be used to solve the RE, the mixed fi nite element method is well suited for the discretization of elliptic and parabolic PDEs on heterogeneous domains. Moreover, it is locally conservative, can handle general irregular grids, and allows simultaneous approximation of both pressure and velocity.Consequently, this method has been used extensively during the last few years (Mosé et al., 1994;Bergamaschi et al., 1998;Younes et al., 1999Younes et al., , 2006Ackerer et al., 1999; Chavent et al., 2003, among others). For practical applications, the lowest order mixed method of Raviart-Th omas (RT0) is frequently applied and was considered in this study. Th e RT0 uses a piecewise constant approximation for pressure (Brezzi and Fortin, 1991). Th e velocity space has three degrees of freedom for triangular elements and four for quadrangular elements. In their original form, the mixed methods require the resolution of algebraic equations that typically lead to indefi nite systems (Chavent and Jaff ré, 1986;Brezzi and Fortin, 1991).Th e most widely used approach to circumvent this mathematical diffi culty is the hybridization technique (Roberts and Th omas, 1990). It consists in introducing pressure Lagrange multipliers at the element edges. Th e MHFE method leads to a symmetric and positive defi nite matrix, which generally does not satisfy the M-matrix property (Raviart and Th omas, 1977;Th omas, 1977;Wheeler and Peszynska, 2002). Th is property (which requires a nonsingular matrix with m ii > 0 and m ij ≤ 0) has nonetheless a nice physical impact, as the scheme in this case satisfi es the discrete maximum principle, i.e., local maxima or minima will not appear in the numerical solution for a domain without local sources or sinks. Th erefore, the resulting numerical state variable and its related fl uxes are consistent with the physics.For elliptic problems, the matrix obtained with the MHFE method is an M-matrix in the case of a weakly acute triangulation (all angles are <π/2) (Brezzi and Fortin, 1991). Th is condition on the angles is not suffi cient for parabolic problems. A fi rst A : MHFE, mixed hybrid fi nite element; RE, Richards equation; RT0, lowest order Raviart-Th omas method.O R Accurate numerical simula on of infi ltra on in the vadose zone remains a challenge, especially when very sharp fronts are modeled. In th...
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