A Meshless Hybrid Method for Convection-Dominated Problems in Curvilinear Unbounded Domains

Abstract This paper presents a meshless hybrid Generalized Finite Difference-Radial Basis Function (GFD-RBF) framework for the numerical solution of convection-dominated partial differential equations (PDEs) in unbounded domains with curvilinear geometry. The method employs GFD for approximating the convective terms and RBF technique for the diffusive terms, thereby preserving the complementary strengths of both approaches and enabling a robust and accurate discretization of the governing equations. The Navier-Stokes equations are solved directly in physical domain, thereby avoiding coordinate transformations and the associated complexities of metric coefficients and Jacobian evaluations. The proposed scheme is applied to simulate flow over bluff bodies in unbounded domains, capturing key flow features in good agreement with results reported in the literature. The convergence behavior of the discretized system resulting from the hybrid method is analysed and the order of accuracy of the results is also presented. Overall, these results highlight the robustness, accuracy and flexibility of the hybrid method, making it a promising method for a wide class of convection-dominated problems in curvilinear unbounded settings.