Verification of numerical solutions of the Richards equation using a traveling wave solution

Efforts to find solutions that can be used for verification of numerical techniques for solving the Richards equation have generated a wealth of approximate and exact analytical solutions. Coefficients of this equation involve two highly non-linear functions related to the soil water potential, the unsaturated hydraulic conductivity, and the soil water content. The known exact solutions for realistic flow geometries are commonly limited to simplified descriptions of unsaturated hydraulic properties, while the approximate solutions involve various simplifications that require additional verification. We present a technique, referred to as the “launch pad” technique, which is based on the traveling wave solution to generate an exact solution of the boundary value problem for the Richards equation. The technique that is applicable to any descriptor of unsaturated hydraulic properties is illustrated on an application involving the infiltration of water into soils with properties described by Brooks–Corey and van Genuchten models. Examples of verification are presented for HYDRUS-1D, a popular numerical computer code for solving the Richards equation.