COMPARISON OF DISCRETISATION SCHEMES FOR CONVECTION TERMS IN THE NAVIER-STOKES EQUATIONS IN OPENFOAM SOFTWARE

Abstract

Laminar vortex shedding behind a circular cylinder is a canonical benchmark for validating numerical methods, yet quantitative predictions at moderate Reynolds numbers remain sensitive to the discretization of convective terms. In opensource CFD frameworks, the wide choice of advection schemes introduces a trade-off between numerical diffusion, dispersion, stability, and boundedness. The objective of this study is to evaluate how different advection discretization schemes available in OpenFOAM influence the accuracy of force coefficients, shedding frequency, and wake structures for two-dimensional incompressible flow past a circular cylinder at Reynolds number Re = 200. The flow is simulated using the transient incompressible solver pimpleFoam on a structured O-type grid, with mesh and time-step independence verification. A consistent computational setup is employed while comparing a range of schemes, including linearUpwind, limitedLinear, cubic, limitedCubic, MUSCL, and SuperBee, including their vector-based (‘V’) variants. The influence of gradient limiters on the solution is studied. The performance is assessed by comparing drag and lift coefficients, Strouhal numbers (St), and the qualitative resolution of vorticity contours against established experimental and numerical data. The results indicate that the choice of scheme profoundly impacts solution fidelity. High-resolution schemes such as MUSCLV and SuperBeeV yielded force coefficients that deviated significantly from reference values, while standard limitedLinear and limitedCubic schemes resulted in under-predictions due to excessive numerical diffusion. However, the use of vector-based limiters noticeably improved accuracy. Among the tested numerical schemes, linearUpwind and linearUpwindV offers the most consistent balance between accuracy, stability, and smooth wake resolution. Furthermore, these were the only schemes capable of resolving smooth, undistorted vorticity contours in the wake, whereas others introduced significant unphysical distortions. These results highlight the critical role of advection scheme selection in vortex-dominated flows. The paper provides practical recommendations for reliable modeling of incompressible fluid flows using OpenFOAM.