An Exact Solution to the Linearized Richards Equation for Layered Media With Flexible Initial Condition

Zhang Long Chen, Yiyi Huang, Hongwei Fang, Tian Chyi Jim Yeh, Yuanyuan Zha

Research output: Contribution to journalArticlepeer-review


Srivastava and Yeh (1991, derived an exact solution to the linearized Richards equation (LRE) for two-layer medium infiltration using the Laplace transform (LT) method with a particular initial condition assumed, making the most pioneering contribution to the derivation of exact solutions to the layered-medium LRE (i.e., ES-LMLREs). However, the LT method is unsuitable for deriving an ES-LMLRE that considers either an arbitrary initial condition or an arbitrary number of layers, or both, preventing further progress in developing ES-LMLREs. Adopting a new solution strategy, namely a conjunctive use of the variable separation method and the transfer matrix method, we develop a novel exact layered-medium-LRE infiltration solution, overcoming the above difficulties. First, the proposed solution is successfully validated against the Srivastava-Yeh solution. As a feature-demonstration example, a layered-medium water absorption process is simulated, and our solution well captures how the heterogeneity of hydraulic parameters affects the dynamics of this process. Moreover, the proposed solution is a valuable benchmark for related numerical models.

Original languageEnglish (US)
Article numbere2023WR035383
JournalWater Resources Research
Issue number9
StatePublished - Sep 2023


  • exact solution
  • layered media
  • Richards equation
  • unsaturated flow

ASJC Scopus subject areas

  • Water Science and Technology


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