Numerical evaluation of a second-order water transfer term for variably saturated dual-permeability models
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abstract
Dual-permeability models contain a lumped mass transfer term that couples equations for water flow in the soil matrix and fracture systems. Linear first-order transfer terms cannot accurately calculate water transfer between the domains during early times of pressure head nonequilibrium. In this study, a second-order equation for water transfer into spherical rock matrix blocks [Zimmerman et al., 1993, 1996] was adapted and evaluated comprehensively for water transfer into and out of variably saturated soil matrix blocks of different hydraulic properties, geometries, and sizes, for different initial and boundary conditions. Numerical solutions of the second-order term were compared with respective results obtained with a first-order term and a one-dimensional horizontal flow equation. Accurate results were obtained after implementing two modifications in the second-order term. First, the hydraulic conductivity was calculated as a weighted arithmetic average of conductivities that used pressure heads in matrix and fracture. For a time-variable pressure head boundary condition, a fixed weighting factor of 17 could be applied irrespective of texture, initial condition, and matrix block size up to 10 cm. Second, if direction of water transfer changed (to or from matrix), the initial pressure head was reset to the equilibrium pressure head at the time of transfer reversal. The modified second-order term was implemented into a dual-permeability model, which closely approximated reference results obtained with a two-dimensional flow model. For rectangular slab-type or comparable geometry of soil matrix, the modified second-order term considerably improves the accuracy of dual-permeability models to simulate variably saturated preferential flow in soil.
