论文标题
混合牛顿 - 普通型纳维尔 - 纳维尔 - 摩托克方程的强大，有效的多级元ILU预处理
Robust and Efficient Multilevel-ILU Preconditioning of Hybrid Newton-GMRES for Incompressible Navier-Stokes Equations
论文作者
论文摘要
我们为混合牛顿 - 烟灰方法引入了强大而有效的预处理，用于求解由不可压缩的Navier-Stokes方程引起的非线性系统。当雷诺数相对较高时，这些系统通常涉及数百万个自由度（DOF），并且非线性系统很难收敛，部分原因是系统的强烈不对称性和鞍点结构。在这项工作中，我们建议通过利用一个名为Hilucsi的多级ILU预处理来减轻这些问题，这对于鞍点问题特别有效，并可以在牛顿 - 格里姆（Newton-Gmres）中实现内部迭代的强大和快速融合。我们进一步将PICARD迭代与Oseen Systems一起热 - 启动牛顿 - 普通，以实现全球融合，也使用Hilucsi进行了预处理。为了进一步提高效率和鲁棒性，我们将OSEEN操作员用作基于物理学的稀疏器，以构建用于牛顿迭代的预调解器，并在Hilucsi中引入适应性的完善和迭代性完善。我们将最终的预处理混合动力牛顿 - 烟灰称为Hilung。我们通过解决RE 5000的标准2D驱动 - 腔问题和低粘度的3D流循环问题来证明Hilung的有效性。我们将Hilung与INS的一些最先进的定制预定器进行了比较，其中包括两种增强的Lagrangian预处理和两个基于物理的预处理的变体，以及一些通用物质近似近似化的基本化技术。我们的比较表明，Hilung在解决高RE问题方面更加可靠，并且在内存和运行时也更有效地解决了中等RE问题。
We introduce a robust and efficient preconditioner for a hybrid Newton-GMRES method for solving the nonlinear systems arising from incompressible Navier-Stokes equations. When the Reynolds number is relatively high, these systems often involve millions of degrees of freedom (DOFs), and the nonlinear systems are difficult to converge, partially due to the strong asymmetry of the system and the saddle-point structure. In this work, we propose to alleviate these issues by leveraging a multilevel ILU preconditioner called HILUCSI, which is particularly effective for saddle-point problems and can enable robust and rapid convergence of the inner iterations in Newton-GMRES. We further use Picard iterations with the Oseen systems to hot-start Newton-GMRES to achieve global convergence, also preconditioned using HILUCSI. To further improve efficiency and robustness, we use the Oseen operators as physics-based sparsifiers when building preconditioners for Newton iterations and introduce adaptive refactorization and iterative refinement in HILUCSI. We refer to the resulting preconditioned hybrid Newton-GMRES as HILUNG. We demonstrate the effectiveness of HILUNG by solving the standard 2D driven-cavity problem with Re 5000 and a 3D flow-over-cylinder problem with low viscosity. We compare HILUNG with some state-of-the-art customized preconditioners for INS, including two variants of augmented Lagrangian preconditioners and two physics-based preconditioners, as well as some general-purpose approximate-factorization techniques. Our comparison shows that HILUNG is much more robust for solving high-Re problems and it is also more efficient in both memory and runtime for moderate-Re problems.
