Fluid Mechanics in the Driven Cavity

Abstract

This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

“…The lid-driven cavity is a well known benchmark problem used to validate fluid flow numerical schemes and reduced order models (Cazemier et al 1998;Shankar & Deshpande 2000;Terragni et al 2011). Specifically, isothermal, incompressible, two-dimensional flow inside a square cavity driven by a prescribed lid velocity, u lid = (1 − x 2 ) 2 is considered.…”

An octree-based solver for the incompressible Navier–Stokes equations with enhanced stability and low dissipation

“…One looks for the steady solution of the flow equations (1) in Ω = (0, 1) 3 , with u = (1, 0, 0) T for z = 1 and no-slip/no-penetration conditions on other parts of the boundary. In spite of the simplest of geometrical settings, the cavity flows display many important fluid mechanical phenomena [34]. Note that due to the discontinues boundary conditions, the solution to the problem is singular in the neighborhood of upper edges.…”

Numerical Simulation of Chaotic Mixing in Lid Driven Cavity: Effect of Passive Plug

“…Driven cavity flow is a standard benchmark problem in CFD studies, primarily due to closed domain and clear boundary conditions (Shankar and Deshpande, 2000). Simulating fluid flow features such as primary, secondary and tertiary eddies and their sizes and vortex centers accurately often makes a good test case for the flow solver under investigation.…”