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A semi-Lagrangian Vortex-In-Cell method and its application to high-Re lid-driven cavity flow

A semi-Lagrangian Vortex-In-Cell method and its application to high-Re lid-driven cavity flow PurposeThe purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.Design/methodology/approachThe VIC method is developed for simulating high Reynolds number incompressible flow. A semi-Lagrangian scheme is incorporated in the convection term to produce unconditional stability, which gets rid of the constraint of the convection Courant-Friedrichs-Lewy (CFL) condition; the adaptive time step is used to maintain the numerical stability of the diffusion term; and the velocity boundary condition is readily converted to the vorticity formulation to suit discontinuous boundary treatment. The VIC simulation results are compared with those produced by other gird methods reported in open literature studies.FindingsThe lid-driven cavity flow is simulated from Re = 100 to 100,000. Similar vortex birth mechanisms are exhibited though, but distinct flow characteristics are revealed. At Re = 100 to 7,500, the cavity flow is confirmed steady. At Re = 10,000, 15,000 and 20,000, the cavity flow is periodical with a primary vortex held spatially at the center. In particular, at Re = 100,000 highly turbulent characteristics is first revealed and an analogous primary vortex is formed but in motion rather than stationary, which is caused by the considerable flow separation at all the boundaries.Originality/valueIn the lid-driven cavity, the flow becomes extremely complex and highly turbulent at Re = 100,000, and the analogous primary vortex structure is observed. Boundary layer separation is observed at all walls, producing small vortices and causing the displacement of the analogous primary vortex. Such a finding original and has not yet been reported by other investigators. It may provide a basis for conducting in-depth studies of the lid-driven cavity flow. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

A semi-Lagrangian Vortex-In-Cell method and its application to high-Re lid-driven cavity flow

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/HFF-08-2015-0320
Publisher site
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Abstract

PurposeThe purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.Design/methodology/approachThe VIC method is developed for simulating high Reynolds number incompressible flow. A semi-Lagrangian scheme is incorporated in the convection term to produce unconditional stability, which gets rid of the constraint of the convection Courant-Friedrichs-Lewy (CFL) condition; the adaptive time step is used to maintain the numerical stability of the diffusion term; and the velocity boundary condition is readily converted to the vorticity formulation to suit discontinuous boundary treatment. The VIC simulation results are compared with those produced by other gird methods reported in open literature studies.FindingsThe lid-driven cavity flow is simulated from Re = 100 to 100,000. Similar vortex birth mechanisms are exhibited though, but distinct flow characteristics are revealed. At Re = 100 to 7,500, the cavity flow is confirmed steady. At Re = 10,000, 15,000 and 20,000, the cavity flow is periodical with a primary vortex held spatially at the center. In particular, at Re = 100,000 highly turbulent characteristics is first revealed and an analogous primary vortex is formed but in motion rather than stationary, which is caused by the considerable flow separation at all the boundaries.Originality/valueIn the lid-driven cavity, the flow becomes extremely complex and highly turbulent at Re = 100,000, and the analogous primary vortex structure is observed. Boundary layer separation is observed at all walls, producing small vortices and causing the displacement of the analogous primary vortex. Such a finding original and has not yet been reported by other investigators. It may provide a basis for conducting in-depth studies of the lid-driven cavity flow.

Journal

International Journal of Numerical Methods for Heat & Fluid Flow – Emerald Publishing

Published: Jun 5, 2017

References

  • MUDPACK: multigrid Fortran software for the efficient solution of linear elliptic partial differential equations
  • Benchmark spectral results on the lid-driven cavity flow
  • The 2D lid-driven cavity problem revisited
  • Numerical study of slightly viscous flow
  • Numerical simulation of hydrodynamics by the method of point vortices
  • Combining the vortex-in-cell and parallel fast multipole methods for efficient domain decomposition simulations