A robust hybrid meshless method for Navier–Stokes equations

In this paper, a hybrid Generalized Finite Difference-Radial Basis Function (GFD-RBF) meshless method is developed for the incompressible Navier-Stokes equations. The method is applied to the three-sided lid-driven cavity flow in a square domain involving complex flow features, and results are obtained for Reynolds numbers up to 10, 000 for the first time. Additionally, the proposed approach captures a third secondary vortex at 𝑅 ⁢ 𝑒 = 1 ⁢ 0 0 0 for the parallel motion of the opposite walls, representing a flow feature that has not been previously reported in the literature. The hybrid formulation preserves the complementary strengths of both methods, enabling a stable and accurate discretization of the governing equations. This is verified through the analysis of the convergence behavior of the resulting discretized system. The order of accuracy of the results obtained using the hybrid meshless method is also presented. Furthermore, the hybrid scheme exhibits favorable computational efficiency by achieving converged solutions on relatively coarse nodal distributions, highlighting its efficiency for nonlinear convection-dominated problems.