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Unformatted text preview: Approximate Analytical Solutions to the Groundwater Flow Problem CWR 6536 Stochastic Subsurface Hydrology 3D Steady Saturated Groundwater Flow K(x,y,z) random hydraulic conductivity field (x,y,z) random hydraulic head field want approximate analytical solutions to the 1st and 2nd ensemble moments of the head field + + = z K z y K y x K x System of Approximate Moment Eqns to order 2 Use (x), as best estimate of (x) Use 2 =P (x,x) as measure of uncertainty Use P (x,x) and P f (x,x) for cokriging to optimally estimate f or based on field observations ) ( ) ' , ( ) ' , ( ) ( ) ' , ( ) ' ( ) ' , ( ) ' , ( ) ' ( ) ' , ( ) ( ) ( ) ( 2 ' ' ' ' 2 ' 2 1 1 1 1 1 1 1 x x x P x x P x F x x P x x x P x x P x F x x P x x F x f x ff x f x x f x + + = + + = + = Possible Solution Techniques Fourier Transform Methods (Gelhar et al.) Greens Function Methods (Dagan et al.) Numerical Techniques (McLaughlin and Wood, James and Graham) Fourier Transform Methods Require A solution that applies over an infinite domain Coefficients in equations that are constant, or can...
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This note was uploaded on 03/27/2012 for the course CWR 6536 taught by Professor Graham during the Spring '11 term at University of Florida.
 Spring '11
 Graham

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