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|Title: ||Theory of diffusions applied to stochastic flow in porous media|
|Author: ||Verwoerd, Wynand S.|
|Date: ||May-1999 |
|Publisher: ||Lincoln University. Applied Computing, Mathematics and Statistics Group.|
|Series/Report no.: ||Research report (Lincoln University (Canterbury, N.Z.). Applied Computing, Mathematics and Statistics Group) ; no. 99/07|
|Item Type: ||Monograph|
|Abstract: ||Contaminant transport by liquid flow in a porous medium is modelled by
the addition of a stochastic term to Darcy's flow equation. The resulting stochastic differential equation is studied using results from the theory of diffusions as embodied in the Dynkin formula.
The resulting integral equation for the probability distribution of fluid
elements is solved for the case of a spatially homogeneous medium without
microdiffusion. This distribution is shown to also solve a deterministic
transport equation containing an effective diffusion constant, analogous to
the hydrodynamic dispersion equation. This relates the stochastic and deterministic
approaches to the contaminant transport problem. The case of a non-homogeneous medium is discussed, leading to a tentative conclusion that the stochastic description will not reduce to a dispersion equation in general.|
|Persistent URL (URI): ||http://hdl.handle.net/10182/932|
|Appears in Collections:||Applied Computing Research Report series|
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