GPU-based Parallel Reservoir Simulators

Nowadays reservoir simulators are indispensable tools to reservoir engineers. They are widely used in the optimization and prediction of oil and gas production. However, for large-scale reservoir simulation, computational time is usually too long. A case with over one million grid blocks may run weeks or even months. High performance processors and well-designed software are demanded. Though today’s CPUs (Central Processing Unit) are much more powerful than before, performance of single CPU tends to slow down due to material and energy consumption and heat dissipation issues. Processor vendors have begun to move to multiple processing units, which form two major directions: multi-core CPUs and many-core GPUs [11]. In reservoir simulation, numerical methods like the finite difference and finite volume methods [7] are often used to discretize the mathematical models. Linear and nonlinear systems arising from the discretized models by those methods are sparse, which are usually time-consuming and difficult to solve. Krylov subspace solvers [18, 1] are general methods to solve these linear systems, and for largescale reservoir simulation with over one million grid blocks, a reservoir simulator may take 90% or even more time on the solution of the linear systems. Fast and accurate linear and nonlinear solvers are essential to reservoir simulators. Saad et al. developed the GMRES solver for general unsymmetric linear systems [1, 18] and Vinsome designed the ORTHOMIN solver, which was originally developed for reservoir simulators [19]. PCG, BICGSTAB, algebraic multigrid and direct linear solvers were also proposed. Commonly used preconditioners were also developed, such as Incomplete LU (ILU) factorization, domain decomposition, algebraic multigrid, and multi-stage preconditioners [1, 18]. GPUs (Graphics Processing Unit) are usually used for display. Since each pixel can be processed simultaneously, GPUs are designed in such a way that they can manipulate data in parallel. Their float point performance and memory speed are very high [16, 15]. In general, GPUs are ten times faster than general CPUs [16, 15], which makes them powerful devices