WRRCTMR No.84 The Cell-Analytical-Numerical Technique for Solving Unsaturated-Flow and Solute-Transport Problems

Abstract

The cell analytical-numerical (CAN) method was developed and applied for the solution of one dimensional water flow and solute transport problems in the unsaturated zone. The flow equation is characterized by a nonlinear governing equation. The CAN method is similar to other numerical techniques in that it divides the domain into a number of computational elements, each homogeneous in nature. It differs, however, by implementing a local analytical solution within the element. The soil moisture flux (for the flow equation) or solute mass flux (for the transport equation) is applied at the interface between two adjacent elements to define an algebraic relationship between the values of pressure head or concentration, respectively, at three neighboring points. Assembling these three-point equations provides a tridiagonal system of equations that can be solved by the Thomas algorithm. The system describing the flow problem is nonlinear in nature, and is solved iteratively within an implicit linearization scheme. For water flow, the method is applied to a number of soil types and the results are compared to Philip's semi-analytical solution and a numerical solution that is based on the finite-element technique. The results indicate the method's high accuracy over a wide range of soil types. However, an upstream weighting approach is needed for coarser soils, a process that may lead to relatively large mass-balance errors. The high accuracy of the solute transport solutions is demonstrated through comparison against available analytical solutions.