Finite Element Modeling of Field Problems

In this chapter a finite element formulation for modeling field problems is presented. General three-dimensional conditions are assumed, and the isoparametric interpolation of physical fields is used. The FE formulation relies on the Galerkin method used to transform the governing partial differential equations into the FE algebraic equations. This general method is first implemented to linear problems of heat conduction and diffusion and then to laminar incompressible viscous flow with and without heat and mass transfer. Next, the FE equations are derived in the case of fluid flow with large changes of the fluid domain; the arbitrary Lagrangian-Eulerian (ALE) formulation is used. Also, the FE modeling of the solid-fluid interaction is presented, according to a weak coupling approach. Finally, the FE balance equations are derived for fluid flow through porous deformable media.