Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis
Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis
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DOI：
10.1007/s10915-015-0005-8
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发表时间：
2015-12
影响因子：
2.5
通讯作者：
Yunhua Xue;Cheng Wang;Jian‐Guo Liu
中科院分区：
文献类型：
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作者：
Yunhua Xue;Cheng Wang;Jian‐Guo Liu
本文采用一种简单的有限元数值方法，对不规则区域上的不可压缩流动进行了高分辨率数值模拟，并分析了其边界层分离。与许多经典的有限元流体求解器相比，该数值方法避免了Stokes求解器，并且在每个时间步/阶段仅需要求解两个Poisson类方程。此外，它与完全显式的四阶龙格库塔（RK 4）时间离散相结合，使我们能够以非常有效的方式计算高雷诺数流动。作为该数值求解器的应用，本文给出了雷诺数为0的三角形空腔流动边界层分离的动力学机制，包括分叉位置和临界时间的精确值。此外，我们提供了一个超收敛分析的简单的有限元数值格式，使用线性元素在一个统一的三角形与直角三角形。
In this paper, we apply a simple finite element numerical scheme, proposed in an earlier work (Liu in Math Comput 70(234):579–593, 2000), to perform a high resolution numerical simulation of incompressible flow over an irregular domain and analyze its boundary layer separation. Compared with many classical finite element fluid solvers, this numerical method avoids a Stokes solver, and only two Poisson-like equations need to be solved at each time step/stage. In addition, its combination with the fully explicit fourth order Runge–Kutta (RK4) time discretization enables us to compute high Reynolds number flow in a very efficient way. As an application of this robust numerical solver, the dynamical mechanism of the boundary layer separation for a triangular cavity flow with Reynolds numbersand, including the precise values of bifurcation location and critical time, are reported in this paper. In addition, we provide a super-convergence analysis for the simple finite element numerical scheme, using linear elements over a uniform triangulation with right triangles.