Numerical Solution of the Continuity Equation for Soil Water Flow Using Precomputed Steady-State Fluxes

2011 ◽  
Vol 10 (2) ◽  
pp. 760-766 ◽  
Author(s):  
P.J. Ross
Keyword(s):  
Steady State ◽  
Numerical Solution ◽  
Soil Water ◽  
Water Flow ◽  
Continuity Equation ◽  
Soil Water Flow

scholarly journals Governing equations of transient soil water flow and soil water flux in multi – dimensional fractional anisotropic media and fractional time

2016 ◽  
Author(s):  
M. Levent Kavvas ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Fractional Derivative ◽  
Soil Water ◽  
Water Flow ◽  
Continuity Equation ◽  
Water Flux ◽  
Anisotropic Media ◽  
Governing Equations ◽  
Soil Matrix ◽  
Soil Water Flow ◽  
Soil Water Flux

Abstract. In this study dimensionally-consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical directions are considered to be different, resulting in multi-fractional multi-dimensional soil space within which the flow takes place. Toward the development of the fractional governing equations, first a dimensionally-consistent continuity equation for soil water flow in multi-dimensional fractional soil space and fractional time is developed. It is shown that the fractional soil water flow continuity equation approaches the conventional integer form of the continuity equation as the fractional derivative powers approach integer values. For the motion equation of soil water flow, or the equation of water flux within the soil matrix in multi-dimensional fractional soil space and fractional time, a dimensionally consistent equation is also developed. Again, it is shown that this fractional water flux equation approaches the conventional Darcy's equation as the fractional derivative powers approach integer values. From the combination of the fractional continuity and motion equations, the governing equation of transient soil water flow in multi-dimensional fractional soil space and fractional time is obtained. It is shown that this equation approaches the conventional Richards equation as the fractional derivative powers approach integer values. Then by the introduction of the Brooks-Corey constitutive relationships for soil water into the fractional transient soil water flow equation, an explicit form of the equation is obtained in multi-dimensional fractional soil space and fractional time. The governing fractional equation is then specialized to the case of only vertical soil water flow and of only horizontal soil water flow in fractional time-space. It is shown that the developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations concerning the diffusive behavior of soil water flow.

scholarly journals Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time

2017 ◽  
Vol 21 (3) ◽  
pp. 1547-1557 ◽  
Author(s):  
M. Levent Kavvas ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Fractional Derivative ◽  
Soil Water ◽  
Water Flow ◽  
Continuity Equation ◽  
Water Flux ◽  
Anisotropic Media ◽  
Governing Equations ◽  
Soil Matrix ◽  
Soil Water Flow ◽  
Soil Water Flux

Abstract. In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical directions are considered to be different, resulting in multi-fractional multi-dimensional soil space within which the flow takes place. Toward the development of the fractional governing equations, first a dimensionally consistent continuity equation for soil water flow in multi-dimensional fractional soil space and fractional time is developed. It is shown that the fractional soil water flow continuity equation approaches the conventional integer form of the continuity equation as the fractional derivative powers approach integer values. For the motion equation of soil water flow, or the equation of water flux within the soil matrix in multi-dimensional fractional soil space and fractional time, a dimensionally consistent equation is also developed. Again, it is shown that this fractional water flux equation approaches the conventional Darcy equation as the fractional derivative powers approach integer values. From the combination of the fractional continuity and motion equations, the governing equation of transient soil water flow in multi-dimensional fractional soil space and fractional time is obtained. It is shown that this equation approaches the conventional Richards equation as the fractional derivative powers approach integer values. Then by the introduction of the Brooks–Corey constitutive relationships for soil water into the fractional transient soil water flow equation, an explicit form of the equation is obtained in multi-dimensional fractional soil space and fractional time. The governing fractional equation is then specialized to the case of only vertical soil water flow and of only horizontal soil water flow in fractional time–space. It is shown that the developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations concerning the diffusive behavior of soil water flow.

scholarly journals Soil water flow due to surface topography in research drainage plots

age ◽  
2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Sally Logsdon ◽  
Cindy Cambardella
Keyword(s):  
Surface Topography ◽  
Soil Water ◽  
Water Flow ◽  
Soil Water Flow

Data Assimilation with Soil Water Content Sensors and Pedotransfer Functions in Soil Water Flow Modeling

2012 ◽  
Vol 76 (3) ◽  
pp. 829-844 ◽  
Author(s):  
Feng Pan ◽  
Yakov Pachepsky ◽  
Diederik Jacques ◽  
Andrey Guber ◽  
Robert L. Hill
Keyword(s):  
Data Assimilation ◽  
Water Content ◽  
Soil Water ◽  
Soil Water Content ◽  
Water Flow ◽  
Pedotransfer Functions ◽  
Flow Modeling ◽  
Soil Water Flow

SIMULATING SOIL WATER FLOW WITH ROOT-WATER-UPTAKE APPLYING AN INVERSE METHOD

Soil Science ◽  
2004 ◽  
Vol 169 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Qiang Zuo ◽  
Lei Meng ◽  
Renduo Zhang
Keyword(s):  
Soil Water ◽  
Water Flow ◽  
Water Uptake ◽  
Inverse Method ◽  
Root Water Uptake ◽  
Soil Water Flow

Unsaturated soil water flow

1983 ◽  
Vol 21 (3) ◽  
pp. 755 ◽  
Author(s):  
Roger E. Smith
Keyword(s):  
Soil Water ◽  
Water Flow ◽  
Unsaturated Soil ◽  
Soil Water Flow
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