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A Transformed Pressure Head‐Based Approach to Solve Richards' Equation for Variably Saturated Soils
Author(s) -
Pan Lehua,
Wierenga Peter J.
Publication year - 1995
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/94wr03291
Subject(s) - richards equation , mathematics , transformation (genetics) , nonlinear system , soil water , pressure head , boundary (topology) , boundary value problem , algorithm , geotechnical engineering , mathematical analysis , soil science , thermodynamics , geology , chemistry , biochemistry , physics , quantum mechanics , gene
This paper presents a new approach to solve Richards' equation. It introduces a nonlinear transformed pressure, P t , as the dependent variable with the modified Picard method. The new approach was compared to, and contrasted with, two efficient existing methods: the ϕ‐based transformation method (Kirkland et al., 1992), and the h ‐based modified Picard method (Celia et al., 1990). A total of 12 different one‐dimensional cases were considered (saturated, unsaturated, layered and uniform soil profiles, with pressure and flux type boundary conditions). The results show that the new method offers excellent CPU efficiency and, unlike the h ‐based method, is numerically robust for all cases of variably saturated, heterogeneous media, and first or second type boundary conditions. The method does not require difficult numerical coding, and its CPU efficiency is not affected by complicated heterogeneous and hysteretic media. The P t transformation is easy to incorporate into existing h ‐based codes.