Influence of momentum interpolation methods on the accuracy and convergence of pressure–velocity coupling algorithms in OpenFOAM®

Checkerboard pressure is one of the most significant problems arising from the use of collocated grids for fluid dynamic simulations using the finite-volume method. The original Rhie–Chow momentum interpolation technique, termed Original Momentum Interpolation Method (OMIM) was proposed to eliminate the non-physical saw-tooth pressure oscillations. However, it was soon proved that the steady-state solutions obtained with this technique were under-relaxation factor dependent. Nevertheless, standard OMIM is still commonly used in several CFD codes like OpenFOAM®, the software used for this work. In this paper the OMIM and a possible correction for under-relaxation dependency, which has been implemented in OpenFOAM®, are discussed in detail. The proposed methodology is compared and contrasted with OMIM in terms of accuracy of the solution and speed of convergence for several classical pressure–velocity segregated algorithms for steady state solvers; namely SIMPLE, SIMPLE-C, SIMPLE-R and PISO. A classical laminar 2D cavity is used as the base test-case. The study is then extended to a more complex 2D airfoil profile (NACA0012). In the cases considered mesh uniformity and orthogonality are progressively reduced and turbulence starts playing an important role, limiting therefore the convergence of the cases and the performance of the correction.