Parallel Scalable Unstructured CPR-Type Linear Solver for Reservoir Simulation

We describe a multistage parallel linear solver framework developed as part of the Intersect (IX) next-generation reservoir simulation project. The object-oriented framework allows for wide flexibility in the number of stages, methods and preconditioners. Here, we describe the specific components of a two-stage CPR 1 (Constraint Pressure Residual) scheme designed for large-scale parallel, structured and unstructured linear systems. We developed a highly efficient in-house Parallel Algebraic Multigrid (PAMG) solver as the first stage preconditioner. For the second stage, we use a parallel ILU-type scheme. This new and powerful combination of CPR and PAMG was the result of detailed analysis of the linear system of equations associated with reservoir simulation. Using several difficult reservoir simulation problems, we demonstrate the robustness and excellent parallel scalability of the IX linear solver. For the field case studies, the IX linear solver with CPR and PAMG is at least five times faster than an established and widely used industrial linear solver. The performance advantage of the IX linear solver over traditional reservoir simulation linear solvers increases with both problem size and the number of processors.