Mimetic Finite Difference Method on GPU: Application in Reservoir Simulation and Well Modeling

Heterogeneous and parallel computing systems are increasingly appealing to high-performance computing. Among heterogeneous systems, the GPUs have become an attractive device for compute-intensive problems. Their many-core architecture, primarily customized for graphics processing, is now widely available through programming architectures that exploit parallelism in GPUs. We follow this new trend and attempt an implementation of a classical mathematical model describing incompressible single-phase fluid flow through a porous medium. The porous medium is an oil reservoir represented by means of corner-point grids. Important geological and mathematical properties of corner-point grids will be discussed. The model will also incorporate pressure- and rate-controlled wells to be used for some realistic simulations. Among the test models are the 10th SPE Comparative Solution Project Model 2. After deriving the underlying mathematical model, it will be discretised using the numerical technique of Mimetic Finite Difference methods. The heterogeneous system utilised is a desktop computer with an NVIDIA GPU, and the programming architecture to be used is CUDA, which will be described. Two different versions of the final discretised system have been implemented; a traditional way of using an assembled global stiffness sparse matrix, and a Matrix-free version, in which only the element stiffness matrices are used. The former version evaluates two GPU libraries; CUSP and THRUST. These libraries will be briefly decribed. The linear system is solved using the iterative Jacobi-preconditioned conjugate gradient method. Numerical tests on realistic and complex reservoir models shows significant performance benefits compared to corresponding CPU implementations