The linearized forms of these equations are
Substituting  and  in Eq. (28.1) yields
At any intermediate stage, the solution is to be advanced from nth time level to  th time level. The velocity is advanced in two steps. First, the momentum equations (27.7) and (28.2) are solved to obtain the provisional values of  and  It is not possible to obtain  and  directly since the provisional velocities have not satisfied the continuity equation as yet.
Making use of the approximate velocity solution  a pressure correction  will evolve which will give  and also a velocity correction  will be obtainable. As such,  will correct  in such a manner that  and will satisfy the continuity Eq. (27.5).
In order to obtain  Eqns. (27.7) and (28.2) are approximate as
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