Scaling analysis of Richards equation for horizontal infiltration and its approximate solution

2021 ◽  
Author(s):  
Ziqing Wang
Keyword(s):  
Approximate Solution ◽  
Richards Equation ◽  
Scaling Analysis ◽  
Horizontal Infiltration

scholarly journals Feasibility Investigation of Improving the Modified Green–Ampt Model for Treatment of Horizontal Infiltration in Soil

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 645 ◽  
Author(s):  
Ding-feng Cao ◽  
Bin Shi ◽  
Hong-hu Zhu ◽  
Hilary Inyang ◽  
Guang-qing Wei ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Linear Functions ◽  
Moisture Distribution ◽  
Water Infiltration ◽  
Richards Equation ◽  
Accurate Estimation ◽  
Wetting Front ◽  
Size Change ◽  
Moisture Profile ◽  
Horizontal Infiltration

Water infiltration in soil is a complex process that still requires appreciation of interactions among three phases (soil particles, water and air) to enable accurate estimation of water transport rates. To simulate this process, the Green–Ampt (GA) model and the Modified Green-Ampt (MGA) model introduced in the paper “A new method to estimate soil water infiltration based on a modified Green–Ampt model” have been widely used. The GA model is based on the hypothesis that the advance of the wetting front in soil under matric suction can be treated as a rectangular piston flow that is instantaneously transformed after passage of the infiltration front, and the MGA model does not contain the influence of pore size change. This cannot accurately reflect the soil moisture change process from unsaturation to saturation. Due to soil stratification and other inhomogeneity, predictions produced with these models often differ widely from observations. To quickly obtain the soil moisture distribution after passage of the wetting front for horizontal infiltration, an improved modified Green–Ampt (IMGA) model is presented, which estimates the soil moisture profile along a horizontal column in a piecewise manner with three functions. A logarithmic function is used to describe the gradual soil saturation process in the transmission zone, and two linear functions are used to represent the wetting zone. The algorithm of the IMGA model for estimating the water infiltration rate and cumulative infiltration is configured. To verify the effectiveness of IMGA model, a lab model test was performed, and a numerical model was built to solve the horizontal one-dimensional Richards equation using the finite–element method. The results show that the IMGA model is more accurate than the GA and MGA models. The horizontal soil moisture profiles obtained by the IMGA model are closer to the measured data than the numerical simulation results. The relative errors of the MGA and IMGA models decrease with an increase in infiltration time, whereas that of the GA model first decreases and then increases with infiltration time. The primary novelty of this study is nonlinear description of soil moisture content distribution, and derivation of unit transfer coefficient.

CRITICAL FIELD IN SPIN GLASSES : A SCALING ANALYSIS

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1071-C8-1072
Author(s):  
M. A. Continentino ◽  
E. Szkatulla ◽  
B. Elschner ◽  
H. Maletta
Keyword(s):  
Critical Field ◽  
Spin Glasses ◽  
Scaling Analysis

Approximate Solution of One Dynamic Problem of Geoinformatics

2010 ◽  
Vol 42 (5) ◽  
pp. 1-11 ◽  
Author(s):  
Vladimir M. Bulavatskiy ◽  
Vasiliy V. Skopetsky
Keyword(s):  
Approximate Solution ◽  
Dynamic Problem

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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