Abstract
Abstract New results for the recirculating flow inside a square cavity obtained by a finite element method are presented. The full Navier-Stokes equations in the form of a single, fourth order equation for stremfunction is recast into arestricted variational principles, which form finite element discretization. A triangular element with Hermitian interpolation is used, such that the velocities are continuous and the incompressibility is satisfied exactly. The resulting nonlinear system is solved by Newton-Raphson iteration. Calculations are carried out with several gridworks of progressive show: (1) the convergence of solutions with refinement for fixed Reynolds number R ; and (2) the loss of accuracy with R for fixed gridwork. The range of R covered is from 10 −4 to 3450. The features illustrated include the enlargement of the inviscid core of rigid rotation, the intensification of primary and secondary vortices and the appearance of a third secondary vortex near the upper upstream corner at R =1500 .
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