583 Lattice Boltzmann approach to Richards' equation Irina Ginzburg ~, Jean-Philippe Carlier ~, and Cyril Kao ~ ~Cemagref, DEAN, Groupement Antony, Parc de Tourvoie, BP 44, 92163 Antony Cedex, France A Lattice Boltzmann model with two relaxation times for the 2D/3D advection and anisotropic diffusion equation (AADE) is introduced. The method is applied to Richards' equation for variably saturated flow in isotropic homogeneous media by extending reten- tion curves into the saturated zone in a linear manner. The Darcy velocity is computed locally from the population solution. The method possesses intrinsic mass conservation, it is explicit and especially suitable for parallel computations. Designed for regular grids, the LB approach meets the boundary conditions accurately with an unified "multi-reflexion" technique, introduced to fit pressure head and/or specified flux conditions on static and seepage boundaries. The physical space can assume an uniform rectangular discretization grid which is transformed into the cubic computational grid after proper rescaling [9] of the AADE. The diffusion term is considered in two forms: the conventional one and the transformed one. The integral transformation may avoid problems encountered with the unbounded diffusion coefficients at the residual and saturated limits. An analytical expression for the transformed diffusion function is obtained for the original and modified VGM retention curves [14]. Analytical instationary solutions for constant flux infiltration with non-linear models [2,15] are revised. An exact unstationary solution [1] valid for unsaturated, sat- urated or variably saturated flow is constructed using the BCM hydraulic conductivity function [3,11], moisture tension being fixed at the surface. Stationary infiltration profiles are generated for the BCM and the VGM conductivity functions. The LB method is validated against these and other reference solutions. 1. LATTICE BOLTZMANN APPROACH 1.1. Two-relaxation-time model for AADE We consider DdQq lattice Boltzmann models [12,5] with rest populations, defined by b~ moving velocities Cq on a cubic lattice in D dimensions, Q - b~ + 1. In what follows, vectors in the D-dimensional (physical) space carry "arrows", e.g. Cq - {Cq~, c~ - 1,... ,D}, q - 0,... ,b,~. Vectors in population space are '%old", e.g. C~ - {Cq~, q - 0,..., b~}, c~ - 1,..., D. Greek indices stand for the spatial coordinates x, y, and so on; repeated Greek indices correspond to implicit summations. We introduce a two- relaxation-time model with source term Q~(~, t) which updates the population solution