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Numerical Simulation of Transport in Porous Media: Some Problems from Micro to Macro Scale

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Advanced Computing

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 93))

Abstract

This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of tracers is strongly influenced by pore scale velocity structure and large scale inhomogeneities in the permeability field. The velocity structure on the pore scale is investigated by direct numerical simulations of the 3D velocity field in a random sphere pack. The velocity probability density functions are strongly skewed, including some negative velocities. The large probability for very small velocities might be the reason for non-Fickian dispersion in the initial phase of contaminant transport. We present a method to determine large scale distributions of the permeability field from point-wise velocity measurements. The adjoint-based optimisation algorithm delivers fully satisfying agreement between input and estimated permeability fields. Finally numerical methods for convection dominated tracer transports are investigated from a theoretical point of view. It is shown that high order Finite Element Methods can reduce or even eliminate non-physical oscillations in the solution without introducing additional numerical diffusivity.

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Authors and Affiliations

  1. Lehrstuhl für Computation in Engineering, Department of Civil Engineering and Surveying, Technische Universität München, Arcisstr, 21, 80333, München, Germany

    Quanji Cai, Ralf-Peter Mundani & Ernst Rank

  2. Fachgebiet Hydromechanik, Technische Universität München, 80333, München, Germany

    Sheema Kooshapur & Michael Manhart

  3. Lehrstuhl für Opimale Steuerung, Fakultät für Mathematik, Technische Universität München, 85748, Garching b. München, Germany

    Andreas Springer & Boris Vexler

Authors
  1. Quanji Cai
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  2. Sheema Kooshapur
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  3. Michael Manhart
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  4. Ralf-Peter Mundani
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  5. Ernst Rank
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  6. Andreas Springer
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  7. Boris Vexler
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Corresponding author

Correspondence to Quanji Cai .

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Editors and Affiliations

  1. Department of Informatics, Technische Universität München, Munich, Germany

    Michael Bader

  2. Department of Informatics, Technische Universität München, Munich, Germany

    Hans-Joachim Bungartz

  3. Department of Informatics, Technische Universität München, Munich, Germany

    Tobias Weinzierl

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Cai, Q. et al. (2013). Numerical Simulation of Transport in Porous Media: Some Problems from Micro to Macro Scale. In: Bader, M., Bungartz, HJ., Weinzierl, T. (eds) Advanced Computing. Lecture Notes in Computational Science and Engineering, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38762-3_3

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