A three-level finite element method for the instationary incompressible Navier?Stokes equations
A three-level finite element method for the instationary incompressible Navier?Stokes equations
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DOI：
10.1016/j.cma.2003.12.027
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发表时间：
2004-04
影响因子：
7.2
通讯作者：
V. Gravemeier;W. Wall;E. Ramm
中科院分区：
文献类型：
--
作者：
V. Gravemeier;W. Wall;E. Ramm
本文提出了一种二阶和三阶有限元法，用于模拟由Navier-Stokes方程控制的不可压缩流动。在变分多尺度方法的理论框架内，利用无残差气泡的概念，我们提出了三种不同尺度群的分离，即大（已解）尺度、小（已解）尺度和未解尺度。在不同的方法的帮助下，大尺度和小尺度的解决发生在1层和2层。表示未解析尺度影响的子网格粘度的动态计算构成了我们算法的第3级。本文对所提出的算法进行了各种层流情况的测试，并与一种不寻常的稳定有限元方法得到的结果进行了比较。在后续的研究中，它也被认为是紊流的基本方案。
We present a two- and a three-level finite element method for the numerical simulation of incompressible flow governed by the Navier–Stokes equations. Within the theoretical framework of the variational multiscale method and exploiting the concept of residual-free bubbles we propose a separation of three different scale groups, namely large (resolved) scales, small (resolved) scales, and unresolved scales. The resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches. The dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of our algorithm. The proposed algorithm is tested for various laminar flow situations and compared to the results obtained via an unusual stabilized finite element method. It is supposed to be the basic scheme also for turbulent flow in a subsequent study.