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

Abstract

Purpose

The 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/approach

The 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.

Findings

The 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/value

In 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.

Citation

Wang, C., Sun, J. and Ba, Y. (2017), "A semi-Lagrangian Vortex-In-Cell method and its application to high-Re lid-driven cavity flow", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 6, pp. 1186-1214. https://doi.org/10.1108/HFF-08-2015-0320