A new method for the solution of time-dependent incompressible viscous flow problems is introduced. The method takes advantage of a predominant flow direction and strongly couples the pressure and velocity fields. The governing equations, using primitive variables, are discretized on a staggered grid, and the solution is generated by a line-by-line sweep of the flow field. Along each computational line, the equations are solved using an efficient block-tridiagonal algorithm. The method is fully implicit and does not have any of the drawbacks of existing methods. Numerical experiments show the method to be robust and efficient. Application of the method to canonical problems in fluid mechanics are presented.
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