RESUMEN
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.