Journal of Theoretical
and Applied Mechanics
36, 3, pp. 535-560, Warsaw 1998
The influence of dimensionless parameter orders of magnitude on the homogenisation process result
Basing on two examples a significant impact of the order of magnitude of dimensionless parameters on the homogenisation process results when using either the direct averaging or classical homogenisation approach has been presented. First, the effect of two dimensionless parameters on the results of amplitude direct homogenisation procedure has been studied. Three examples of different values of dimensionless parameters Q and R_el have been shown for filtration of an incompressible Newtonian liquid. The presented methodology proves that certain classes of physical processes can be treated in a similar way. Dissimilar descriptions of the processes appearing in, for instance optics or dynamics result from neglecting certain effects when changing the observation method or scale.
Keywords: homogenisation; dynamics; fluid flow