A lattice gas automaton simulation of the nonlinear diffusion equation: A model for moisture flow in unsaturated porous media

We investigate a two-dimensional lattice gas automaton (LGA) for simulating the nonlinear diffusion equation in a random heterogeneous structure. The utilility of the LGA for computation of nonlinear diffusion arises from the fact that, the diffusion coefficient in the LGA depends on the local densi ty rho of 'fluid' particles which statistically determines the collision ra te and thus, the mean free path lambda of the particles at the microscopic scale. The LGA may therefore be used as a physical analogue to simulate moi sture flow in unsaturated porous media. The capability of the LGA to accoun t for unsaturated flow is tested through a set of numerical experiments sim ulating one-dimensional infiltration in a simplified semi-infinite homogeno us isotropic porous material. Different mechanisms of interactions are used between the fluid and the solid phase to simulate various fluid-solid inte rfaces. The heterogeneous medium, initially at low density is submitted to a steep density gradient by continuously injecting fluid particles at high concentration and zero velocity along one face of the model. The propagatio n of the infiltration front is visualized at different time steps through c oncentration profiles parallel to the applied concentration gradient and th e infiltration rate is measured continuously until steady-state flow is rea ched. The numerical results show close agreement with the classical theory of flow in unsaturated porous media. The cumulative absorption exhibits the expected t(1/2) dependence. The evolution of the effective diffusion coeff icient with the particle concentration is estimated from the measured densi ty profiles for the various porous materials. Depending on the applied flui d-solid interactions, the macroscopic effective diffusivity may vary by mor e than two orders of magnitude with density.