Comparison of collocated methods of MCIM and PWIM for different solution algorithms in CVFEM

Abstract

The pressure-velocity coupling method of MCIM (Mass Corrected Interpolation Method) and different solution algorithms of this method were previously developed and tested for steady and unsteady incompressible flows. But the effect of under-relaxation factors in cell-face velocities and the main equations never have been investigated. On the other hand, this method and its different algorithms never have been compared with similar and more common methods in the formulation of primitive variables and non-staggered grid arrangements. In this paper, the accuracy, performance, and computational efficiency of the different solution algorithms of MCIM are compared with the well-known PWIM (Pressure Weighted Interpolation Method) of Rhie & Chow. In this study, a fully coupled, segregated approach without any pressure correction and SIMPLE-like segregated algorithms are proposed for two methods of MCIM and PWIM on the control volume-based finite element (CVFEM) framework. Also, for each method, the proper under-relaxation factors for the main equations and cell-face velocities are introduced. The accuracy and performance of the proposed algorithms are demonstrated by solving different steady and unsteady benchmark problems, and the results of both methods for different algorithms are compared. The results indicate that the both methods have spatial 2nd-order accuracy approximately and are not very different from each other. The results also show that the numerical dissipation of the MCIM is much less than PWIM. Comparing the computational cost of the different algorithms of both methods shows that the coupled algorithm of the MCIM for steady and unsteady problems with different time steps and various grid numbers is at least 10% better than other algorithms.

KEYWORDS:

• Incompressible flow
• control volume-based finite element
• pressure-based algorithm
• collocated grid
• primitive variable
• PWIM
• MCIM

Disclosure statement

No potential conflict of interest was reported by the authors.