Optimal Finite Difference Method for Potential Flows
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The optimal finite-difference (FD) method for two-dimensional potential flows is studied. The nine-point FD coefficients for Laplace equations are derived for rectangular cells with an arbitrary length-to-width ratio r. The accuracy and performance of the present optimal FD formula are compared with the finite-analytic (FA) formulas. It is found that the present FD formula gives better results than those given by the FA formulas, and that it produces more stable results than those in other studies for large values of r. An example of potential flow in a channel with an abrupt change in its width is also given. ASCE.
