Simulation of momentum and energy transfer in a porous medium nonsaturated by an incompressible fluid

This work studies the transport phenomena in a nonsaturated flow of a newtonian fluid through a rigid porous matrix. A mixture theory approach is used in the modelling of the fluid flow and the heat transfer problem. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas, assumed with zero mass density and thermal conductivity. A set of four nonlinear partial differential equations describes the problem which is approximated by means of a Glimm's scheme, combined with an operator splitting technique, for the hyperbolic equations and a finite-difference scheme for the elliptic ones.