A shock-capturing meshless scheme using RBF blended interpolation and moving least squares

Abstract

Solving the full Navier-Stokes equations requires the use of numerical methods, especially for engineering application involving complex geometry. Numerical methods commonly used today all require a mesh before a solution attempt. Developing the mesh can require expensive preprocessing time, and the quality of the mesh can have major effects on the solution. Meshless methods have become a research interest due to the simplicity of using scattered data points. Radial basis functions (RBF) interpolation is a class of meshless method, and many of these methods have been developed to solve partial differential equations. Schemes using RBF interpolation are capable of multivariate interpolation over scattered data even for data with discontinuities. A meshless method scheme is presented capable of solving the compressible Navier-Stokes equations. A blended RBF interpolation method switching between low and high shape parameter interpolation is used to approximate the inviscid fluxes, while the viscous fluxes are approximated using moving least squares (MLS).