A second-order reproducing kernel for SPH method to enhance accuracy and consistency

Abstract

The application of smoothed particle hydrodynamics (SPH) encounters challenges related to consistency, stability, and accuracy. Inconsistencies in SPH arise from non-uniform particle distribution and a lack of neighboring particles at the boundary, leading to numerical instability and inaccurate particle approximations. Various methods have been proposed to address these issues. One such framework is the corrected SPH, designed to ensure consistency of the method. In this work, performance of some correction procedures are analysed through gradient calculations of a function. The root mean square error of the gradient approximation is analysed to justify the method’s convergence and accuracy