Almost all problems in science and engineering involve processes and mechanisms that act on multiple spatial and temporal scales. Physical and man-made systems can be described on many levels, from quantum mechanics and molecular dynamics, via the mesoscale or nano-level, to continuum and system-level descriptions. For a specific problem, it is common to refer to the particular scale one is interested in as the macroscale. Scales smaller than the macroscale are often referred to as microscale, and sometimes one also introduces intermediate scales that are referred to as mesoscales.
A multiscale problem can be defined as a problem where the macroscopic behaviour of a system is strongly affected by processes and properties from micro- and mesoscales. Solving the 'whole' problem at once is seldom possible as it would involve too many variables or too large scale differences to be computationally tractable, even on today's largest supercomputers. The traditional alternative has therefore been to compute effective parameters and usethese to communicate information between models on different scales. However, as the need for more accurate modelling increases, traditional homogenization and upscaling methods are becoming inadequate to answer advanced queries about multiscale problems. In some cases, effective properties may not be suffcient to properly describe complex interactions between macroscale and microscale processes; in other cases, one may not even know what are the correct properties to average.
In this winter school, we will focus on a few selected and challenging multiscale problem from material science and subsurface flow, and present mathematical and numerical methods suitable for these problems.
The participants are expected to stay at Dr. Holms Hotel, where we have reserved a limited number of rooms. Please register early. NB! The registration is binding after the deadline.
Published October 13, 2010