FPM改进算法及在应力波传播问题中的应用

有限粒子法(FPM)是传统SPH方法的重要发展,大大提高了边界区域粒子的计算精度。然而在迭代计算过程中,高耗时和潜在的数值不稳定性是制约FPM应用的关键因素。通过对FPM基本方程进行矩阵分解,建立了一种特殊格式的FPM改进算法。该方法保持FPM方法在边界区域较高计算精度的同时,成功地规避了传统FPM方法对系数矩阵可逆性的限制,大大提高了计算效率。最后,将改进算法在一维应力波传播问题中予以实现,获得了较好的数值结果。

A specified improved algorithm for Finite Particle Method and i ts application to wave propagation

Finite Particle Method (FPM ) is a significant improvement to the traditional SPH method , which can greatly improve the computational accuracy for boundary particles .However ,in the iteration process ,long computing time and potential numerical instability are the key factors restricting the appli‐cation of FPM .By conducting matrix decomposition and structural analysis on the basic equations of FPM ,a Specified FPM method (SFPM ) is proposed ,w hich can not only maintain the high computational accuracy of FPM for boundary particles ,but also avoid the restriction on the invertibility of the coeffi‐cient matrix in traditional FPM and greatly reduce the computing time .Finally ,SFPM method is applied to the one‐dimensional stress wave propagation problem ,and the ideal simulation results show that SFPM is an effective improvement for traditional FPM .