Solution of lid-driven cavity problems with an improved SIMPLE algorithm at high Reynolds numbers

The SIMPLE algorithm and its variants have been successfully employed to solve the driven-cavity problem at Re < 10,000. However, converged steady solutions cannot be achieved at higher Re (15,000-30,000) by SIMPLE-family algorithms owing to its inherent drawbacks. In this work, a new segregated solver, ISTEC-N (incompressible flow solver with two explicit N correction loops), for determining the solution of incompressible flow on structured collocated grid systems is proposed. A pressure equation is deduced from the discretized continuity equation to overcome the “Semi-Implicit” characteristic of the SIMPLE algorithm. An explicit velocity update loop is introduced to improve the consistency between the pressure field and the velocity field in each outer iteration. The performance of the ISTEC-N algorithm is evaluated by solving the driven-cavity problem at high Re number of (15,000 < Re < 30,000). It is shown that the ISTEC-N algorithm manifests a strong robustness feature under these high convection conditions. The computational results given by the ISTEC-N algorithm are in excellent agreement with the benchmarking data.