From multi- to single-grid CFD on massively parallel computers: Numerical experiments on lid-driven flow in a cube using pressure–velocity coupled formulation

Theoretical analysis of three-dimensional bifurcated flow inside a diagonally lid-driven cavity

“…The spatial reflection symmetry of the base velocity of perturbed flow originates from that of the steady flow reported by [21,24] and preserves during transition to unsteadiness. In contrast, transition to unsteadiness of the "classical" lid-driven cavity flow is characterized by the symmetry breaking of the base flow [12] with the subsequent energy bursts of the bifurcated flow [14].…”

“…A maximum value of 10 −6 for all residuals was set as the convergence criterion. The results from the icoFoam solver were compared with the results previously published by Feldman and Gelfgat [21] for the same flow configuration. Table 1 summarizes the results of the two studies for the velocity and pressure fields obtained for Re = 1000 along the vertical centerline of the cavity.…”

“…The diagonally lid-driven cavity essentially hosts a fully three-dimensional, highly separated vortical flow, whose steady state is characterized by a diagonal plane of reflection symmetry. The precise values of the pressure and velocity components of the steady flow along the cavity centerlines at different Re values can be found in [21]. Fig.…”

“…The arrows indicate the direction of lid movement. Reprinted with permission from [21] During the past decade, steady diagonally lid-driven flow has become a popular benchmark for verification of state-of-the-art numerical methods [25][26][27][28]. Surprisingly, neither the mechanism of transition to unsteadiness nor the classification of the complex bifurcated flow has so far been addressed.…”

An Adaptive Explicit 3D Discontinuous Galerkin Solver for Unsteady Problems<br />

“…This problem is relatively new in terms of three-dimensional code validation and was introduced in references. 41,42,43,44,45 …”