Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {J.D.~Moulton and S.~Knapek and J.E.~Dendy},
  title = {Multilevel upscaling in heterogeneous porous media},
  institution = {CNLS Research highlight, Los Alamos Nat.~Lab.},
  year = {1999},
  month = {Jan.},
  annote = {unrefereed},
  abstract = {The multiscale structure of heterogeneous porous media
		  prevents a straightforward numerical treatment of the
		  underlying mathematical flow models. In particular, fully
		  resolved flow simulations are intractible and yet the
		  fine-scale structure of a porous medium may significantly
		  influence the coarse-scale properties of the solution
		  (e.g., average flow rates). Consequently, homogenization or
		  upscaling procedures are required to define approximate
		  coarse-scale models suitable for efficient computation.
		  Unfortunately, inherent in such a procedure is a compromise
		  between its computational cost and the accuracy of the
		  resulting coarse-scale solution. In general, most popular
		  methods do not balance these competing demands. In this
		  paper we highlight our new efficient, numerical method,
		  which combines our recent work on multigrid homogenization
		  (MGH) with the work of Dvorak to compute bounded estimates
		  of the homogenized permeability for single phase saturated
		  flows. Our approach is motivated by the observation that
		  the coarse-scale influence of multiscale structures are
		  captured automatically by robust variationally defined
		  multigrid methods. The effectiveness of this new algorithm
		  is demonstrated with numerical examples.},
  ps = { 1}