翻訳と辞書 Words near each other ・ Finite state transducer ・ Finite strain theory ・ Finite strip method ・ Finite subdivision rule ・ Finite thickness ・ Finite topological space ・ Finite topology ・ Finite type invariant ・ Finite verb ・ Finite Volume Community Ocean Model ・ Finite volume method ・ Finite volume method for one-dimensional steady state diffusion ・ Finite volume method for three-dimensional diffusion problem ・ Finite volume method for two dimensional diffusion problem ・ Finite volume method for unsteady flow ・ Finite water-content vadose zone flow method ・ Finite wing ・ Finite-difference frequency-domain method ・ Finite-difference time-domain method ・ Finite-dimensional distribution ・ Finite-dimensional von Neumann algebra ・ Finite-rank operator ・ Finite-state machine ・ Finitely generated ・ Finitely generated abelian group ・ Finitely generated algebra ・ Finitely generated group ・ Finitely generated module ・ Finitely generated object ・ Finitely presented Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Finite water-content vadose zone flow method ： ウィキペディア英語版 Finite water-content vadose zone flow method The finite water-content vadose zone flux method〔Talbot, C.A., and F. L. Ogden (2008), A method for computing infiltration and redistribution in a discretized moisture content domain, ''Water Resour. Res.'', 44(8), doi: 10.1029/2008WR006815.〕〔Ogden, F. L., W. Lai, R. C. Steinke, J. Zhu, C. A. Talbot, and J. L. Wilson (2015), A new general 1-D vadose zone solution method, ''Water Resour.Res.'', 51, doi:10.1002/2015WR017126.〕 represents a one-dimensional alternative to the numerical solution of Richards' equation 〔Richards, L. A. (1931), Capillary conduction of liquids through porous mediums, ''J. Appl. Phys.'', 1(5), 318–333.〕 for simulating the movement of water in unsaturated soils. The finite water-content method is an ordinary differential equation alternative to the Richards partial differential equation. The Richards equation is difficult to approximate in general because it does not have a closed-form analytical solution. The finite water-content method, is perhaps the first generic replacement for the numerical solution of the Richards' equation. The finite water-content solution has several advantages over the Richards equation solution. First, as an ordinary differential equation it is explicit, guaranteed to converge 〔Yu, H., C. C. Douglas, and F. L. Ogden, (2012), A new application of dynamic data driven system in the Talbot–Ogden model for groundwater infiltration, ''Procedia Computer Science'', 9, 1073–1080.〕 and computationally inexpensive to solve. Second, using a finite volume solution methodology it is guaranteed to conserve mass. The finite water content method readily simulates sharp wetting fronts, something that the Richards solution struggles with.〔Tocci, M. D., C. T. Kelley, and C. T. Miller (1997), Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines, ''Adv. Wat. Resour''., 20(1), 1–14.〕 The main limiting assumption required to use the finite water-content method is that the soil be homogeneous in layers. The finite water-content vadose zone flux method is derived from the same starting point as the derivation of Richards' equation. However, the derivation employs a hodograph transformation〔Philip, J. R. 1957. The theory of infiltration: 1. The infiltration equation and its solution, ''Soil Sci'', 83(5), 345–357.〕 to produce an advection solution that does not include soil water diffusivity, wherein $z$ becomes the dependent variable and $\backslash theta$ becomes an independent variable:〔 :$\backslash left(\backslash frac\backslash right)\_\backslash theta\; =\; \backslash frac$ \left(1- \left (\frac\right) \right )\ where: :$K$ is the unsaturated hydraulic conductivity (T−1 ), :$\backslash psi$ is the capillary pressure head () (negative for unsaturated soil), :$z$ is the vertical coordinate () (positive downward), :$\backslash theta$ is the water content, (−) and :$t$ is time (). This equation was converted into a set of three ordinary differential equations (ODEs) 〔 using the Method of Lines〔http://www.scholarpedia.org/article/Method_of_lines〕 to convert the partial derivatives on the right-hand side of the equation into appropriate finite difference forms. These three ODEs represent the dynamics of infiltrating water, falling slugs, and capillary groundwater, respectively. ==Derivation== The derivation of the 1-D finite water-content method equation for calculating vertical flux $q$ of water in the vadose zone starts with conservation of mass for an unsaturated porous medium without sources or sinks: :$\backslash frac\; +\; \backslash frac=\; 0.$ Next, the cyclic chain rule and chain rule are used to perform a hodograph transformation and convert the conservation of mass equation into a kinematic equation with z as the dependent variable〔Philip, J. R., 1969., Theory of infiltration, ''Adv. Hydrosci''., 5, 215–296.〕 : :$\backslash frac=\backslash frac.$ We next insert the unsaturated Buckingham–Darcy flux:〔Jury, W. A., and R. Horton, 2004. Soil physics. John Wiley & Sons.〕 :$q=-K(\backslash theta)\backslash frac\; +\; K(\backslash theta),$ which yields: :$\backslash frac=\backslash frac\; \backslash left(\backslash left(1-\backslash frac\backslash right)\backslash right)=\backslash frac\; \backslash left\; (\; 1-\; \backslash frac\; \backslash right)\; -\; K(\backslash theta)\; \backslash frac.$ The term on the far right-hand side of the above equation is negligible in the case of infiltration because we assume the soil has a delta-function diffusivity 〔Warrick A.W.. 2003. Soil Water Dynamics, Oxford Univ. Press, USA, pp. 159-162.〕 so that $\backslash psi$ is constant along the infiltration wetting front.〔 Furthermore, evidence suggests that this term is small and negligible along the capillary groundwater wetting front when the groundwater table velocity is less than 0.92 $K\_s$.〔Ogden, F. L., W. Lai, R. C. Steinke, and J. Zhu (2015b), Validation of finite water-content vadose zone dynamics method using column experiments with a moving water table and applied surface flux, ''Water Resour. Res.'', 10.1002/2014WR016454.〕 Therefore, the resulting finite water-content vadose zone flow equation is: :$\backslash left(\backslash frac\backslash right)\_\backslash theta\; =\; \backslash frac\; \backslash left(1-\; \backslash left\; (\backslash frac\backslash right)\; \backslash right).$ One way to solve this equation is to solve it for $q(\backslash theta,t)$ and $z(\backslash theta,t)$ by integration:〔Wilson, J. L. (1974), Dispersive mixing in a partially saturated porous medium, PhD dissertation, 355pp., Dept. of Civil Engrg., Mass. Inst. Tech., Cambridge, MA.〕 : $\backslash int\; \backslash frac\; \backslash ,\; d\backslash theta\; =\; \backslash int\; \backslash frac\; \backslash ,\; d\backslash theta$ Instead, a finite water-content discretization is used and the integrals are replaced with summations: : where $N$ is the total number of finite water content bins. Using this approach, the conservation equation for each bin is: : The method of lines is used to replace the partial differential forms on the right-hand side into appropriate finite-difference forms. This process results in a set of three ordinary differential equations that describe the dynamics of infiltration fronts, falling slugs, and groundwater capillary fronts using a finite water-content discretization. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Finite water-content vadose zone flow method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.