Assessment of implicit adaptive mesh-free CFD modelling

This work presents details and assesses implicit and adaptive mesh-free CFD modelling approaches, to alleviate laborious mesh generation in modern CFD processes. A weighted-least-squares-based, mesh-free, discretisation scheme was first derived for the compressible RANS equations, and the implicit dual-time stepping was adopted for improved stability and convergence. A novel weight balancing concept was introduced to improve the mesh-free modelling on highly irregular point clouds. Automatic point cloud generations based on strand and level-set points were also discussed. A novel, polar selection approach, was also introduced to establish high-quality point collocations. The spatial accuracy and convergence properties were validated using 2D and 3D benchmark cases. The impact of irregular point clouds and various point collocation search methods were evaluated in detail. The proposed weight balancing and the polar selection approaches were found capable of improving the mesh-free modelling on highly irregular point clouds. The mesh-free flexibility was then exploited for adaptive modelling. Various adaptation strategies were assessed using simulations of an isentropic vortex, combining different point refinement mechanisms and collocation search methods. The mesh-free modelling was then successfully applied to transonic aerofoil simulations with automated point generation. A weighted pressure gradient metric prioritising high gradient regions with large point sizes was introduced to drive the adaptation. The mesh-free adaptation was found to effectively improve the shock resolution. The results highlight the potential of mesh-free methods in alleviating the meshing bottleneck in modern CFD.