The black oil model is widely used to describe multiphase porous media flow in the petroleum industry. The fully implicit method features strong stability and weak constraints on time step-sizes; hence, commonly used in the current mainstream commercial reservoir simulators. In this paper, a CPR-type preconditioner with an adaptive "setup phase" is developed to improve parallel efficiency of petroleum reservoir simulation. Furthermore, we propose a multi-color Gauss-Seidel (GS) algorithm for algebraic multigrid method based on the coefficient matrix of strong connections. Numerical experiments show that the proposed preconditioner can improve the parallel performance for both OpenMP and CUDA implements. Moreover, the proposed algorithm yields good parallel speedup as well as same convergence behavior as the corresponding single-threaded algorithm. In particular, for a three-phase benchmark problem, the parallel speedup of the OpenMP version is over 6.5 with 16 threads and the CUDA version reaches more than 9.5.

翻译：黑色石油模型被广泛用来描述石油工业多阶段多孔化介质流。完全隐含的方法在时间步数上具有很强的稳定性和薄弱的限制;因此,在目前的主流商业储油层模拟器中常用。在本文中,开发了具有适应性“设置阶段”的CPR型先决条件,以提高石油储油层模拟的平行效率。此外,我们提议根据强连系数矩阵,为代数多格法使用多色高斯-Seidel(GS)算法。数字实验表明,拟议的前提条件可以改进OpenMP和CUDA执行工具的平行性能。此外,拟议的算法产生良好的平行加速,与相应的单轨算法具有相同的趋同行为。特别是,对于三阶段的基准问题,OpenMP版本的平行加速速度超过6.5分之6.5,有16条线,CUDA版本达到9.5以上。