Abstract:

An Algebraic Multiscale Solver (AMS) for the pressure system of equations arising from incompressible flow in heterogeneous porous media is developed. The algorithm allows for several independent preconditioning stages to deal with the full spectrum of errors. In addition to the fine-scale system of equations, AMS requires information about the superimposed (dual) coarse grid, which is used for the construction of a wirebasket ordering. The primal coarse grid is used in the construction of a conservative coarse-scale operator and in the reconstruction of a conservative fine-scale velocity field as the last step of the solution process. The convergence properties of AMS are studied for various combinations including (1) the MultiScale Finite-Element (MSFE) method, (2) the MultiScale Finite-Volume (MSFV) approach, (3) Correction Functions (CF), (4) Block ILU with zero fill-in (BILU), and (5) point-wise ILU with zero fill-in (ILU). The reduced-problem boundary condition, which is used for localization, is investigated and improvements are proposed. For a wide range of test cases, including the highly heterogeneous (with over a million cells) SPE 10 permeability field, the performance of the different preconditioning options is analyzed. It is found that the best overall performance is obtained by combining MSFE and ILU as the global and local preconditioners, respectively. Comparison between AMS and the widely used SAMG solver illustrates that AMS and SAMG are comparable, especially for very large heterogeneous problems.

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Copyright 2012, Yixuan Wang: Please note that the reports and theses are copyright to their original authors. Authors have given written permission for their work to be made available here. Readers who download reports from this site should honor the copyright of the original authors and may not copy or distribute the work further without the permission of the author, Yixuan Wang.