Restoring particle consistency in smoothed particle hydrodynamics

Though the smoothed particle hydrodynamics (SPH) method has been widely applied to different areas, it is associated with some inherent numerical problems. One notable problem is the particle inconsistency that results from the particle approximation process and can lead to low approximation accuracy. In this paper, the particle inconsistency problem is investigated and some methods to improve the particle inconsistency are discussed. A new approach is proposed to restore the particle consistency. The new approach retains the conventional non-negative smoothing function instead of reconstructing a new smoothing function. A series of numerical studies have been carried out to verify the performance of the new approach. It is found the new approach can successfully restore the particle consistency and can therefore significantly improve the approximation accuracy.