Numerical solution of the Kirchhoff-transformed Richards equation for simulating variably saturated flow in heterogeneous layered porous media

Abstract

A new numerical method was developed to accurately and efficiently compute a solution of the nonlinear Richards equation with a layered soil. In the proposed method, the Kirchhoff integral transformation was applied. However, in the Kirchhoff integral transformation approach, the transformed Kirchhoff head has dyadic characteristics at the material interface between different soil types. To avoid the dyadic characteristics at the material interface, a truncated Taylor series expansion was applied to the Kirchhoff head at the material interface and so the Kirchhoff head was replaced with a single pressure head value at the material interface. Accordingly, through the Taylor series expansion, a set of algebraic equations in the one-dimensional control volume finite difference discretized system formed a tridiagonal matrix system. Through a series of numerical experiments, the new method was compared to other numerical methods to determine its superiority. The results clearly demonstrated that the approach was not only more computationally efficient, but also more accurate and robust than other numerical methods. Computational performance was greatly enhanced with the proposed method, and which could be used to simulate complicated heterogeneous flow at a large-scale watershed or regional scale.