An improved meshfree scheme based on radial basis functions for solving incompressible Navier–Stokes equations

In this paper, an improved meshfree scheme based on radial basis functions (RBFs) is provided for solving the incompressible viscous Navier–Stokes equations and two enhancements are proposed to mitigate the typical numerical oscillations. The first one is the combination of the RBFs-based finite difference (RBF-FD) method with the semi-Lagrangian RBFs (SLM-RBF), with the former being used for the viscous diffusion term and pressure Poisson equation and the latter being used for the advection term. The second enhancement is a regularization term that constructs smooth constraints for RBFs interpolations instead of clipping operations. The capability of the proposed scheme in mitigating numerical fluctuations is demonstrated by validating it against the one-dimensional (1-D) advection problem and the advection–diffusion problem with step field functions. The overall performance of the proposed scheme is also validated by the lid-driven cavity flow and laminar flow around a circular cylinder, showing good agreement with the existing results, indicating that the proposed scheme has good stability in both temporal and spatial domains.