Analysis of inconsistency of SIMPLE-like algorithms and an entirely consistent update technique - The CUT algorithm

The inconsistency of the second hypothesis of the SIMPLE-like algorithms is analyzed and a remedy - the Consistent Update Technique (CUT algorithm) - for velocity and pressure is proposed. In the CUT algorithm, at each iterative level the mass conservation condition is satisfied implicitly while the momentum equation is satisfied explicitly. In CUT algorithm, a modified equation for the explicit-velocity is suggested, and an adjustable coefficient is introduced. Four 2-D fluid flow and heat transfer problems are solved numerically by both the CUT and SIMPLER algorithms under the same other conditions. Comparisons of CPU time are made and it is found that for the four examples studied, the CUT can at least reduce CPU time by 15-63% with much better robustness.