On the Finite Volume Reformulation of the Mixed Finite Elements Method on Triangles

We analyse the finite volume reformulation of the triangular mixed finite element approximation for the porous flow equation, as proposed in [10] [9]. We show that the finite volumes are obtained by aggregation of finite elements (usually one, sometimes two or more), that the matrix of the finite volume equations is regular, but generally not symmetrical, and that the finite volume formulation is algebraically equivalent to the mixed approximation. The finite volume matrix becomes symmetrical in the stationary case, and positive definite when the triangulation satisfies the Delaunay condition

Efficient approximations for the simulation of density driven flow in porous media

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Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Fluid flow in a charged porous medium generates electric potentials called streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, global sensitivity analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse polynomial chaos expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap information criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov chain Monte Carlo (MCMC) method and the first-order approximation (FOA) approach based on the Levenberg-Marquardt algorithm. The comparison between both approaches allows us to check whether FOA can provide a reliable estimation of parameters and associated uncertainties for the highly non-linear hydrogeophysical problem investigated. GSA results show that in short time periods, the saturated hydraulic conductivity (K-s) and the voltage coupling coefficient at saturation (C-sat) are the most influential parameters, whereas in long time periods, the residual water content (theta(s)), the Mualem-van Genuchten parameter (n) and the Archie saturation exponent (n(a)) become influential, with strong interactions between them. The Mualem-van Genuchten pa-rameter (alpha) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (K-s, theta(s), alpha, n) and geophysical parameters (n(a),C-sat) can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions

Hydraulic and transport parameter assessment using column infiltration experiments

The quality of statistical calibration of hydraulic and transport soil properties is studied for infiltration experiments in which, over a given period, tracer-contaminated water is injected into an hypothetical column filled with a homogeneous soil. The saturated hydraulic conductivity, the saturated and residual water contents, the Mualem-van Genuchten shape parameters and the longitudinal dispersivity are estimated in a Bayesian framework using the Markov chain Monte Carlo (MCMC) sampler. The impact of the kind of measurement sets (water content, pressure inside the column, cumulative outflow and outlet solute concentration) and that of the solute injection duration is investigated by analyzing the calibrated model parameters and their confidence intervals for different scenarios. The results show that the injection period has a significant effect on the quality of the estimation, in particular, on the posterior uncertainty range of the parameters. All hydraulic and transport parameters of the investigated soil can be well estimated from the experiment using only the outlet concentration and cumulative out-flow, which are measured non-intrusively. An improvement of the identifiability of the hydraulic parameters is observed when the pressure data from measurements taken inside the column are also considered in the inversion

D'un code de simulation thermique du bâtiment à l'observation d'état : présentation de deux applications

International audienceCet article traite de la possibilité d'effectuer une simulation à l'aide d'un code de simulation en contraignant le modèle par les mesures de certaines températures. L'automatique des systèmes d'état fournit un cadre théorique à la démarche d'estimation de variables internes à un système, ce à des fins de régulation. Le code de calcul peut alors être considéré comme un observateur d'état. Après une présentation rapide de l'incidence de la démarche au niveau du code de calcul et de l'interface, deux applications sont présentées, l'une visant à la vérification de la cohérence de la démarche, l'autre l'appliquant dans la cadre de la validation d'un support expérimental de laboratoire