VERIFICATION OF NUMERICAL SOLUTIONS OF THE RICHARDS EQUATION: TRAVELING WAVE SOLUTION

Various processes of soil moisture movement in the vadose zone are commonly investigated using the Richards equation. This equation involves two highly nonlinear functions of soil water content, namely soil water potential and the unsaturated hydraulic conductivity. Efforts to find the Richards equation solutions for verification of numerical techniques have generated a wealth of approximate and exact analytical approaches. The known exact solutions for realistic flow geometry are always limited to simplified or very narrow descriptions of hydraulic properties of the vadose zone, while the approximate solutions involve various simplifications that require additional verification. Therefore, an inter-comparison of various numerical approaches for realistic soil properties is commonly used as a substitute for verification of existing codes, while a more rigorous approach requires a benchmark test that would be valid for a broad variety of descriptors of soil hydraulic properties, and realistic initial and boundary conditions. For this purpose, we propose a "launch pad" technique, which is based on the traveling wave solution. This technique generates exact solutions for specific, but realistic initial and boundary conditions that describe vertical infiltration in semi-infinite domain. The technique is applicable to any descriptor of unsaturated hydraulic properties, and is illustrated through application to the soils with nonlinear properties described by Brooks-Corey and van Genuchten models. Examples of code verification using HYDRUS-1D, a popular numerical computer code for solving the Richards equation, indicate efficiency of a new approach.