Comparison of different solution algorithms for collocated method of MCIM to calculate steady and unsteady incompressible flows on unstructured grids

In this paper, the collocated method of MCIM (Mass Corrected Interpolation Method) is employed for solving two-dimensional incompressible flows on unstructured grid systems. A control-volume-based finite element (CVFEM) approach has been taken in which conservation equations are formed for each control volume throughout the solution domain. In this study, three different algorithms are proposed and investigated. In the first algorithm a fully coupled formulation is used, however in the second algorithm a segregated approach without pressure correction is employed. In the third solution algorithm, the scheme of MCIM is implemented to SIMPLE-like segregated algorithm. The linear system of equations obtained in these algorithms is solved using a direct sparse solver. The accuracy and performance of the proposed algorithms are demonstrated by solving different steady and unsteady benchmark problems.