Flow topology in a steady three-dimensional lid-driven cavity

Abstract

We present in this paper a thorough investigation of three-dimensional flow in a cubical cavity, subject to a constant velocity lid on its roof. In this steady-state analysis, we adopt the mixed formulation on tri-quadratic elements to preserve mass conservation. To resolve difficulties in the asymmetric and indefinite large-size matrix equations, we apply the BiCGSTAB solution solver. To achieve stability, weighting functions are designed in favor of variables on the upstream side. To achieve accuracy, the weighting functions are properly chosen so that false diffusion errors can be largely suppressed by the equipped streamline operator. Our aim is to gain some physical insight into the vortical flow using a theoretically rigorous topological theory. To broaden our understanding of the vortex dynamics in the cavity, we also study in detail the longitudinal spiralling motion in the flow interior.