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Interpretation Of Closure Variables In Upscaling, Francisco J. Valdes-Parada, Mark L. Porter, Brian D. Wood
Interpretation Of Closure Variables In Upscaling, Francisco J. Valdes-Parada, Mark L. Porter, Brian D. Wood
Francisco J. Valdes-Parada
In many engineering applications, it is common to nd systems that involve transport at several scales. Despite the increasing computational capabilities, it is still not feasible to model a complete macroscopic system by direct numerical simulations at the microscale. Actually, it is more convenient to derive models at an intermediate level of scale between the microscale and the macroscale; this is the average scale. The derivation of models at this scale can be carried out by means of the method of volume averaging. The results from this method are averaged transport equations expressed in terms of eective medium coecients that …
Integral Formulation For The Solution Of Closure Problems In Upscaling Processes, Francisco J. Valdes-Parada
Integral Formulation For The Solution Of Closure Problems In Upscaling Processes, Francisco J. Valdes-Parada
Francisco J. Valdes-Parada
The derivation of transport models at macroscopic scales can be carried out using upscaling techniques such as the method of volume averaging. This upscaling technique consists on averaging the transport equations that describe phenomena at the microscale. The result is the so-called eective medium models, which are expressed in terms of eective coecients that can be computed from the solution of the corresponding closure problems. In this work, we present an integral formulation based on Green's functions to carry out the formal solution of closure problems. This methodology not only provides a physical interpretation of the closure variables, but it …