Local and virtual RBF meshless method for high-speed flows

Abstract

Existing Computational Fluid Dynamic solutions suffer from several major limitations that prevent widespread use within the scope of many complex aerospace flow situations. These limitations include requiring significant model setup time, requiring skilled labor to generate the underlying computational grid, and requiring extensive computational resources to construct large-scale models using conventional techniques. In response to these issues, this work has developed a solution utilizing a novel Meshless method that eliminates the need for structured meshes, and thus, the need for complicated meshing procedures that demand both time and labor to complete. The presented Meshless method, which is based upon two collocation techniques, Local Radial Basis Function (LRBF) collocation and Virtual Radial Basis Function (VRBF) collocation, has shown promising results within the areas of heat transfer and elasticity, as well as incompressible and compressible fluid flow. Incorporation of an automated refinement process based on boundary and interior values provides the method with a high level of robustness with respect to initial point distribution. Additionally, the inclusion of shadow nodes in near-boundary regions allows the method to accurately capture the high gradients present in typical high-speed boundary layers. Several examples are presented within the area of high-speed flow in an attempt to highlight the ease of use, as well as the accuracy of the described techniques.