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Version: publishedVersion × Subject: Darcy equation ×

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    Stochastic simulation of flows and particle transport in porous tubes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Sabelfeld, Karl; Kurbanmuradov, Orazgeldi; Levykin, Alexander
    A Monte Carlo method is developed for stochastic simulation of flows and particle transport in tubes filled with a porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modelled in a tube with prescribed boundary conditions. Numerical experiments are carried out by solving the random Darcy equation for each sample of the hydraulic conductivity by a SOR iteration method, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, diffusion coefficients, the mean and variance of Lagrangian trajectories, and discuss a ''stagnation" effect which was found in our simulations.
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    Stochastic flow simulation and particle transport in a 2D layer of random porous medium
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Kurbanmuradov, Orazgeldi A.; Sabelfeld, Karl K.
    A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.
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    Mathematical modeling of channel-porous layer interfaces in PEM fuel cells
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Ehrhardt, Matthias; Fuhrmann, J.; Holzbecher, E.; Linke, A.
    In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary. After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them. The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur. We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster.