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Multiscale methods summer school


Multiscale methods summer school

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PROGRAM (JUNE 26-29, 2017)

The lectures are given by Profs. Knut-Andreas Lie (SINTEF Oslo and Norwegian University of Science and Technology, Norway) and Sorin Pop (Computational Mathematics group, Hasselt University, Belgium).

Below you can find the preliminary program.

Monday 9:00-9:30 Registration & Welcome
9:30-13:00 Introduction/Basic idea/Perforated media
13:00-14:00 Lunch
14:00-17:00 Introduction/Basic idea/Perforated media
17:00-18:00 Reception, poster session
Tuesday 9:15-13:00 Darcy law/Reactive flows in porous media
Two-phase flow in heterogeneous porous media
13:00-14:00 Lunch
14:00-17:00 Introduction to flow simulation as used in reservoir engineering
Wednesday 9:15-13:00 Introduction to the MATLAB Reservoir Simulation Toolbox (MRST)
13:00-14:00 Lunch
14:00-17:00 Flow-based upscaling of reservoir models
18:00 Dinner
Thursday 9:15-12:00 Multiscale methods for reservoir simulation
  12:00-13:00 Lunch

*We warmly welcome further suggestions. Possible topics include: reactive flows in porous media, combustion processes, two phase flow in heterogeneous porous media, mechanical problems, advanced discretization techniques, rigorous mathematical methods. Do you have some specific issues? Please let us know!

First part: basic upscaling techniques

In the first day the accent will be on basic ideas, in particular the method of asymptotic expansion and how this can be applied to problems with highly oscillatory characteristics. The aim is to develop effective (upscaled) equations in which the oscillations are averaged out, but which are still able to describe the averaged behaviour of the system.

The techniques are further employed for dealing with complex (perforated) domains, such as porous media. Specifically, these idea will be employed for the derivation of the Darcy law and for constructing upscaled models for diffusion, convection, reaction and adsorption in porous media.

Second part: numerical methods

The focus will be on numerical methods for the discretization of the (multiscale) mathematical models. This includes a general presentation of different numerical schemes, and of the (publicly available) software MRST that is being developed at SINTEF. Building on this, multi scale methods and numerical upscaling techniques are being presented.

Remarks:

Besides lectures, assignments/exercises sessions are being organised. Here we rely on your active participation. The participants are welcome to pose questions!

The first day ends with an ice-breaking reception and on the third day a "course dinner" will be offered to all participants.

Recommended reading:

  • Ulrich Hornung (Editor), Homogenization and porous media (Chapters 1 and 6). Interdisciplinary Applied Mathematics, 6. Springer-Verlag, New York, 1997.
  • Knut-Andreas Lie - An Introduction to Reservoir Simulation Using MATLAB, User Guide for the Matlab Reservoir Simulation Toolbox (MRST) SINTEF ICT, Departement of Applied Mathematics, Oslo, Norway
  • Iuliu Sorin Pop – Homogenization. An introduction based on reactive porous media flow models, Hasselt University, 2017