Factor  is chosen in such a way that the differencing scheme retains “something” of second-order accuracy and the required up-winding is done for the sake of stability. A typical value of  is between 0.2 and 0.3. As mentioned earlier, the quantity  is now evaluated explicitly form the discretized form of equation (27.2) as
where
Similarly, we evaluate
As discussed earlier, the explicitly advanced tilde velocities may not necessarily lead to a flow field with zero mass divergence in each cell. This implies that, at this stage the pressure distribution is not correct, the pressure in each cell will be corrected in such a way that there is no net mass flow in or out of the cell. In the original MAC method, the corrected pressures were obtained from the solution of a Poisson equation for pressure. A related technique developed by Chorin (1967) involved a simultaneous iteration on pressure and velocity components. Vieceli (1971) showed that the two methods as applied to MAC are equivalent. We shall make use of the iterative correction procedure of Chorin (1967) in order to obtain a divergence-free velocity field. The mathematical methodology of this iterative pressure-velocity correction procedure will be discussed herein.
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