Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition

Abstract

Research on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However, the computation process is often hampered by a high spatial resolution and long simulation period as well as the non-linearity of the equation. A new highly efficient and accurate method for solving the 2D Richards equation has been proposed in the paper. The developed algorithm is based on dimensional splitting, the result of which means that 1D equations can be solved more efficiently than as is the case with unsplit 2D algorithms. Moreover, such a splitting approach allows any algorithm to be used for space as well as time approximation, which in turn increases the accuracy of the numerical solution. The robustness and advantages of the proposed algorithms have been proven by two numerical tests representing typical engineering problems and performed for typical properties of soil.

A Hybrid Interpolating Meshless Method for 3D Advection–Diffusion Problems

“…Comparing results obtained by the above three methods, it is demonstrated that the HIM method significantly increases calculation efficiency and accuracy. Moreover, by solving a 3D Richards' equation [41,42], the effectiveness of the HIM method in the nonlinear problem is verified.…”

Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil: Numerical Simulations

“…Richards' equation consists of a governing equation that is used to describe the water flow in subsurface porous media such as soil in unsaturated conditions [1]. It is continuously subjected to numerical investigation [2][3][4][5][6][7][8][9][10][11]. The modeling of water distribution using the equation has essential applications in climate science, agriculture and also ecosystem management [12].…”

Richards’ Equation: Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil

“…Richards' equation consists of a governing equation that is used to describe water flow in subsurface porous media such as soil [1]. It is continuously subjected to numerical investigation [2][3][4][5][6][7][8][9].The modeling of water distribution using the equation has important application in climate science, agriculture and also ecosystem management [10]. Among many applications, Zeide [11] has reported the use of Richards' equation in the tree growth modeling prediction.…”