Finite analytic method for modeling variably saturated flows

Zaiyong Zhang; Wenke Wang; Chengcheng Gong; Tian-Chyi Jim Yeh; Zhoufeng Wang; Yu-Li Wang; Li Chen

doi:10.1016/j.scitotenv.2017.10.112

Finite analytic method for modeling variably saturated flows

Sci Total Environ. 2018 Apr 15:621:1151-1162. doi: 10.1016/j.scitotenv.2017.10.112. Epub 2017 Nov 13.

Authors

Zaiyong Zhang¹, Wenke Wang², Chengcheng Gong³, Tian-Chyi Jim Yeh⁴, Zhoufeng Wang³, Yu-Li Wang⁴, Li Chen³

Affiliations

¹ Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region, Chang'an University, Ministry of Education, PR China; School of Environmental Science and Engineering, Chang'an University, PR China; Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721, USA.
² Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region, Chang'an University, Ministry of Education, PR China; School of Environmental Science and Engineering, Chang'an University, PR China. Electronic address: wenkew@chd.edu.cn.
³ Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region, Chang'an University, Ministry of Education, PR China; School of Environmental Science and Engineering, Chang'an University, PR China.
⁴ Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721, USA.

PMID: 29146077
DOI: 10.1016/j.scitotenv.2017.10.112

Abstract

This paper develops a finite analytic method (FAM) for solving the two-dimensional Richards' equation. The FAM incorporates the analytic solution in local elements to formulate the algebraic representation of the partial differential equation of unsaturated flow so as to effectively control both numerical oscillation and dispersion. The FAM model is then verified using four examples, in which the numerical solutions are compared with analytical solutions, solutions from VSAFT2, and observational data from a field experiment. These numerical experiments show that the method is not only accurate but also efficient, when compared with other numerical methods.

Keywords: Finite analytic method; Kirchhoff transformation; Richards' equation; Variably saturated flow.