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Perrochet, Pierre

Nom
Perrochet, Pierre
Affiliation principale
Fonction
Professeur ordinaire
Email
pierre.perrochet@unine.ch
Identifiants
https://libra.unine.ch/handle/123456789/144

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  • Publication
    Métadonnées seulement
    Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling
    (2005)
    Cartwright, Nick
    ;
    Nielsen, Peter
    ;
    Perrochet, Pierre 
    [1] Comprehensive measurements of the water table response to simple harmonic forcing at the base of a sand column are presented and discussed. In similar experiments, Nielsen and Perrochet ( 2000) observed that fluctuations in the total moisture were both damped and lagged relative to the water table fluctuations. As a result, the concept of a complex effective porosity was proposed as a convenient means to account for the damping and phase lag through its magnitude and argument, respectively. The complex effective porosity then enables simple analytical solutions for the water table ( and total moisture) dynamics including hysteresis. In this paper, these previous experiments are extended to cover a wider range of oscillation frequencies and are conducted for three well-sorted materials with median grain diameters of 0.082, 0.2, and 0.78 mm, respectively. In agreement with existing theory, the influence of the capillary fringe is shown to increase with the oscillation frequency. However, the complex effective porosity model corresponding to the classical Green and Ampt (1911) capillary tube approximations is shown to be inadequate when compared to the data. These limitations are overcome by the provision of an empirical, frequency-dependent complex effective porosity model fit to the data. Using measured moisture retention parameters, numerical simulation of the data solving a nonhysteretic van Genuchten - Richards' equation type model is unable to replicate the observations. Existing results of a hysteretic numerical model are shown to be in good agreement with the extended database.
  • Publication
    Métadonnées seulement
    Improved Computation of Nonlinear Advection in Porous-Media Using slightly Modified Basic Finite-Element Algorithms
    (1995)
    Perrochet, Pierre 
    The numerical stability of standard finite element schemes applied to the advection-diffusion equation is evaluated using a space-time eigenvalue analysis. Unlike the usual approaches which only consider temporal aspects of stability, this analysis also describes the spatial stability of the solutions. To this end, the one-dimensional advection-diffusion equation is put into an alternative semi-discrete form which allows the derivation of a very practical stability condition. In multidimensional flow situations the latter is applied along the streamlines by means of a tensorial corrective function that prevents excessive numerical smearing of fronts or phase interfaces. The efficiency of the procedure is illustrated by an example which successfully simulates the coupling of two low miscible fluid phases in a variably saturated porous medium.
  • Publication
    Métadonnées seulement
    A Perspective on the numerical-Solution of Convection-dominated Transport Problems - a Price to Pay for the Easy Way Out
    (1992)
    Noorishad, J
    ;
    Tsang, C F
    ;
    Perrochet, Pierre 
    ;
    Musy, André
    In a brief but fundamental review of the evolution of the conventional numerical techniques used in the solution of convection-dominated transport problems, we explore the difficulties that have been remedied to various degrees by various workers. In the course of this review we obtain the performance characteristic of the Crank-Nicolson Galerkin finite element method in the form of a curve in Peclet number and Courant number space. We show that the performance can be altered through a new upwind parameter that can easily be incorporated into many of the existing numerical solution methods. By providing an insight into the limitations of some of these methods we demonstrate, by means of numerical experiments, that the proposed upwinding procedure ensures acceptable solutions throughout the Pe-Cr space at a reasonable cost of the smearing effect.