Gridless method for Navier-Stokes equations with high Reynolds number

A gridless method for simulating high Reynolds number viscous flows is developed. Considering the characteristics of high Reynolds number viscous flows, a normal directional advancing layer method is adopted to generate points and combine anisotropic clouds of points in the boundary region, and a quadrantal point infilling strategy is employed to construct isotropic clouds of points in the residual flow region automatically. According to the difference of structure between the anisotropic and isotropic clouds of points, a uniform format for calculating spatial derivatives based on AUSM⁺-up scheme is proposed by Green's formula and local least-squares fit method. Baldwin-Lomax turbulence model is used to enclose Reynolds-averaged Navier-Stokes equations. Time is advanced by an implicit Gauss-Seidel relaxation procedure which is constructed by the first-order linearizing of flux vector and the maximal eigenvalue splitting of flux Jacobi matrix. To demonstrate the validity and practicality of the presented gridless method, high Reynolds number viscous flows around the NACA0012 airfoil, RAE2822 airfoil and 2D cylinder are simulated, and the comparisons between computational results and the experimental data are also presented.