TY - JOUR
T1 - Finite analytic method
T2 - Analysis of one-dimensional vertical unsaturated flow in layered soils
AU - Zhang, Zaiyong
AU - Wang, Wenke
AU - Gong, Chengcheng
AU - Yeh, Tian chyi Jim
AU - Duan, Lei
AU - Wang, Zhoufeng
N1 - Funding Information:
This study was supported by the National Natural Science Foundation of China (No. 40472131, U1603243), the Key Research and Development Program of Shaanxi (Program No. 2020SF-405), the Fundamental Research Funds for the Central Universities CHD (300102290302) and the special fund for basic scientific research business of central public research institutes (No. Y519015). The first author is grateful to the Outstanding Chinese and Foreign Youth Exchange Program of China Association of Science and Technology. Gong Chengcheng is very grateful to the Chinese Scholarship Council (No. 201906560022) for providing an opportunity to be a visiting student at the University of the Neuchatel, Switzerland.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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.
KW - Analytical solution
KW - Finite analytic method
KW - Layered soils
KW - Modified Picard finite different method
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U2 - 10.1016/j.jhydrol.2020.125716
DO - 10.1016/j.jhydrol.2020.125716
M3 - Article
AN - SCOPUS:85097055309
SN - 0022-1694
VL - 597
JO - Journal of Hydrology
JF - Journal of Hydrology
M1 - 125716
ER -