Multiscale model reduction technique for fluid flows with heterogeneous porous inclusions

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dc.contributor.authorVasilyeva, Maria
dc.contributor.authorMallikarjunaiah, S. M.
dc.contributor.authorPalaniappan, D.
dc.creator.orcidhttps://orcid.org/0000-0001-8664-8921en_US
dc.creator.orcidhttps://orcid.org/0000-0001-8664-8921
dc.date.accessioned2022-09-20T15:47:05Z
dc.date.available2022-09-20T15:47:05Z
dc.date.issued2022-09-02
dc.description.abstractNumerical treatment of the problem of two-dimensional viscous fluid flow in and around circular porous inclusions is considered. The mathematical model is described by Navier-Stokes equation in the free flow domain Ωf and nonlinear convective Darcy-Brinkman-Forchheimer equations in porous subdomains Ωp. It is well-known that numerical solutions of the problems in such heterogeneous domains require a very fine computational mesh that resolve inclusions on the grid level. The size alteration of the relevant system requires model reduction techniques. Here, we present a multiscale model reduction technique based on the Generalized Multiscale Finite Element Method (GMsFEM). We discuss construction of the multiscale basis functions for the velocity fields based on the solution of the local problems with and without oversampling strategy. Three test cases are considered for a given choice of the three key model parameters, namely, the Reynolds number (Re), the Forchheimer coefficient (C) and the Darcy number (Da). For the test runs, the Reynolds number values are taken to be Re = 1, 10, 100 while the Forchheimer coefficient and Darcy number are chosen as C = 1, 10 and Da = 10−5 , 10−4 , 10−3 , respectively. We numerically study the convergence of the method as we increase the number of multiscale basis functions in each domain, and observe good performance of the multiscale method.en_US
dc.identifier.citationVasilyeva, M., Mallikarjunaiah, S. M., & Palaniappan, D. (2022, September 2). Multiscale model reduction technique for fluid flows with heterogeneous porous inclusions. arXiv.org. Retrieved from https://doi.org/10.48550/arXiv.2209.01155en_US
dc.identifier.doihttps://doi.org/10.48550/arXiv.2209.01155
dc.identifier.urihttps://hdl.handle.net/1969.6/94046
dc.language.isoen_USen_US
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectmultiscale modelen_US
dc.subjectfluid flowsen_US
dc.subjectheterogeneous porous inclusionsen_US
dc.subjectporous inclusionsen_US
dc.subjectstatisticsen_US
dc.titleMultiscale model reduction technique for fluid flows with heterogeneous porous inclusionsen_US
dc.typeArticleen_US

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