A numerical study of viscous, incompressible fluid flow problems Public Deposited

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  • The mathematical technique of overrelaxation is used here to speed the convergence of a numerical method for solving viscous, incompressible fluid flow problems. The method, called MAC, involves approximating the complete two-dimensional incompressible Navier-Stokes equations with analogous finite-difference equations. The MAC method was developed by the Los Alamos Scientific Laboratory of the University of California and is described in detail in "The MAC Method," by J. Eddie Welch, Francis H. Harlow, John P. Shannon, and Bart J. Daly (LA-3425). The most time-consuming part of this method involves iterating on a finite-difference form of Poisson's equation; hence overrelaxation is applied to this iteration process. Overrelaxation theory is presented and is applied to the above method to show that overrelaxation does speed convergence, Examples of fluid problem solutions are presented both with and without the use of overrelaxation, showing the amount of computer time saved. In addition, computer plots of several typical solutions are included to show the diversity of the above method.
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