Numerical modelling of coupled transient phenomena

The basic phenomena involved in thermo-hydro-mechanical processes in geomaterials have been described in the 1st chapter. The equations describing these phenomena are non-linear differential equations. Their solution can generally only be approximated thanks to numerical methods. This is the main subject of the present chapter. First the type of problems and the set of equations to be solved will be shortly recalled. Emphasis will be given on the non-linear contributions. In a second section, the mostly developed numerical method, i.e. the finite difference and the finite element methods will be discussed under the light of the problems to be treated. The iterative techniques allowing the solution of non linear equations will be described. A third section will be dedicated to the coupling terms and to their modelling. The question that rises then is How to model efficiently problems, which may differ highly from, the point of view of the time and length scales?