An Effective Improved Algorithm for Finite Particle Method

The low accuracy near the boundary or the interface in SPH method has been paid extensive attention. The Finite Particle Method (FPM) is a significant improvement to the traditional SPH method, which can greatly improve the computational accuracy for boundary particles. However, there are still some inherent defects for FPM, such as the long computing time and the potential numerical instability. By conducting matrix decomposition on the basic equations of FPM, an improved FPM method (IFPM) is proposed, which can not only maintain the high accuracy of FPM for boundary particles, but also keep the invertibility of the coefficient matrix in FPM. The numerical results show that the IFPM is really an effective improvement to traditional FPM, which could greatly reduce the computing time. Finally, the modified method is applied to two transient problems.