A reconstruction method for finite volume flowfield solving based on incremental radial basis functions

A reconstruction method of flow field solving, based on incremental RBF (Radial Basis Functions) interpolation, has been developed in the paper. Since the fluctuation of flow parameters in the stencil cells used to reconstruct is small compared with the mean value in flow field reconstruction, direct RBF reconstruction will bring large numerical oscillations. The incremental RBF reconstruction developed in this paper effectively improves convergence and stability of the interpolation scheme. In first example, a simple one-dimensional model is used to illustrate the effective of this method when the fluctuation of the objective function is much smaller than the mean value. Furthermore, applicability and effectiveness of incremental RBF reconstruction method is proved by using four typical flow fields, namely, two-dimensional subsonic, transonic inviscid steady flow fields around NACA0012, the viscid unsteady flow around a stationary cylinder and a Mach 3 wind tunnel case with a step problem. Research shows that incremental RBF reconstruction method can smoothly capture steep shock and effectively improve the convergence and stability of flow solver with small numerical dissipation and high computational efficiency.