A New Iterative Solution Technique for Reservoir Simulation Equations on Locally Refined Grids

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Abstract
Summary: This paper presents an incomplete LU (ILU) factorization technique coupled with generalized conjugate-gradient acceleration especially designed for linear equations resulting from locally refined grids. The factorization is based on a special ordering scheme. This repeated red/black (RRB) ordering can cope naturally with grid irregularities introduced by local refinement. The scheme is also very effective on regular grids, where the condition number (a measure of the convergence rate) of the preconditioned linear system increases asymptotically with the number of gridblocks more slowly than it does for conventional ILU preconditionings. For large linear systems, fewer iterations are needed to reach convergence. This makes the method highly competitive compared with other techniques even on regular grids, although the new ordering scheme requires more data handling than standard orderings. Results for several idealized test cases [implicit-pressure, explicit-saturation (LMPES) equations] show the new method to be faster than standard iterative methods.

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