NDLI: The Buckley--Leverett Equation with Spatially Stochastic Flux Function

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Holden, Lars
Copyright Year	1997
Abstract	When the reservoir parameters are stochastic, then the flow in a reservoir is described by stochastic partial differential equations. Spatial stochastic relative permeability in one spatial dimension is modeled by the stochastic Buckley--Leverett equation s(x,t)t+f(s(x,t),x)x=0 for x > 0 and t > 0. f is the stochastic flux function and s is the saturation. This equation is analyzed, and it is proved that the solution of this equation with Riemann initial data converges to the solution of $s(x,t)_{t}+\bar{f}(s(x,t))_{x}=0$, where $\bar{f}(s)$ is the spatial average of f(s,x) when f(s,x) varies randomly with position.
Starting Page	1443
Ending Page	1454
Page Count	12
File Format	PDF
ISSN	00361399
DOI	10.1137/S0036139994273077
e-ISSN	1095712X
Issue Number	5
Volume Number	57
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	Conservation laws Stochastic partial differential equations Buckley--Leverett equation scalar conservation law stochastic partial differential equations Partial differential equations with randomness, stochastic partial differential equations Flows in porous media; filtration; seepage
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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The Buckley--Leverett Equation with Spatially Stochastic Flux Function