By Dongxiao Zhang
ISBN-10: 0127796215
ISBN-13: 9780127796215
Stochastic equipment for movement in Porous Media: dealing with Uncertainties explores fluid stream in complicated geologic environments. The parameterization of uncertainty into circulation types is necessary for dealing with water assets, maintaining subsurface water caliber, storing strength and wastes, and enhancing the protection and economics of extracting subsurface mineral and effort resources.This quantity systematically introduces a couple of stochastic tools utilized by researchers locally in an instructional means and offers methodologies for spatially and temporally desk bound in addition to nonstationary flows. the writer compiles a few recognized effects and necessary formulae and comprises routines on the finish of every bankruptcy.
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Extra info for Stochastic Methods for Flow in Porous Media: Coping with Uncertainties
Example text
Zhang, 1998] that for uniform mean flow the magnitude of this second-order correction term decreases as the domain size L increases and that it is zero for an unbounded domain. It is seen from Eqs. 61) that the head terms are recursive. That is, the higherorder terms are in terms of lower-order ones. ,(h~l)(x)h~l)(y)h~l)(z)) , (h~l)(x)h~l)(y)h~l)(z)h~l)(x)) , (h (2) ( x ) h (2) (y)),and so on). It is the formal advantage of this approach that one does not have to decide a priori at which order to stop and what terms to disregard.
90) Higher-order terms can be given similarly. 2, to first order in a I the mean head is (h(x)) = h~~ and the fluctuation is h'(x) = h~l)(x). The first order head covariance is Ch(X, y) -- (h~l)(x)h~l)(y)) in terms of a}. The mean head may be corrected with higher-order terms such as (h~2)). 91) where J(X) = -dh~~ In the case under study, J = (Ho - HL)/L. Integrating the right-hand side of Eq. 92) Substitution of Eq. 80) into Eq. 93) 26 CHAPTER I I N T R O D U C T I O N which can be used to obtain the expressions for the head covariance Ch (x, y) and the cross-covariance C fh(X, y) between f (x) and h(y), Ch(x, y) -- j2 Cf(X - rl)dx do Lxf y J2x L L L Y L j2y -[- f x~foL C f ( x - n ) d x dn J2xy L L L L Cf(X -- rl)dx do + L2.....
103) becomes trivial with the solution of gr (0)(x) being a constant, and the head covariance depends on the separation vector r -- x - y rather than the actual locations of the two points. Hence the head field (and other flow variables) is stationary in space. 121) Solutions for these equations may be derived analytically. , Cf~(r) = 0), the cross-covariances 34 CHAPTER I INTRODUCTION Cf,o(r) and C~o(r) read as Cfv'(r) = 1 - (u)2,k2. 123) which are derived with the condition of Cf~v(-oo) = Cfv,(oo) = O.
Stochastic Methods for Flow in Porous Media: Coping with Uncertainties by Dongxiao Zhang
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