粘性不可压缩流动问题的两层有限元数值计算
Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method
AI总结：
本文提出并验证了用于Navier-Stokes方程流函数形式的两层有限元方法，通过粗网格非线性求解和细网格线性求解实现高效逼近，并在已知解问题和驱动方腔问题中展示了其有效性。
摘要：
我们考虑Navier-Stokes方程的流函数公式的两层有限元离散方法。该方法先在粗网格上求解一个小型非线性系统，然后在细网格上求解一个线性系统。基本结果表明，粗网格与细网格之间的误差呈超线性关系。本文证明了两层方法可以高效地逼近Navier-Stokes方程的解。我们考虑了两个流体流动计算，用于测试具有已知解的问题以及驱动方腔问题。展示了流函数等值线，显示了流动的主要特征。
英文摘要：
We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear system on the fine mesh. The basic result states that the errors between the coarse and fine meshes are related superlinearly. This paper demonstrates that the two-level method can be implemented to approximate efficiently solutions to the Navier-Stokes equations. Two fluid flow calculations are considered to test problems which have a known solution and the driven cavity problem. Stream function contours are displayed showing the main features of the flow.
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