隐式非牛顿不可压缩流的增广拉格朗日预条件子
An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow
摘要：
本文提出了一种增广拉格朗日预条件子，用于求解具有幂律型隐式本构关系的定常非牛顿不可压缩流的应力-速度-压力三场离散问题。所采用的离散化利用无发散的Scott-Vogelius对的速度和压力。预条件子建立在工作的基础上[P.E.法雷尔湖Mitchell和F. Wechsung，SIAM J. Sci.计算：41（2019），pp. A3073-A3096]，其中引入了三维牛顿系统的鲁棒预条件子。预处理采用了一个专门的多重网格方法的应力-速度块，涉及到一个发散捕捉空间分解和自定义的延长运营商。求解器表现出良好的鲁棒性相对于本构关系中出现的参数，允许模拟范围广泛的材料。
英文摘要：
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.
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