Study on the smoothed particle hydrodynamics method

Smoothed particle hydrodynamics (SPH) is an effective method for modeling problems involving large deformation. However, particle inconsistency can lead to low accuracy. The kernel function estimation and its first derivative estimation are investigated in the smoothed particle hydrodynamics method. The discrete scheme of the conventional and the corrective SPH (CSPH) methods are introduced. Based on Taylor series expansion, modified SPH (MSPH) method is proposed. The discrete forms of the function and the first derivative estimations of the kernel function are deduced in both one and two dimensional space. Then several numerical examples are carried out to compare the accuracy of the three different methods. The results show that CSPH and MSPH can both improve the numerical accuracy effectively, especially at the points near the boundary of a domain. In two dimensional cases, the accuracy of MSPH method is higher than that of CSPH method.