Handling the water content discontinuity at the interface between layered soils within a numerical scheme

Abstract

In general, the water content (¸) form of Richards' Equation is not used when modelling water flow through layered soil since ¸ is discontinuous at soil layers. Within the literature, there have been examples of models developed for layered soils using the ¸-form of Richards' Equation. However, these models usually rely on an approximation of the discontinuity at the soil layer interface. For the first time, this paper will develop an iterative solution based on Newton's Method to explicitly solve for ¸ at the interface between two soils within a numerical scheme. The numerical scheme used within this paper is the Method of Lines, however, the principles of the iterative solution could be used in other numerical techniques. The paper will show that the iterative scheme is highly efficient converging mostly within 2 iterations. The iterative solution will be tested on two main test cases 1) fine over coarse soil, 2) a coarse over fine soil to ensure that the convergence behaviour holds. A test case from the literature is also considered to ensure the accuracy of the solution.