Meshless Simulation of Flows Past Airfoils with Wall-Distance-Free Turbulence Model

In this study, the wall-distance-free one-equation Wray–Agarwal (WA) turbulence model is implemented for the first time in the meshless frame for solving two-dimensional turbulent flows. Benefited by meshless and wall-distance-free flexibility, the computational domain is discretized only with clouds of points, and the spatial derivatives are approximated through weighted least-squares fitting. The convective and viscous fluxes of governing Navier–Stokes equations are usually calculated by a Roe-type upwind scheme and a central scheme, respectively. The validations of the resulting WA turbulence model-based meshless implementations are carried out for a standard turbulent flat plate flow to show the reported feature that the WA turbulence models are competitive with a two-equation SST model. A careful numerical check at the mean squared error of the eddy viscosity associated with available two-equation SST values is performed together with the mean squared error of skin-friction distribution, and indicates that such competitive ability can be further enhanced through adopting a modified model coefficient, newly formulated with a user-defined parameter within a range of variation presented. The performance of the wall-distance-free WA model is demonstrated with a typical modified model coefficient. The resulting meshless implementation of the WA turbulence model with the newly fixed coefficient is further applied to simulate turbulent flows over aerodynamic bodies like symmetric and multi-element airfoils, and the obtained results are in good agreement with available experimental data or other numerical solutions in the literature.