Preconditioning can be used to damp slowly varying error modes in the linear solver residuals, corresponding to extreme eigenvalues. Existing multiscale solvers use a sequence of aggressive restriction, coarse-grid correction and prolongation operators to handle low-frequency modes on the coarse grid. High-frequency errors are then resolved by employing a smoother on fine grid. In reservoir simulations, the Jacobian system is usually solved by FGMRES method with two-level Constrained Pressure Residual (CPR) preconditioner. In this paper, a parallel fully implicit smoothed particle hydrodynamics (SPH) based multiscale method for solving pressure system is presented. The prolongation and restriction operators in this method are based on a SPH gradient approximation (instead of solving localized flow problems) commonly used in the meshless community for thermal, viscous, and pressure projection problems. This method has been prototyped in a commercially available simulator. This method does not require a coarse partition and can be applied to general unstructured topology of the fine scale. The SPH based multiscale method provides a reasonably good approximation to the pressure system and speeds up the convergence when used as a preconditioner for an iterative fine-scale solver. In addition, it exhibits expected good scalability during parallel simulations. Numerical results are presented and discussed.


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