Abstract

Computation of Multiple Parameters in Porous Media Problems I Knowles Flow in porous media is commonly modelled via a diffusion equation \begin{displaymath} \nabla\cdot[P(x)\nabla w(x,t)]=S(x) \frac{\partial w}{\partial t}-R(x,t) \end{displaymath} over a region $\Omega \subset R^n$, in which $w$ represents the piezometric head, $P$ the hydraulic conductivity (or sometimes, for a two dimensional aquifer, the transmissivity), $R$ the recharge, and $S$ the storativity of the aquifer. The inverse problem of recovering $P$, $S$, and $R$ from measured values of $u(x,t)$ is of considerable interest in the study of groundwater flow, and in oil reservoir simulation. We present a new method for the computation of these coefficient functions based upon transforming to an elliptic equation and minimizing an energy-type functional with a unique global minimum and a unique stationary point.

General Enquiries Dr. Malcolm Brown. Computer Science Cardiff University PO Box 916 Cardiff CF24 3XF, U.K. Malcom@cs.cf.ac.uk

N.B. All Mathematics appears in TeX/LaTeX source.

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