Abstract
The way in which the boundary values of the vorticity are approximated in the numerical solution of the Navier-Stokes equations affects the rate of convergence and accuracy of the solutions. In this paper two classes of boundary approximations are studied. The problem of viscous flow in a square cavity is chosen as a model. Numerical solutions are obtained for Reynolds numbers 1, 10, 50, 100, 500 and 1000 and the iterative procedure is found to become faster with a decrease in the local accuracy of the boundary approximation. Detailed comparisons are carried out in order to determine accuracy of various numerical solutions. Several parameters, based on the numerical solutions, are found to vary monotonically and approach certain limiting values. These parameters are considered to be reliable indicators of accuracy and are recommended for comparison of numerical results obtained by different methods.
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