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Talk Abstract
Multiblock Discretizations and Solvers for Multiphase Flow in Heterogeneous Reservoirs

Ivan Yotov
 Department of Mathematics
University of Pittsburgh
yotov@math.pitt.edu
http://www.math.pitt.edu/~yotov/


A recently developed multiblock (mortar) methodology has gained popularity in modeling complex flows on irregular reservoirs. The simulation domain is decomposed into a series of blocks with possibly different physical and numerical models employed in each block. Proper matching conditions along the interfaces are imposed through the use of specially chosen mortar finite element spaces. The accuracy of the method will be discussed. Critical for the success of this approach is the ability to efficiently solve the resulting discrete nonlinear system. We have developed an efficient parallel algorithm that reduces the global system to an interface problem, which is solved via a nonlinear multigrid with Newton-GMRES smoothing. An approximate Neumann-Neumann preconditioner is constructed for accelerating the GMRES convergence. A relation of the mortar method to certain upscaling techniques will also be discussed.


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1999-2000 Reactive Flow and Transport Phenomena

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