Effects of Grid Arrangement and Convection-Scheme Discretisation on Projection-Method Accuracy for the Lid-Driven Cavity: A Verification Study

Published verification studies of the lid-driven cavity rarely isolate how much of a solver’s accuracy comes from grid arrangement versus convection-term discretisation, since most report only a single configuration. This study reports a systematic 2×2 verification comparison – collocated versus staggered (MAC) grid arrangement, crossed with first-order upwind versus second-order TVD (Van Leer) convection discretisation – for a projection-method solver at Re = 100, all four variants validated against Ghia et al. (1982) using an identical quantitative error metric (cubic interpolation onto the benchmark’s sample points, maximum absolute deviation). All four variants agree with the benchmark to within approximately 1% in both velocity components, with TVD improving on upwind in at least one component, consistent with reduced numerical diffusion. A companion 1D screening study compares five convection schemes (up-wind and four TVD limiters – minmod, Van Leer, superbee, MC) on a linear advection test using both an L2 accuracy metric and overshoot/undershoot as a monotonicity metric, giving an a priori, quantitative basis for selecting Van Leer over the more diffusive minmod or the less monotonic superbee and MC. A collocated-grid TVD configuration previously reported by the author to exhibit pressure-solver convergence difficulty is re-examined and found to converge cleanly, achieving the lowest v-velocity error of all four configurations tested – a result discussed alongside the checkerboard-pressure-mode literature for collocated grids (Rhie and Chow, 1983).