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

  • Quanji Cai
  • Sheema Kooshapur
  • Michael Manhart
  • Ralf-Peter Mundani
  • Ernst Rank
  • Andreas Springer
  • Boris Vexler
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 93)


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.


Porous media Pore scale High order FEM Parameter identification 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Quanji Cai
    • 1
  • Sheema Kooshapur
    • 2
  • Michael Manhart
    • 2
  • Ralf-Peter Mundani
    • 1
  • Ernst Rank
    • 1
  • Andreas Springer
    • 3
  • Boris Vexler
    • 3
  1. 1.Lehrstuhl für Computation in Engineering, Department of Civil Engineering and SurveyingTechnische Universität MünchenMünchenGermany
  2. 2.Fachgebiet HydromechanikTechnische Universität MünchenMünchenGermany
  3. 3.Lehrstuhl für Opimale Steuerung, Fakultät für MathematikTechnische Universität MünchenGarching b. MünchenGermany

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