论文标题
Scott-Vogelius离散化的固定式Navier-Stokes方程
A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
论文作者
论文摘要
增强的Lagrangian预处理已成功地为固定的不可压缩的Navier-Stokes方程提供了Reynolds-bubust Preponditioner，但仅用于特定的离散化。这些预处理程序已设计的离散化具有取决于雷诺数的误差估计，随着雷诺数的增加，离散误差恶化。在本文中，我们提出了一个增强的Lagrangian先验器，用于在Barycentrientripertripertriend的网眼上离散化。这既可以实现雷诺（Reynolds）固定的性能和雷诺（Reynolds）射击误差估计。一个关键的考虑因素是设计合适的空间分解，该空间分解捕获了添加的毕业生术语的内核，以控制Schur的补体；保证INF-SUP稳定性的同样的barycentric改进也提供了差异核的局部分解。该方案的鲁棒性通过两个维度和三个维度的数值实验证实。
Augmented Lagrangian preconditioners have successfully yielded Reynolds-robust preconditioners for the stationary incompressible Navier-Stokes equations, but only for specific discretizations. The discretizations for which these preconditioners have been designed possess error estimates which depend on the Reynolds number, with the discretization error deteriorating as the Reynolds number is increased. In this paper we present an augmented Lagrangian preconditioner for the Scott-Vogelius discretization on barycentrically-refined meshes. This achieves both Reynolds-robust performance and Reynolds-robust error estimates. A key consideration is the design of a suitable space decomposition that captures the kernel of the grad-div term added to control the Schur complement; the same barycentric refinement that guarantees inf-sup stability also provides a local decomposition of the kernel of the divergence. The robustness of the scheme is confirmed by numerical experiments in two and three dimensions.
