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In this paper, we present a new multiscale model reduction technique for theStokes flows in heterogeneous perforated domains. The challenge in thenumerical simulations of this problem lies in the fact that the solutioncontains many multiscale features and requires a very fine mesh to resolve alldetails. In order to efficiently compute the solutions, some model reductionsare necessary. To obtain a reduced model, we apply the generalized multiscalefinite element approach, which is a framework allowing systematic constructionof reduced models. Based on this general framework, we will first construct alocal snapshot space, which contains many possible multiscale features of thesolution. Using the snapshot space and a local spectral problem, we identifydominant modes in the snapshot space and use them as the multiscale basisfunctions. Our basis functions are constructed locally with non-overlappingsupports, which enhances the sparsity of the resulting linear system. In orderto enforce the mass conservation, we propose a hybridized technique, and uses aLagrange multiplier to achieve mass conservation. We will mathematicallyanalyze the stability and the convergence of the proposed method. In addition,we will present some numerical examples to show the performance of the scheme.We show that, with a few basis functions per coarse region, one can obtain asolution with excellent accuracy.

A conservative local multiscale model reduction technique for Stokes flows in heterogeneous perforated domains