Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis


Journal Article

© 2015, Springer Science+Business Media New York. 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 $$Re=10^4$$Re=104 and $$Re=10^5$$Re=105, 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.

Full Text

Duke Authors

Cited Authors

  • Xue, Y; Wang, C; Liu, JG

Published Date

  • March 14, 2015

Published In

Volume / Issue

  • 65 / 3

Start / End Page

  • 1189 - 1216

International Standard Serial Number (ISSN)

  • 0885-7474

Digital Object Identifier (DOI)

  • 10.1007/s10915-015-0005-8

Citation Source

  • Scopus