Numerical simulation of one-dimensional flows through porous media with shock waves

This work studies an unsaturated /ow of a Newtonian /uid through a rigid porous matrix, using a mixturethe ory approach in its modelling. Themixtureconsists of threeove rlapping continuous constituents: a solid (porous medium), a liquid (Newtonian /uid) and an inert gas (to account for the mixture compressibility). A set of two nonlinear partial di=erential equations describes the problem, which is approximated by means of a Glimm’s scheme, combined with an operator splitting technique