403 Multiphysics Modeling: Integration of Different Physical Levels

Ismael Herrera-Revilla, National Autonomous University of Mexico (UNAM)
Miguel-Ángel Moreles-Vázquez, Centro de Investigación en Matemáticas (CIMAT)
Octavio Manero-Brito, UNAM
Andrés Fraguela Collar, Benemérita Universidad Autonoma de Puebla (BUAP)
Scientific behavior-prediction of nature and other systems of human interest is carried out by means of physicomathematical and computational models. In the case of macroscopical physical systems of engineering and science, up to now, such models have been based on continuum mechanics, which adopts a macroscopical point of view to treat physical systems. However, as Paul Dirac recognized when quantum mechanics was born, the Schroedinger equation is the ultimate basis of scientific prediction of nature-behavior and, therefore, continuum mechanics is only an approximation in which the quantic response of the ultra-microscopic constituents of matter is incorporated in the models by means of empirical constitutive equations. Although thus far this approach has been very successful, unsurmountable barriers have been found for extending it to many other, more complex systems and at present intensive international scientific research is being carried out on multiscale-modeling. Given a physical system, we can model it at many different levels of detail. This results in a hierarchy of models, each of which is a refinement of the models at the higher levels of the hierarchy. According to Fish (2013), there are two categories of multiscale approaches: information-passing (or hierarchical), and concurrent. In Fish’s terms: In the information-passing multiscale approach, the fine-scale response is idealized (approximated or unresolved) and its overall (average) response is infused into the coarse scale. In the concurrent approaches, fine and coarse-scale resolutions are simultaneously employed in different portions of the problem domain, and the exchange of information occurs through the interface. The subdomains where different scale resolutions are employed can be either disjoint or overlapping. In this mini symposium we invite participants to present their contributions in different aspects of these problems.
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Fish, J., Practical Multiscaling, John Wiley and Sons, Hoboken, NJ, 2013.
Weinan, E., Principles of Multiscale Modeling, Cambridge University Press, Cambridge, 2011