Improvement of an interpolation scheme used for discretization of Navier–Stokes equations

The FLow-oriented interpolation scheme (FLO scheme) is widely used in the control volume finite element method (CVFEM) for discretizing Navier–Stokes equations (considering triangular finite element meshes). The FLO scheme is designed to avoid the appearance of numerical instabilities for dominant convective problems, as it responds appropriately to Peclet number values. In this paper, cases of 2D laminar flow in a square cavity (Re = 1000) and 2D laminar flow crossed with a circular cylinder (Re = 40) were used to test a modified FLO scheme that uses the average triangular element length for Peclet number calculation. To perform the simulations, the Navier–Stokes equations were discretized with CVFEM and a computational fluid dynamics (CFD) code was programmed in the Matlab software language. The results obtained from the simulations indicated that the modified FLO scheme is more accurate for predicting the 2D laminar flow field than its traditional version.