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Simple finite element numerical simulation of incompressible flow over non-rectangular domains and the super-convergence analysis

Yunhua Xue Nankai University Cheng Wang University of Massachusetts Dartmouth Jian-Guo Liu Duke University

Numerical Analysis and Scientific Computing mathscidoc:1702.25023

Journal of Scientific Computing, 65, (3), 1189–1216, 2015.12
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 numbers \(Re=10^4\) and \(Re=10^5\) , 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.
Incompressible flowsBoundary layer separation Structural bifurcationSimple finite element method Super-convergence analysis
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@inproceedings{yunhua2015simple,
  title={Simple finite element numerical simulation of incompressible flow over non-rectangular domains and the super-convergence analysis},
  author={Yunhua Xue, Cheng Wang, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207233419850707275},
  booktitle={Journal of Scientific Computing},
  volume={65},
  number={3},
  pages={1189–1216},
  year={2015},
}
Yunhua Xue, Cheng Wang, and Jian-Guo Liu. Simple finite element numerical simulation of incompressible flow over non-rectangular domains and the super-convergence analysis. 2015. Vol. 65. In Journal of Scientific Computing. pp.1189–1216. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207233419850707275.
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