Improvement of SIMPLER algorithm for incompressible flow on collocated grid system

In this article an Improved SIMPLER (CLEARER) algorithm is proposed to solve incompressible fluid flow and heat transfer problems. Numerical study shows with the CLEARER algorithm on a collocated grid, in the correction stage the velocities on the main nodes are overcorrected with the pressure correction, which lowers the convergence rate; hence a second relaxation factor is introduced to overcome this disadvantage. By setting this factor less than the underrelaxation factor for velocities, the convergence performance can be significantly enhanced; meanwhile, the robustness can also be increased. Four numerical examples with reliable solutions are computed to validate the CLEARER algorithm, and the results show that this algorithm can predict the numerical results accurately. Compared with the SIMPLER algorithm, CLEARER can enhance the convergence rate greatly, and in some cases it only needs as little as 17% of the iterations required by SIMPLER to reach the same convergence criterion.