Finite analytic method: Analysis of one-dimensional vertical unsaturated flow in layered soils

Zaiyong Zhang, Wenke Wang, Chengcheng Gong, Tian chyi Jim Yeh, Lei Duan, Zhoufeng Wang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


A new finite analytic method (FAM) was proposed to obtain a stable and accurate solution of highly nonlinear Richards’ equation (RE) for simulating flow through heterogeneous soils. While the exponent hydraulic conductivity function (Gardner model) was used to linearize RE, the variable has dyadic characteristics at the interface node between two different soil materials. To overcome the dyadic characteristics at the interface node, we derived a formula of FAM based on the conversations of mass and energy at the interface node. This new formula does not require additional iteration steps. Besides, the proposed method is easy for coding and takes advantage of the strengths in mixed-form RE. Through three numerical experiments, FAM was compared to analytical solutions and modified Picard finite different method (MPFD) to evaluate its accuracy and efficiency. Our results indicated that the proposed method could obtain highly accurate and stable numerical solutions and reduce the mass balance errors significantly. Also, FAM is less sensitive to the grid size compared to MPFD.

Original languageEnglish (US)
Article number125716
JournalJournal of Hydrology
StatePublished - Jun 2021


  • Analytical solution
  • Finite analytic method
  • Layered soils
  • Modified Picard finite different method

ASJC Scopus subject areas

  • Water Science and Technology


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