Porous media upscaling in terms of mathematical epistemic cognition
Journal
SIAM Journal on Applied Mathematics
Journal Volume
66
Journal Issue
2
Pages
433-446
Date Issued
2006
Author(s)
Christakos, G.
Abstract
In this work we revisit the meaning of the term "solution" with respect to a mathematical model representing a physical media upscaling system. A central aim is to combine the science of mind with human mathematical ideas to solve real-world upscaling problems. We propose that in certain cases a (nonconventional) epistemic cognition solution (which assumes that the model describes incomplete knowledge about nature and focuses on conceptual mechanisms and thinking processes) can lead to a more realistic upscaling analysis than a (conventional) ontologic approach (which assumes that the model describes nature as is and focuses on form manipulations). In the present work we apply the epistemic cognition approach to the solution of the two-dimensional bounded porous media upscaling problem. A formal framework is presented, and implementation issues related to the epistemic cognition methodology are considered. Numerical experiments are presented involving effective conductivities in bounded two-dimensional spatial domains, and insight is gained by comparing the results to existing ontologic upscaling solutions. In addition to dealing with new and more general upscaling situations, the proposed approach can reproduce some well-known results, a fact that further demonstrates its power and nesting capabilities.
SDGs
Type
journal article