A framework for multi-scale modelling

We review a methodology to design, implement and execute multi-scale and multi-science numerical simulations. We identify important ingredients of multi-scale modelling and give a precise definition of them. Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels. With concepts such as the scale separation map, the generic submodel execution loop (SEL) and the coupling templates, one can define a multi-scale modelling language which is a bridge between the application design and the computer implementation. Our approach has been successfully applied to an increasing number of applications from different fields of science and technology.