Compact scheme based on the simpler algorithm for steady incompressible flow problems

A new compact scheme based on the SIMPLER algorithm is developed for solving steady flow problems on three different coordinate systems. The compact corrective source term based on a compact and upwind formulation can be calculated by a deferred correction technique. The developed method is used to simulate some typical steady flow problems, including lid-driven flow, fully developed flow in a pipe, and channel flow with multiple obstacles. There are good agreements between the present results for coarser grids and the benchmark solutions. The numerical results indicate that the compact scheme is an efficient method for solving flow problem and has higher-order accuracy.