00:00:00 / 00:00:00

Multiscale model reduction for flows in heterogeneous porous media

By Victor Calo

Appears in collection : MoMaS Conference / Colloque MoMaS

We combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on the fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach enables a significant reduction in the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.

Keywords: generalized multiscale finite element method - nonlinear PDEs - heterogeneous porous media - discrete empirical interpolation - proper orthogonal decomposition

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.18630803
  • Cite this video Calo Victor (11/19/14). Multiscale model reduction for flows in heterogeneous porous media. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18630803
  • URL https://dx.doi.org/10.24350/CIRM.V.18630803

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback