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  • 1
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    Stochastic flow simulation and particle transport in a 2D layer of random porous medium (2010)
    WIAS, Berlin
    Details
    Publication Date: 2021-03-29
    Description: 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.
    Description: research
    Keywords: 550.28 ; 550 ; ZfM : Darcy equation ; ZfM : random hydraulic conductivity ; ZfM : randomized spectral models ; ZfM : diffusion regime ; ZfM : long-range correlations
    Language: English
    Type: article , draft
    Format: 24 S.
    Format: application/pdf
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    CITATION GEO-LEO
  • 2
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    Modelling of surface waves in poroelastic saturated materials by means of a two component continuum (2010)
    WIAS, Berlin
    Details
    Publication Date: 2021-03-29
    Description: These lecture notes are devoted to an overview of the modelling and the numerical analysis of surface waves in two-component saturated poroelastic media. This is an extension to the part of the lecture notes by K. Wilmanski (WIAS-Preprint No. 945) which is primarily concerned with the classical surface waves in single component media. We use the ''simple mixture model'' which is a simplification of the classical Biot's model for poroelastic media. Two interfaces are considered here: firstly the interface between a porous half space and a vacuum and secondly the interface between a porous halfspace and a fluid halfspace. For both problems we show how a solution can be constructed and a numerical solution of the dispersion relation can be found. We discuss the results for phase and group velocities and attenuations, and compare some of them to the high and low frequency approximations. For the interface porous medium/vacuum there exist in the whole range of frequencies two surface waves - a leaky Rayleigh wave and a true Stoneley wave. For the interface porous medium/fluid one more surface wave appears - a leaky Stoneley wave. For this boundary velocities and attenuations of the waves are shown in dependence on the surface permeability. The true Stoneley wave exists only in a limited range of this parameter ...
    Description: report
    Keywords: 550.28 ; 550 ; VAE 130 ; TOE 000 ; TM 300 ; ZfM : surface waves ; ZfM : porous media ; ZfM : geophysics ; ZfM : numerical analysis of dispersion relation ; Geomechanik ; Physikalisches Verhalten der Erde {Geophysik} ; Methodik. Arbeitsmittel. Abkürzungsverzeichnisse {Geophysik}
    Language: English
    Type: article , draft
    Format: application/pdf
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    CITATION GEO-LEO
  • 3
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    Stochastic Eulerian model for the flow simulation in porous media (2010)
    WIAS, Berlin
    Details
    Publication Date: 2021-03-29
    Description: This work deals with the stochastic flow simulation in statistically isotropic and anisotropic saturated porous media in 3D case. The hydraulic conductivity is assumed to be a random field with lognormal distribution. Under the assumption of smallness of fluctuations in the hydraulic conductivity we construct a stochastic Eulerian model for the incompressible flow as a divergenceless Gaussian random field with a spectral tensor of a special structure derived from Darcy's law. A randomized spectral representation is then used to simulate this random field. Numerical results are compared with the analytical results obtained by the small pertrubation expansion. A series of test calculations confirmed the high accuracy and computational efficiency of the method. Comparisons with asymptotically exact results show a good agreement.
    Description: report
    Keywords: 550.28 ; 550 ; TOW 000 ; ZfM : hydraulic conductivity ; ZfM : lognormal random field ; ZfM : small fluctuation ; ZfM : darcy law ; ZfM : randomized spectral representation ; Fluiddynamik {Geophysik}
    Language: English
    Type: article , draft
    Format: application/pdf
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    CITATION GEO-LEO
  • 4
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    A stochastic fractal model of the universe related to the fractional Laplacian (2010)
    WIAS, Berlin
    Details
    Publication Date: 2021-03-29
    Description: A new stochastic fractal model based on a fractional Laplace equation is developed. Exact representation for the spectral and correlation functions under random boundary excitation are obtained. Randomized spectral expansion is constructed for simulation of the solution of the fractional Laplace equation. We present calculations for 2D and 3D spaces for a series of fractional parameters showing a strong memory effect: the decay of correlations is several order of magnitudes less compared to the conventional Laplace equation model.
    Description: research
    Keywords: 520 ; 550 ; TCM 000 ; ZfM : stochastic fractals ; ZfM : fractal dimension of the universe ; ZfM : fractional Laplace equation ; ZfM : boundary excitations ; ZfM : spectral and correlation functions ; Mathematische und EDV-Verfahren {Astronomie}
    Language: English
    Type: article , draft
    Format: application/pdf
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  • 5
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    Unsteady thermal convection in the North-East German Basin (2010)
    WIAS, Berlin
    Details
    Publication Date: 2021-03-29
    Description: We describe a Voronoi box based finite volume method for the numerical simulation of thermal convection in sedimental basins. The method shows a temperature maximum principle and consistent velocity approximation. We present results of simulation runs in vertical slices of the North-East German basin. These indicate that the system is far from a stationary state, it shows quasi-periodic, and possibly chaotic behaviour. The chaos hypothesis is formulated based on the analysis of the Nusselt number time series obtaind from simulation runs.
    Description: report
    Keywords: 551.1 ; 550 ; ZfM : termal convection ; ZfM : finite volumes ; ZfM : nonlinear time series analysis
    Language: English
    Type: article , draft
    Format: application/pdf
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    CITATION GEO-LEO
  • 6
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    Stochastic Eulerian model for the flow simulation in porous media (2010)
    WIAS, Berlin
    Details
    Publication Date: 2021-03-29
    Description: report
    Keywords: 550.28 ; 550 ; TOW 000 ; ZfM : hydraulic conductivity ; ZfM : lognormal random field ; ZfM : small fluctuations ; ZfM : Darcy law ; ZfM : randomized spectral representation ; Fluiddynamik {Geophysik}
    Language: English
    Type: article , draft
    Format: application/pdf
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    CITATION GEO-LEO
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