Parallel Sparsified Solvers for Reservoir Simulation

The premise of the present work lies on the fact that a large number of system coefficients may be disregarded without compromising the robustness of the overall solution process. That is, given a linear system it is possible to construct a preconditioner by dropping a large number of off-diagonal nonzeros and use it as a suitable proxy to approximate the original matrix. This proxy system can be in turn factored to generate a new class of block ILU preconditioners, approximated inverses and algebraic multigrid implementations. We propose two parallel algorithms to sparsify a given linear system: (a) random sampling sparsification (RSS), and (b) percolation-based sparsification (PBS). The former one relies on the idea that coefficients are included into the sparsified system with a probability proportional to its effective transmissibility. The latter relies on capturing highly connected flow paths described by whole set of transmissibility coefficients. Depending on the case, the RSS and PS algorithms have the potential to reduce in orders of magnitude the number of floating point operations associated with the preconditioner. Results confirming the benefits of sparsified solvers are illustrated on a wide set of field cases arising in black-oil and compositional simulations.