At the end of this checking step, every totally- or partially-desaturated cell needs to be connected with the surface, in order to allow air to infiltrate into the porous medium. First, a recursive function searches for every continuous path connecting partially- or totally-desaturated cells with the uppermost active cells.
#Ontour interval code#
When the solution procedure is completed (Section 2.3), the computer code checks the physical reliability of the solution reached. Instead, if the adjacent cells have a non-vanishing, possibly small, thickness, then the physical situation implies that there is a horizontal transfer of water. , internal) cells, to reach the water table. This choice permits one to transfer the fixed source terms to deeper cells: this is necessary, e.g., to permit the aquifer recharge, which is assigned at the top active ( i.e. If also the adjacent cells along the horizontal directions are dry, then the terms corresponding to horizontal fluxes in Equation (5) vanish, and therefore, the cell under examination is involved only for a balance along the vertical direction. The proposed model does not solve equations for variably-saturated conditions, but aims at finding a solution for fully-saturated groundwater flow: the cells that become dry during the iterative algorithm of solution are not eliminated from the domain, but are used as auxiliary cells in the sense to be specified below. Several tests showed that the generalization of relaxation methods is in general quite robust, in particular for complex physical situations. However, it should be noted that the specific problem addressed in this paper includes non-differentiable terms in the system of equations, like those introduced by Equation (6) and by the sequence of equations from Equations (7) to (11). Other approaches, e.g., Newton’s or conjugate-gradient methods, could be more efficient in terms of elapsed running time, if the code is properly modified to profit from parallel computers. This choice is optimal from the point of view of the memory requirement. In YAGMod, a simple approach, based on a generalization of the relaxation methods for the solution of systems of algebraic linear equations, is proposed. The solution to Equation (12) could be obtained with any of the methods of solution for non-linear equations that can be found in textbooks of numerical analysis.
A is a sparse, symmetric, diagonally-dominant matrix, which is strictly diagonally dominant if at least one D node is present in the domain its elements are built with transmittances and, therefore, depend on x, as shown by Equations (3) and (4). x includes the values of the water head in the internal nodes, b ( ) includes the fixed source/sink terms (Section 2.2.1), b ( var ) includes the source/sink terms that depend on the water head of the aquifer (Sections 2.2.2 and 2.2.3) and the terms appearing in the left-hand side of Equation (5) that involve the water head at D nodes.
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