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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On a numerical subgrid upscaling algorithm for StokesBrinkman equations
 Computers and mathematics with applications 65 (2013), No.3, pp.435448 ISSN: 00974943 ISSN: 08981221 

 English 
 Journal Article 
 Fraunhofer ITWM () 
Abstract
This paper discusses a numerical subgrid resolution approach for solving the StokesBrinkman system of equations, which is describing coupled flow in plain and in highly porous media. Various scientific and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil filtration. In many complicated filters, the filter medium or the filter element geometry are too fine to be resolved by a feasible computational grid. The subgrid approach presented in this paper is aimed at describing how these fine details are accounted for by solving auxiliary problems in appropriately chosen grid cells on a relatively coarse computational grid. This is done via a systematic and careful procedure of modifying and updating the coefficients of the StokesBrinkman system in chosen cells. This numerical subgrid approach is motivated from one side from homogenization theory, from which we borrow the formulations for the socalled cell problem, and from the other side from the numerical upscaling approaches, such as Multiscale Finite Volume, Multiscale Finite Element, etc. Results on the algorithm's efficiency, both in terms of computational time and memory usage, are presented. Comparison of the full fine grid solution (when possible) of the StokesBrinkman system with the subgrid solution of the upscaled StokesBrinkman system (including effective permeabilities for the quasiporous cells), are presented in order to evaluate the accuracy and the efficiency. Advantages and limitations of the considered subgrid approach are discussed.