A 4-day summer school 'Upscaling techniques for mathematical models involving multiple scales' is organised at Hasselt University.
June 26-29, 2017
The course presents basic mathematical techniques for upscaling of models posed in complex domains, or involving highly oscillatory characteristics. Such problems appear as mathematical models for many real-world applications. Typical examples in this sense are the flow, diffusion, reaction and adsorption in porous media and are encountered e.g. in the sub-surface, chemical reactors, building materials, or biological tissues.
The series of lectures provide appropriate techniques for a rational derivation of macro-scale models (involving effective coefficients and equations) starting from the micro scale models (posed in complex media, or involving rapidly changing characteristics). A particular emphasis is on asymptotic and numerical homogenization. In the first instance, these techniques are applied to relevant mathematical models describing diffusion in layered and perforated media; diffusion, convection, reaction and adsorption in media with a complex microstructure; fluid flow through porous media (Darcy law). Next, more complex situations as encountered e.g. in enhanced oil recovery will be considered.
The lectures are given by Prof. Knut-Andreas Lie (SINTEF Oslo and Norwegian University of Science and Technology, Norway) and Prof. Sorin Pop (Computational Mathematics group, Hasselt University, Belgium).
The course is addressed to PhD students and postdoctoral researchers working on fluid-mechanics, chemical and mechanical engineering as well as geo-sciences, informatics or mathematics. It requires the standard mathematical background (calculus, differential equations, numerical methods) as taught at undergraduate/MSc level.