PROBABILISTIC CHARACTERIZATION OF TRANSPORT IN HETEROGENEOUS MEDIA

The mechanics of transport and flow in a random porous medium are addr essed in this paper. The hydraulic properties of the porous medium are modeled as spatial random processes. The random aspect of the problem is treated by introducing a new dimension along which spectral approx imations are implemented. Thus, the hydraulic processes are discretize d using the spectral Karhunen - Loeve expansion. This expansion repres ents the random spatial functions as deterministic modes of fluctuatio n with random amplitudes. These amplitudes form a basis in the manifol d associated with the random processes. The concentrations over the wh ole domain are also random processes, with unknown probabilistic struc ture. These processes are represented using the Polynomial Chaos basis . This is a basis in the functional space described by all second orde r random variables. The deterministic coefficients in this expansion a re calculated via a weighted residual procedure with respect to the ra ndom measure and the inner product specified by the expectation operat or. Once the spatio-temporal variation of the concentrations has been specified in terms of the Polynomial Chaos expansion, individual reali zations can be readily computed. (C) 1998 Elsevier Science S.A.