EFFET DU CONDITIONNEMENT DES TRANSMISSIVITES SUR LES CARACTERISTIQUES SPECTRALES DE LA MATRICE DE L’ECOULEMENT EN MILIEU POREUX
Mots-clés :
groundwater modeling, condition number, ill-conditioning, modèles numériques, conditionnement, rayon spectral, hydrogéologieRésumé
Usually to determine a measure of the degree of ill-conditioning of an algebraic system, we invoke a condition number for the coefficients matrix. In groundwater modeling these coefficients are depending on the
parameters of the heteregeneous porous medium i.e. trans- missivities T. Therefore an estimate of the condition number of the flow matrix is of a considerable interest to assess the accuracy and the reliability of the solution relevant to the numerical method. Ill-conditioning ofthe system may ascribe to many well-known sources.
Herein we inspect condition numbers of flow matricesarising in groundwater modeling flow through synthetics porous media slowly variable. The flow matrices are build up via the numerical generation of conditional log T fields whose variability is indexed on the corresponding variograms. Numerical experiments of Monte Carlo type allowed to study multiple replications of the flowmatrices incorporating available information into estimating the log T values. Results obtained confirm what it was roughly suspected : condition number and spectral radius of the flow matrix are sensitive to the constraints of the local information only if the distance between these points is greater than the correlation length. In such case, the number of the measurement points increases the influence of the standard deviation σY. Otherwise, the a prioriinformation is unvaluable i.e.redundant
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