论文标题
并行多级限制的Schwarz预处理，用于使用状态的彭 - 罗宾森方程对地下流的隐式模拟
Parallel multilevel restricted Schwarz preconditioners for implicit simulation of subsurface flows with Peng-Robinson equation of state
论文作者
论文摘要
具有良好可缩小性的并行算法和模拟器对于具有大量处理器的现代超级计算机上的大规模储层模拟尤其重要。在本文中，我们介绍和研究了一个高度可扩展的多级限制添加剂Schwarz（RAS）方法，用于在两个维度和三个维度中使用Peng-Robinson方程的地下流完全隐含的解决方案。通过使用二阶完全隐式方案，所提出的模拟器无条件地稳定，而稳定性条件将时间步长放松。然后，调查着重于开发几种类型的多级重叠添加剂Schwarz方法，用于预处理牛顿迭代不切实际的线性系统的预处理，并提供了一些快速求解器技术，以确保多级接近效率和可扩展性。我们从数字上表明，提出的完全隐式框架对于解决标准基准和现实问题非常有效，而Tianhe-2超级计算机上的数亿未知数以及可扩展到8192处理器的现实问题。
Parallel algorithms and simulators with good scalabilities are particularly important for large-scale reservoir simulations on modern supercomputers with a large number of processors. In this paper, we introduce and study a family of highly scalable multilevel restricted additive Schwarz (RAS) methods for the fully implicit solution of subsurface flows with Peng-Robinson equation of state in two and three dimensions. With the use of a second-order fully implicit scheme, the proposed simulator is unconditionally stable with the relaxation of the time step size by the stability condition. The investigation then focuses on the development of several types of multilevel overlapping additive Schwarz methods for the preconditioning of the resultant linear system arising from the inexact Newton iteration, and some fast solver technologies are presented for the assurance of the multilevel approach efficiency and scalability. We numerically show that the proposed fully implicit framework is highly efficient for solving both standard benchmarks as well as realistic problems with several hundreds of millions of unknowns and scalable to 8192 processors on the Tianhe-2 supercomputer.
