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

Vitaly A. Zlotnik, Tiejun Wang, John L. Nieber, Jirka Šimunek

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1973-1980
Number of pages8
JournalAdvances in Water Resources
Issue number9
StatePublished - Sep 2007

Bibliographical note

Funding Information:
We thank G.I. Barenblatt (UC Berkeley) and T. Witelski (Duke University) for fruitful discussion. This study was partially supported by NSF’s Biocomplexity in the Environment Program BE03-22067 (V. Zlotnik); and the Terrestrial Sciences Program of the Army Research Office (J. Šimunek).

Copyright 2008 Elsevier B.V., All rights reserved.


  • Code verification
  • Numerical solution
  • Richards equation
  • Soil descriptors
  • Traveling wave


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