Numerical simulation of 2D forced convection problems via coupled generalized finite difference and projection methods

A meshless framework coupling the generalized finite difference method (GFDM) with a first-order projection scheme is developed for two-dimensional laminar forced-convection problems. The incompressible Navier–Stokes and energy equations are discretized on nodal clouds without background cells or domain integration. The formulation incorporates consistent treatments of the local GFDM operators, pressure boundary conditions, wall-gradient reconstruction, and steady-state marching. Three benchmarks involving a backward-facing step, a T-shaped channel, and a periodically grooved channel are examined. Validation is performed using velocity and pressure fields, reattachment length, local Nusselt numbers, node-density studies, and conservation diagnostics. The velocity and heat-transfer results follow the trends reported in published numerical and experimental studies over the tested laminar range 10 ≤ Re ≤ 1076 . The largest discrepancies occur near non-smooth corners, where wall-normal gradient reconstruction is most sensitive. The inlet–outlet mass imbalance decreases with node refinement, whereas both the root-mean-square and maximum pointwise divergence norms increase with node refinement across all benchmarks. The results demonstrate that the coupled GFDM-projection formulation provides a meshless nodal framework for simulating flow separation, recirculation, pressure loss, and local wall heat transfer in geometrically non-smooth two-dimensional domains.