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Let $\\Gamma ^1$ and $\\Gamma ^2$ be two disjoint open subsets of $\\Gamma$ representing the parts of $\\Gamma$ through which some water can enter and escape from $\\Omega$. We investigate the asymptotic behavior of the flow $\\phi_n$ through a discrete version $\\Omega_n$ of $\\Omega$ between the corresponding discrete sets $\\Gamma ^1_n$ and $\\Gamma ^2_n$. 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Let $\\Gamma ^1$ and $\\Gamma ^2$ be two disjoint open subsets of $\\Gamma$ representing the parts of $\\Gamma$ through which some water can enter and escape from $\\Omega$. We investigate the asymptotic behavior of the flow $\\phi_n$ through a discrete version $\\Omega_n$ of $\\Omega$ between the corresponding discrete sets $\\Gamma ^1_n$ and $\\Gamma ^2_n$. 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