Parallel Fully Implicit Smoothed Particle Hydrodynamics Based Multiscale Method

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.