High-order averaging method of hydraulic conductivity for accurate soil moisture modeling

- We propose a new averaging method of hydraulic conductivity for accurate simulation of Richards equation.
- Performance of the proposed method is evaluated using various one- and two-dimensional cases.
- The advantage of the proposed method is high accuracy with coarse and nonorthogonal grids.

SummaryRichards' equation (RE) is the most common mathematical expression for soil water movement in a porous medium. Despite advancements in numerical schemes and high-performance computing, the requirements of iterative computations and fine grids hinder further extension of the RE to multi-dimensional and large-scale applications. Averaging methods of hydraulic conductivity have been known to be one of the significant factors affecting the accuracy of numerical solutions of the RE, especially when coarse grids are used. In this study, we developed a high-order averaging method of hydraulic conductivity for accurate numerical modeling of the RE, which has a straightforward formula regardless of the soil conditions and produces high simulation accuracy when used on coarse grids. The developed method is based on the high-order upwind scheme, which is widely used for hyperbolic partial differential equations within a finite volume framework in order to prevent numerical oscillations near a discontinuity while preserving high-order accuracy. Numerical simulations of several one- and two-dimensional cases performed in the study indicate that the proposed method outperforms existing simple averaging methods and is also superior, or at least equivalent, to complex averaging methods over a wide range of soil textures, especially on coarse grids. In addition, the proposed method is straightforwardly extended to nonorthogonal grids by being combined with the coordinate transformation method and the extension is verified through multi-dimensional test cases as well as tests on a heterogeneous soil domain.