An Introduction to Computational Multiphysics: Motivations for Triple-M Modeling

Modern science is increasingly faced with problems of ever greater complexity, straddling across the traditional disciplinary boundaries between physics, chemistry, material science and biology. Computational science is responding to this challenge with a steadfast development of innovative modeling techniques, designed in such a way as to offer an optimal handling of the information transfer procedures connecting the different scales/levels involved in the quantitative description of the aforementioned complex phenomena. This entails the seamless coupling between different mathematical representations of various physical phenomena at widely disparate scales, from continuum fields to probability distribution functions and atomistic trajectories, all the way down to many-body quantum wave functions. In this series of lectures, we shall provide an introduction to the basic ideas behind these triple-M (multiscale/multiphysics/multilevel) techniques, together with the illustration of a few practical examples, drawn from concrete applications in leading areas of multiphysics research, such as micro/nanofluidics, turbulence and material science.