Multilevel upscaling through variational coarsening

A new efficient multilevel upscaling procedure for single‐phase saturated flow in porous media is presented. While traditional approaches to this problem have focused on the computation of an upscaled hydraulic conductivity, here the coarse‐scale model is created explicitly from the fine‐scale model through the application of operator‐induced variational coarsening. This technique, which originated with robust multigrid solvers, has been shown to accurately capture the influence of fine‐scale heterogeneous structure over the complete hierarchy of coarse‐scale models that it generates. Moreover, implicit in this hierarchy is the construction of interpolation operators that provide a natural and complete multiscale basis for the fine‐scale problem. Thus this new multilevel upscaling methodology is similar to the multiscale finite element method, and indeed, it attains similar accuracy in computations of the fine‐scale hydraulic head and coarse‐scale normal flux on a variety of problems; yet it is an order of magnitude faster on the examples considered here.

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