A high-order SPH method by introducing inverse kernels

The smoothed particle hydrodynamics (SPH) method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square (LS) and Moving-Least-Square (MLS) methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.