Gradient reconstruction on Voronoi meshes for finite-volume source-term evaluation: Accuracy and computational cost

Eight cell-centred gradient reconstruction operators are benchmarked on Cartesian, hexagonal and random Voronoi meshes, using four analytical field configurations and six refinement levels. Gradient accuracy, reconstructed source-term accuracy and the per-cell cost of repeated evaluations on a fixed mesh are the comparison criteria. Mesh topology controls the ranking: the inverse-distance-squared weighted least-squares operators, including the QR-based variant, are the most robust on irregular meshes, whereas the Green–Gauss family and the curvilinear operator depend on stencil regularity. At random-mesh boundary cells the least-squares operators carry a source-derivative penalty, so the cost–accuracy trade-off depends on whether boundary accuracy is a primary objective.