Space time discretization is based on implicit finite

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Unformatted text preview: (50) (51) We observe that this φ-equation is equivalent to a stochastic groundwater flow equation with 2D random field transmissivity in a confined aquifer (cf. “infinite domain” spectral perturbation solutions by [Mizell et al. 1982]). Thus, σΦ can be evaluated from the spectral solution of Eq.(51), at least far enough from the sea and the saltwedge tip. The “theoretical” standard deviation of φ is deduced from the Mizell et al (1982) solution, for a “modified Wittle” correlation structure: (σ Φ )THEORY ≈ c σ ln K λln K J x ≈ c σ ln K λln K a (52) where Jx is the mean Φ-gradient denoted “a” in this paper. The coefficient “c” is a dimensionless constant of order 0(1) [Mizell et al 1982]. For the problem at hand, the value of “c” can be obtained by matching numerical and theoretical “σΦ” at low levels of heterogeneity (σlnK ≤ 1). This procedure gives: Modélisation stochastique de l'intrusion saline en 2D plan c ≈ 1.10 67 (53) Similarly, the relevant value of the mean Φ-gradient, a...
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