A computational method for viscous flow problems

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Abstract
A digital computer method for solving certain problems involving two-dimensional incompressible viscous flow is described. The time-dependent case is treated; the mathematical problem is thus that of solving a non-linear fourth-order partial differential equation in three variables. The choice of difference equations, of relaxation procedure, the kind of approximation to boundary conditions, and the resulting computational stability, speed, and accuracy are considered. Most experience so far has been for a rectangular region for which boundary velocities are prescribed as certain functions of time; an example of one such problem showing vortex formation and break-up is given.