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Short Course "Homogenization for Porous Media"

The short course takes place from 27 November to 11 December 2020 in the framework of the "Short Course Series: Mathematics of Porous Media" and is given by Sorin Pop (Hasselt University). The short cours series is organized by the Porous Media Group of the University of Bergen (Norway).

General Information

The short course will take place on each Friday from 27 November to 11 December 2020, 2-4 pm (CET).

Online short course

This short course series is presented by the Porous Media Group at the University of Bergen, in collaboration with the University of Oslo, Norwegian University of Science and Technology and Simula. The series is supported by RCN project 250223, Wintershall Dea, and Equinor via the Akademia agreement and the VISTA Center for Modeling of Coupled Subsurface Dynamics. 

The course is free of charge. 

Send an email to Eirik.Keilegavlen@uib.no, with name, institution and email address. The email should be linked to the Zoom account you will use to access the meeting. Login information for the individual lectures will be sent out no later than lunchtime at the Friday of the lecture.

In a porous medium, one has to deal with processes encountered at different, well-separated scales, involving complex media with hierarchically-organized structures and highly oscillatory characteristics. This imposes severe limitations on simulations that are necessary to quantify the model behaviour at a larger, laboratory, or even field scale, at least when starting from the scale of the pore. A natural way to deal with this issue is to derive effective models describing the averaged behaviour of the system at the scale of interest, but incorporating the micro-scale processes. Given by Professor Sorin Pop (Hasselt University/University of Bergen), these lectures are introducing the homogenization methods, based on standard models for flow and reactive transport in porous media.

Lecture I: Introduction to homogenization

• Asymptotic expansions and the underlying idea of homogenization
• The diffusion problem: highly oscillatory coefficients, perforated media

Lecture II: Flow and reactive transport in a porous medium (from the pore scale to the Darcy scale)

• The derivation of the Darcy law
• Homogenization for reactive flow in porous media

Lecture III: Situations of practical interest

• Scaling in reactive porous media flow models
• Applications

Prof. Sorin Iuliu Pop, Hasselt University


Sorin Pop studied informatics at the Faculty of Mathematics and Computer Science of the Babes-Bolyai University in Cluj-Napoca (Romania) and went to the University of Heidelberg (Germany), where he worked as a doctoral researcher together with Prof. Willi Jäger. In 1998 he finished his Ph'D degree in Mathematics at the Babes-Bolyai University with his thesis "Regularization Methods in the Numerical Analysis of Some Degenerate Parabolic Equations". From 2000 to 2015 he worked in the Department of Mathematics and Computer Science at the Eindhoven University of Technology (Netherlands), before he moved to the University of Hasselt (Belgium), where he is a professor in the Discipline group Mathematics and statistics. In between, he got a part-time appointment at the University of Bergen (Norway), at the Department of Mathematics – a so-called Professor II appointment –, which still goes on.

Research interest

1) Partial differential equations:

  • Analysis: existence, uniqueness of weak solutions, qualitative properties, travelling waves
  • Upscaling: homogenization, multiple scales, asymptotic expansions, heterogeneous media, perforated media, rough boundaries
  • Numerical methods: convergence, error estimates, discretization (FEM/MFEM/DG, finite volumes), linearization schemes, domain decomposition

2) Applications:

  • Flow in porous media: unsaturated, two-phase, non-standard models, dynamic capillarity
  • Reactive transport: adsorption, desorption, reactions, precipitation, dissolution
  • Media with variable porosity
  • Biofilm growth
  • Geothermal energy
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