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  • 1
    Electronic Resource
    Electronic Resource
    Effective Diffusion Coefficient: From Homogenization to Experiment (1997)
    Springer
    Transport in porous media 27 (1997), S. 205-223 
    Details
    ISSN: 1573-1634
    Keywords: effective diffusion coefficient ; model test ; numerical calculations ; homogenization.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper, an example of the application of the homogenization approach (asymptotic expansion technique) to predict the effective diffusion coefficient for an equivalent continuum, together with the experimental verification of the theoretical results is presented. The experimental setup was constructed for the measurements of diffusion in a model periodic porous medium made of Plexiglas. The computer program using the FEM was elaborated to solve the local boundary value problem for a period and to calculate the effective diffusion coefficient. The comparison between the theory and the experiment indicates good agreement between the numerical and experimental values of the effective diffusion coefficient. Interpretation of the test data from the point of view of the homogenization theory is also incorporated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006599410942
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Non-gaussian diffusion modeling in composite porous media by homogenization: Tail effect (1995)
    Springer
    Transport in porous media 21 (1995), S. 47-70 
    Details
    ISSN: 1573-1634
    Keywords: ‘Long-tail’ effect ; pollutant ; diffusion ; double porosity ; homogenization ; modelization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In the paper anomalous diffusion appearing in a porous medium composed of two porous components of considerably different diffusion characteristics is examined. The differences in diffusivities are supposed to result either from two medium types being present or from variations in pore size (double porosity media). The ‘long-tail’ effect is predicted using the homogenization approach based on the application of multiple scale asymptotic developments. It is shown that, if the ratio of effective diffusion coefficients of two porous media is of the order of magnitude smaller or equal O(ε 2), whereε is a homogenization parameter, then the macroscopic behaviour of the composite may be affected by the presence of ‘tail-effect’. The results of the theoretical analysis were applied to a problem of diffusion in a bilaminate composite. Analytical calculations were performed to show the presence of the ‘long-tail’ effect in two particular cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00615334
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On the cross-effects of coupled macroscopic transport equations in porous media (1994)
    Springer
    Transport in porous media 16 (1994), S. 31-52 
    Details
    ISSN: 1573-1634
    Keywords: coupled flows ; homogenization ; Onsager relations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper, the derivation of macroscopic transport equations for this cases of simultaneous heat and water, chemical and water or electrical and water fluxes in porous media is presented. Based on themicro-macro passage using the method of homogenization of periodic structures, it is shown that the resulting macroscopic equations reveal zero-valued cross-coupling effects for the case of heat and water transport as well as chemical and water transport. In the case of electrical and water transport, a nonsymmetrical coupling was found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01059775
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Transient quasi-static gas flow through a rigid porous medium with double porosity (1994)
    Springer
    Transport in porous media 17 (1994), S. 33-57 
    Details
    ISSN: 1573-1634
    Keywords: double porosity ; fractured porous media ; gas filtration ; homogenization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The highly compressible fluid flow through a three-scales rigid porous medium (pore, fracture, macroscopic sample) is investigated using a homogenization method. The macroscopic description is strongly dependent on the separation of the different scales, and three cases are considered. The pores either play the role of a compressible fluid reservoir, introduce a memory effect, or are ignored, respectively. The homogenization result is compared to classical phenomenological models that are available in the case of slightly compressible fluids. Pseudo-steady state models are shown to give a rough description of the phenomenon.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00624049
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  • 5
    Electronic Resource
    Electronic Resource
    High-Velocity Laminar and Turbulent Flow in Porous Media (1999)
    Springer
    Transport in porous media 36 (1999), S. 131-147 
    Details
    ISSN: 1573-1634
    Keywords: Forchheimer ; high-velocity ; laminar ; turbulence ; inertia ; Navier–Stokes ; homogenization.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We model high-velocity flow in porous media with the multiple scale homogenization technique and basic fluid mechanics. Momentum and mechanical energy theorems are derived. In idealized porous media inviscid irrotational flow in the pores and wall boundary layers give a pressure loss with a power of 3/2 in average velocity. This model has support from flow in simple model media. In complex media the flow separates from the solid surface. Pressure loss effects of flow separation, wall and free shear layers, pressure drag, flow tube velocity and developing flow are discussed by using phenomenological arguments. We propose that the square pressure loss in the laminar Forchheimer equation is caused by development of strong localized dissipation zones around flow separation, that is, in the viscous boundary layer in triple decks. For turbulent flow, the resulting pressure loss due to average dissipation is a power 2 term in velocity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006582211517
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  • 6
    Electronic Resource
    Electronic Resource
    Homogenization of Wall-Slip Gas Flow Through Porous Media (1999)
    Springer
    Transport in porous media 36 (1999), S. 293-306 
    Details
    ISSN: 1573-1634
    Keywords: Klinkenberg ; wall-slip ; Knudsen ; gas flow ; low pressure ; Navier–Stokes ; homogenization.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The permeability of reservoir rocks is most commonly measured with an atmospheric gas. Permeability is greater for a gas than for a liquid. The Klinkenberg equation gives a semi-empirical relation between the liquid and gas permeabilities. In this paper, the wall-slip gas flow problem is homogenized. This problem is described by the steady state, low velocity Navier–Stokes equations for a compressible gas with a small Knudsen number. Darcy's law with a permeability tensor equal to that of liquid flow is shown to be valid to the lowest order. The lowest order wall-slip correction is a local tensorial form of the Klinkenberg equation. The Klinkenberg permeability is a positive tensor. It is in general not symmetric, but may under some conditions, which we specify, be symmetric. Our result reduces to the Klinkenberg equation for constant viscosity gas flow in isotropic media.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006572324102
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Comments on the Paper 'Local and Global Transitions to Chaos and Hysteresis in a Porous Layer Heated from Below', by P. Vadasz (1999)
    Springer
    Transport in porous media 37 (1999), S. 247-249 
    Details
    ISSN: 1573-1634
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006649900908
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Modelling of pollutant migration in porous media with interfacial transfer: local equilibrium/non-equilibrium (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Mechanics of Cohesive-frictional Materials 2 (1997), S. 205-221 
    Details
    ISSN: 1082-5010
    Keywords: pollutant diffusion ; advection ; porous media ; surface transfer resistance ; physical modelling ; homogenization ; model classification ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In the paper, an attempt to model local equilibrium and local non-equilibrium in pollutant migration in porous media is presented. Diffusion is assumed to occur in the pores as well as in the solid porous matrix. The macroscopic models are developed using the homogenization method (asymptotic expansion technique). The resulting macroscopic equations show either a one-concentration field or two-concentration fields or memory effects. The domains of validity of all the presented models are also determined. Local cell problems are provided to compute the effective diffusion tensors. The conditions for the local mass equilibrium assumption to be valid are derived in terms of the dimensionless characteristic parameters. The effect of pollutant source distributions is also investigated. © 1997 John Wiley & Son, Ltd.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Conforming finite element computations applied to a spatially periodic, harmonic Navier-Stokes problem (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 685-707 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes Problem ; Monochromatic Dynamic Behaviour ; Uzawa Algorithm ; Darcy's Law ; Conforming Finite Element Methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper computations in the two dimensional case of a harmonic Navier-Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non-symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm).Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so-called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050803
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    Paper (German National Licenses)
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