An improved specified finite particle method and its application to transient heat conduction

Compared with the traditional Smoothed Particle Hydrodynamics (SPH), Finite Particle Method (FPM) has higher accuracy for boundary region. However, there are still two inherent defects which are the time consuming and the numerical instability in FPM. In this paper, a high-order algorithm based on the Taylor series expansion and the matrix theory is proposed and the corresponding particles selected mode is discussed. It is validated that the algorithm has higher-order accuracy than the previous low-order improvement algorithm for FPM. Further, transient heat conduction examples have been discussed to verify the feasibility and effectiveness of the new algorithm.