BOUNDARY INTEGRAL SOLUTIONS TO THE UNSATURATED MOISTURE FLOW EQUATION

The boundary integral equation method is formulated for problems conce rning unsaturated moisture flow in porous media. The boundary integral formulation presented here is derived using the time-dependent fundam ental solution of the governing partial differential equation. Two bou ndary integral approaches are presented. The first approach solves the unsaturated moisture flow problem by directly applying the time-depen dent Green's function. The second method is based on the expansion of moisture content into a perturbation series. The governing equation is decomposed into a moisture flow equation without a known gravity term on the right-hand side. The perturbation equations are then solved in succession by evaluating the gravity term of the unsaturated leachate flow equation from the preceding solution level. The two boundary int egral approaches, the direct Green's function and the perturbation Gre en's function, are closely related because the same time-dependent fun damental solution is used to formulate the boundary integral expressio ns. The direct Green's function formulation solves the boundary integr al expression in one step. However, the perturbation Green's function approach requires solution of the integral expression for homogeneous boundary conditions. The solutions obtained by both methods are compar ed with the exact solution. A close agreement of the internal fluxes b etween boundary integral methods and the exact solution, for an unsatu rated portion of a landfill, shows the stability of the boundary integ ral methods to compute accurate recharge from the unsaturated zone to the saturated leachate mound.