Title:        Mortar upscaling for multiphase flow in porous media

Authors:      M. Peszynska, Mary F. Wheeler, and Ivan Yotov

Source:       Computational Geosciences 6:1 (2002) 73-100

Status:       Published

Abstract: In mortar space upscaling methods, a reservoir is decomposed
into a series of subdomains (blocks) in which independently
constructed numerical grids and possibly different physical models and
discretization techniques can be employed in each block. Physically
meaningful matching conditions are imposed on block interfaces in a
numerically stable and accurate way using mortar finite element
spaces.  Coarse mortar grids and fine subdomain grids provide
two-scale approximations. In the resulting effective solution flow is
computed in subdomains on the fine scale while fluxes are matched on
the coarse scale.  In addition the flexibility to vary adaptively the
number of interface degrees of freedom leads to more accurate
multiscale approximations.  This methodology has been implemented in
the Center for Subsurface Modeling's multiphysics multiblock simulator
IPARS (Integrated Parallel Accurate Reservoir Simulator).
Computational experiments demonstrate that this approach is scalable
in parallel and it can be applied to non-matching grids across the
interface, multinumerics and multiphysics models, and mortar
adaptivity.  Moreover unlike most upscaling approaches the underlying
systems can be treated fully implicitly.