Abstract
Abstract The effects of grid orthogonality and smoothness on the accuracy of finite-difference solutions of the two-dimensional Laplace, convection-diffusion, and Navier-Stokes equations are studied analytically and numerically. The examples include flow past an airfoil and in a branching channel. It is concluded that orthogonality has little impact on accuracy in general, provided the angle between grid lines is not too small. Rather, accuracy is very sensitive to the clustering of points in the regions of rapid variation of the solution, and orthogonality may in fact have an adverse effect on the quality of the solution when it leads to a coarser resolution of these regions. These conclusions also extend to orthogonality at boundaries (either physical or computational), where Neumann conditions are implemented by one-sided derivatives.
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