论文标题
一个增强的Lagrangian预处理，用于隐式构成的非牛顿不可压缩流
An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow
论文作者
论文摘要
我们提出了一个增强的Lagrangian预处理，用于对固定的非Newtonian不可压缩流的三场应力压力离散化，并具有幂律类型的隐式构成关系。所采用的离散化利用无差异的Scott-Vogelius对达到了速度和压力。预处理以工作为基础[P. E. Farrell，L。Mitchell和F. Wechsung，Siam J.Sci。 Comput。，41（2019），pp。A3073-A3096]，其中引入了三维牛顿系统的Reynolds-bobust预处理。预处理使用了一种专门的多机方法，用于应力速度块，涉及捕获空间分解和定制延长操作员。求解器相对于在本构之间产生的参数表现出极好的鲁棒性，从而允许模拟各种材料。
We propose an augmented Lagrangian preconditioner for a three-field stress-velocity-pressure discretization of stationary non-Newtonian incompressible flow with an implicit constitutive relation of power-law type. The discretization employed makes use of the divergence-free Scott-Vogelius pair for the velocity and pressure. The preconditioner builds on the work [P. E. Farrell, L. Mitchell, and F. Wechsung, SIAM J. Sci. Comput., 41 (2019), pp. A3073-A3096], where a Reynolds-robust preconditioner for the three-dimensional Newtonian system was introduced. The preconditioner employs a specialized multigrid method for the stress-velocity block that involves a divergence-capturing space decomposition and a custom prolongation operator. The solver exhibits excellent robustness with respect to the parameters arising in the constitutive relation, allowing for the simulation of a wide range of materials.
