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Unformatted text preview: heads are applied in the direction of flow, and no flux Neumann conditions perpendicular to the flow. This heterogeneous “bar shape” configuration has a lnK contrast that can be expressed in terms of a geometric mean and a standard deviation (Ababou, 1988): ⎡⎛ ⎧ ( K1 )α1 ⎫ ⎞ 2 ⎛ ⎧ ( K 2 )α 2 ⎫ ⎞ 2 ⎤ K G = ( K1 ) ( K 2 ) σ ln K = ⎢⎜ ln ⎨ (6) ⎬⎟ ⎥ ⎬ ⎟ + ⎜ ln ⎨ ⎜ KG ⎭ ⎟ ⎜ ⎩ KG ⎭ ⎟ ⎥ ⎠⎦ ⎠⎝ ⎢⎝ ⎩ ⎣ where αi is the area fraction of the domain associated with permeability Ki (α1+α2=1). We conducted seawater intrusion simulations for several values of the permeability contrast (K1/K2 or σlnK) and we analysed mass balance (not shown here for lack of space). Mass balance remains quite good even for extremely high contrasts: the relative error on the net computed flux is 0.5 % for K1/K2 = 108 or σlnK = 5.58. Fig. 2(b) shows the analytical solution and the numerical hydraulic head transect H(x) in the middle of the domain, for K1/K2 = 10+8; the local relative error is less than 10-7. α1 α2 Fig 2 (a) Domain configuration (left). Fig 2 (b)...
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