This study deals with unsaturated, unsteady water movement through hetergeneous porous media. The specific problem investigated is the transient three-dimensional sxisymmetric flow resulting from water being applied on a horizontal circular area. The heterogeneity of the soil is described by allowing any or all of the five parameters in the Brooks-Corey equations to be any continuous function of depth. Methodologies for obtaining numerical solutions to the resulting nonlinear partial differential equation and its associated initial-boundary value problem have been developed an dimplemented in a computer program. The numerical solution is based on the Crank-Nicolson method of finite differencing and the solution to the resulting system of non-linear algebraic equations for each time step is by the Newton method combined with the line successive over-relaxation (LSOR) method. The numerical solutions provide the follwoing at each time step used: (1) the distribution of soil water saturation throughout the region, (2) the distribution of capillary pressure throuout the region, (3) the distribution of hydraulic head throughout the region, (4) the rate of infiltration if the area of application is specified at a given moisture level, (5) the extent and amount of lateral and vertical water movement, and (6) the rate of advance position of the wetting front. The solutions resulting from various variations of linearly specified heterogeneities have been studied and their influence of such quantitites are infiltration rate or intake capacities and wetting front movement, have been analyzed. To determine the effects of lateral water movement, solution results from the axisymmetric solutions have been compared with solutions from a one-dimensional vertical flow model that permitted the same specification of heterogeneity. A number of graphs are presented that illustrate influences of different soil hetergeneities. Coaxial graphs were developed to summarize the results of a number of solutions that relate the different in infiltration in hetergeneous and homogeneous soils to the variations of the five parameters in the Brooks-Corey equations. The numerical solutiosn are verified with reasonable agreement with field data at the Reynolds Creek experimental watershed obtained from experiments which duplicate the geometry of the mathematical model clostely, if not the heterogeneity, also.
Nassehzadeh-Tabrizi, Abdolhossien; Jeppson, Roland W.; and Willardson, Lyman S., "Unsaturated Transient Flow Through Heterogeneous Soils: Numerical Solutions and Analyses of Three-dimensional Axisymmetric Flows" (1978). Reports. Paper 176.