In this paper, we combine discrete empirical interpolation techniques, globalmode decomposition methods, and local multiscale methods, such as theGeneralized Multiscale Finite Element Method (GMsFEM), to reduce thecomputational complexity associated with nonlinear flows inhighly-heterogeneous porous media. To solve the nonlinear governing equations,we employ the GMsFEM to represent the solution on a coarse grid with multiscalebasis functions and apply proper orthogonal decomposition on a coarse grid.Computing the GMsFEM solution involves calculating the residual and theJacobian on the fine grid. As such, we use local and global empiricalinterpolation concepts to circumvent performing these computations on the finegrid. The resulting reduced-order approach enables a significant reduction inthe flow problem size while accurately capturing the behavior of fully-resolvedsolutions. We consider several numerical examples of nonlinear multiscalepartial differential equations that are numerically integrated usingfully-implicit time marching schemes to demonstrate the capability of theproposed model reduction approach to speed up simulations of nonlinear flows inhigh-contrast porous media.
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