论文标题
在异质多孔介质中的两相流的非线性场分裂预处理的比较
Comparison of nonlinear field-split preconditioners for two-phase flow in heterogeneous porous media
论文作者
论文摘要
这项工作着重于开发两步场分裂的非线性预处理器，以加快异质多孔介质中两相流量和运输的收敛。我们提出了一种名为field-Split乘法Schwarz Newton（FSMSN）的场分裂算法，该算法由两个步骤组成：首先，我们通过以顺序方式应用了大约两个子问题来非线性地更新压力和饱和度。然后，我们采用一个全局步骤，依靠在预处理状态下对系统进行线性化获得的牛顿更新。使用具有挑战性的测试用例，将FSMSN与现有的现场分解预处理，繁殖型牛顿（MSPIN）（MSPIN）的乘法性施瓦兹进行了比较，以及标准解决方案策略，例如顺序完全隐式（SFI）方法或完全隐式方法（FIM）。该比较突出了前风方案在预处理的算法性能中的影响以及在预处理步骤中子问题耐受性动态适应的重要性。我们的结果表明，与SFI和FIM方法相比，两步非线性预处理方法，尤其是在外环收敛速度更快的FSMSN-RESULT中。预处理对计算绩效的影响，即通过墙锁定时间来衡量，将在随后的出版物中研究。
This work focuses on the development of a two-step field-split nonlinear preconditioner to accelerate the convergence of two-phase flow and transport in heterogeneous porous media. We propose a field-split algorithm named Field-Split Multiplicative Schwarz Newton (FSMSN), consisting in two steps: first, we apply a preconditioning step to update pressure and saturations nonlinearly by solving approximately two subproblems in a sequential fashion; then, we apply a global step relying on a Newton update obtained by linearizing the system at the preconditioned state. Using challenging test cases, FSMSN is compared to an existing field-split preconditioner, Multiplicative Schwarz Preconditioned for Inexact Newton (MSPIN), and to standard solution strategies such as the Sequential Fully Implicit (SFI) method or the Fully Implicit Method (FIM). The comparison highlights the impact of the upwinding scheme in the algorithmic performance of the preconditioners and the importance of the dynamic adaptation of the subproblem tolerance in the preconditioning step. Our results demonstrate that the two-step nonlinear preconditioning approach-and in particular, FSMSN-results in a faster outer-loop convergence than with the SFI and FIM methods. The impact of the preconditioners on computational performance-i.e., measured by wall-clock time-will be studied in a subsequent publication.
