On the convergence of numerical solutions for 2-D flows in a cavity at large Re

The lid-driven square cavity flow: numerical solution with a 1024 x 1024 grid

“…For all variables of interest, the discretization error estimated (U) with Eqs. (13) and (14) The main focus of this work was to solve the problem of laminar flow inside a square cavity of which lid moves at a constant velocity and analytical solution is unknown (Kawaguti, 1961;Burggraf, 1966;Rubin and Khosla, 1977;Benjamin and Denny, 1979;Ghia, Ghia and Shin, 1982). Results were presented for 42 variables of interest (φ), and their estimated discretization errors (U) on a grid of 1024 x 1024 nodes and Reynolds numbers (Re) = 0.01, 10, 100, 400 and 1000.…”

“…Some studies (Benjamin and Denny, 1979;Schreiber and Keller, 1983;Erturk, Corke and Gökçöl, 2005) achieved excellent results when employing multiple Richardson extrapolations (MRE) to reduce the discretization error of ψ min . However, these authors used this process with at most four grids, resulting in up to three extrapolations for the finest grid they used.…”

“…1 This work addresses the classical problem (Kawaguti, 1961;Burggraf, 1966;Rubin and Khosla, 1977;Benjamin and Denny, 1979;Ghia, Ghia and Shin, 1982) of laminar flow inside a square cavity of which lid moves at constant velocity: Fig. 1; where u and v are the components of the velocity vector in x and y directions, ρ and µ are fluid density and viscosity.…”

Effect of boundary vorticity discretization on explicit stream-function vorticity calculations

“…This problem has long served as the prototype for the incompressible Navier-Stokes equations; see, References [7,[25][26][27], to mention only a few. We assume u = 0 and v = 0 on all the ÿxed walls and that on the moving wall at y = 1, u = 1 and v = 0.…”

Finite Element Technique for Optimal Pressure Recovery from Stream Function Formulation of Viscous Flows

“…The purpose of this paper is to provide a formulation and analysis of the stream function approach to the solution of the two-dimensional Navier-Stokes equations in polygonal simply connected domains. As with related approaches [2], [3], [4], [9], [10], [11], the pressure must be computed separately if it is required, and we give a natural algorithm for this purpose. In addition, we prove that the computed pressure will be "optimal" in the approximation-theoretic sense, for a particular kind of finite element space.…”