Adaptively Refined Hybrid FDM-RBF Meshless Scheme with Applications to Laminar and Turbulent Viscous Fluid Flows

The focus of this work is to demonstrate a novel approach to true CFD automation based on an adaptive Cartesian point distribution process coupled with a Mesh less flow solution algorithm. As Mesh less method solutions require only an underlying nodal distribution, this approach works well even for complex flow geometries with non-aligned domain boundaries. Through the addition of a so-called shadow layer of body-fitted nodes, application of boundary conditions is simplified considerably, eliminating the stair-casing issues of typical Cartesian-based techniques. This paper describes the approach taken to automatically generate the Mesh less nodal distribution, along with the details of an automatic local refinement process. Also, as the primary interest of this automated CFD solver is for aerospace applications, this work includes the development of standard two-equation turbulence models for use in this Mesh less based solver. Finally, results are shown for several relevant compressible, turbulent flows example configurations, demonstrating the benefits of the automatic refinement as well as the quality of the Mesh less solutions in high-speed flow applications