Large reservoirs usually consist of several distinct drainage regions. Moreover, for simulation it may be desirable to use different grids in some regions. Such cases motivate a domain decomposition strategy at the reservoir level. The problem is split into several subproblems, corresponding to different drainage regions or grid types (or whatever other physical reasons there may be that motivate such a splitting). The subproblems can be solved separately, and by exchanging boundary information, the error at the interfaces can be reduced iteratively.

Such algorithms are attractive for parallel computation because of their coarse granularity and less communication, as compared to domain decomposition methods within the linear solver. A straightforward implementation of such methods, however, may converge slowly. The reason is the nonlinearity of the problem and the fact that in case of a linear problem, such methods would reduce to a simple block-Gauss-Seidel method, which is not an efficient solver. It is essential to apply acceleration techniques for such domain decomposition methods.

We present here two dynamic acceleration techniques for nonlinear domain decomposition methods. They use information from the previous time step, to calculate relaxation parameters. To test the robustness and efficiency of these techniques, three-phase black-oil examples with significant flow across subdomain boundaries and examples using locally refined grid have been computed. Results for our approach are compared with standard linear solvers. They show that with suitable acceleration techniques, a domain decomposition on the nonlinear (physical, reservoir) level is a feasible way to obtain coarse-grain parallelism.

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