Finite analytic method based on mixed-form Richards' equation for simulating water flow in vadose zone

Zaiyong Zhang, Wenke Wang, Tian chyi Jim Yeh, Li Chen, Zhoufeng Wang, Lei Duan, Kedong An, Chengcheng Gong

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


In this paper, we develop a finite analytic method (FAMM), which combines flexibility of numerical methods and advantages of analytical solutions, to solve the mixed-form Richards' equation. This new approach minimizes mass balance errors and truncation errors associated with most numerical approaches. We use numerical experiments to demonstrate that FAMM can obtain more accurate numerical solutions and control the global mass balance better than modified Picard finite difference method (MPFD) as compared with analytical solutions. In addition, FAMM is superior to the finite analytic method based on head-based Richards' equation (FAMH). Besides, FAMM solutions are compared to analytical solutions for wetting and drying processes in Brindabella Silty Clay Loam and Yolo Light Clay soils. Finally, we demonstrate that FAMM yields comparable results with those from MPFD and Hydrus-1D for simulating infiltration into other different soils under wet and dry conditions. These numerical experiments further confirm the fact that as long as a hydraulic constitutive model captures general behaviors of other models, it can be used to yield flow fields comparable to those based on other models.

Original languageEnglish (US)
Pages (from-to)146-156
Number of pages11
JournalJournal of Hydrology
StatePublished - Jun 1 2016


  • Analytical solution
  • Finite analytic method
  • Mass conservative property
  • Mixed-form Richards' equation

ASJC Scopus subject areas

  • Water Science and Technology


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