Premium
Analysis of mass transport with uncertain physical parameters
Author(s) -
Tang D. H.,
Pinder G. F.
Publication year - 1979
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/wr015i005p01147
Subject(s) - variance (accounting) , mathematics , function (biology) , partial differential equation , mass transport , probability density function , uncertainty analysis , convection–diffusion equation , probability distribution , differential equation , matrix (chemical analysis) , mathematical optimization , statistical physics , mathematical analysis , statistics , physics , materials science , accounting , engineering physics , evolutionary biology , business , biology , composite material
The coefficients of the mass transport equation are often characterized by considerable uncertainty. Where the functional form of this uncertainty is known the transport equation can be solved to yield a solution also characterized by uncertainty. The spatial and temporal dependencies of this uncertainty are dependent upon the variance of the velocity and dispersivity, the magnitude of the dispersivity, the functional form of the probability distribution function, and the number of uncertain parameters considered in the analysis. In general the uncertainty, as measured by the coefficient of variation, is considerably smaller for the solution than for the input parameters. While any finite variance theoretically can be accommodated by the method employed for solution of the stochastic partial differential equations, it is nevertheless essential to select numerical parameters (Δ x and Δ t ) such that certain constraints on the form of the coefficient matrix are not violated.