Premium
On spectral measure and Monte Carlo Approaches to flow in heterogeneous media
Author(s) -
Deng FeiWen,
Cushman John H.
Publication year - 1992
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/92wr00469
Subject(s) - monte carlo method , statistical physics , measure (data warehouse) , spectral method , flow (mathematics) , fourier transform , head (geology) , field (mathematics) , integral equation , conductivity , mathematics , physics , mathematical analysis , computer science , quantum mechanics , statistics , geology , geometry , database , geomorphology , pure mathematics
A pedagogical approach to the spectral integral method as applied to flow problems is presented. The deterministic Fourier analog to the random spectral integral is highlighted, thus illustrating the close ties between the two. The general solution to the deterministic flow problem is used to illustrate that a weakly stationary conductivity field does not in general lead to a weakly stationary head field. Several alternative Monte Carlo methods are presented and compared to illustrate the problems associated with dropping terms of the form ƒ′h′ from the flow equation, where ƒ and h are respectively perturbations in the conductivity and head fields.