Robert Charlier[25], Lyesse Laloui, Mihael Brencic, SigurSur Erlingsson, Klas Hansson and Pierre Hornych
Abstract Different physical problems have been analysed in the preceding chapters: they relate to water transfer, to heat transfer, to pollutant transfer and to mechanical equilibrium. All these problems are governed by differential equations and boundary conditions but analytical solutions are, in general, unobtainable because of the complex interaction of the various aspects which are always present in real-world situations. In such circumstances, numerical modelling can give a valuable alternative methodology for solving such highly coupled problems. The first part of this chapter is dedicated to a brief statement of the finite element method for highly coupled phenomena. In the second part, a number of numerical simulations are summarised as an illustration of what could be done with modern tools. The chapter shows that it is possible to achieve realistic results although, at present, some simplification is often required to do so.
Keywords Finite element method ■ multi-physics coupling ■ partial differential equation ■ examples of applications
