Accuracy Improvement of Smoothed Particle Hydrodynamics

Abstract

The smoothed particle hydrodynamics (SPH) is a mesh-free particle method, which has been successfully applied to a wide range of astrophysical problems. So far, the SPH method has been extended to elastic dynamics and computational fluid dynamics. High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. The present paper proposes a novel method to improve the accuracy of SPH method by the lemma proved by the authors. The proposed method shows the relationship between the selected functions and their SPH approximations. In addition, error comparisons are made between SPH methods with and without the improvement.