有限粒子法计算精度的敏感性分析

有限粒子法(FPM)是一种特殊格式的无网格SPH方法,可在计算流体力学领域中应用。无网格方法的计算精度和稳定性通常会受到核函数形式及光滑长度的影响。一方面,选取常用的高斯型、二次和三次B样条核函数,针对FPM方法再生k阶多项式的数值算例对核函数形式的敏感性进行了分析。另一方面,设置不同的光滑长度,对传统SPH方法和FPM方法计算精度随光滑长度变化的敏感性进行了对比分析。数值结果表明,FPM方法对核函数形式和光滑长度的敏感性较低,在工程应用中具有更广的适用范围和较强的鲁棒性。

Sensitivity analysis on the computational accuracy by using Finite Particle Method

Finite Particle Method is a special format of meshfree Smoothed Particle Hydrodynamics method, which has some applications in Computational Fluid Dynamics. Computational accuracy and stability of meshfree methods are usually affected by the form of the kernel function and the smooth length. On the one hand, by selecting the commonly used Gaussian kernel, quadratic kernel and cubic B-spline function, the sensitivity of FPM to the kernel function is analyzed based on the simulation on the reproducibility of k-order polynomial. On the other hand, by setting different smooth lengths, the sensitivities are compared between conventional SPH and FPM method. Numerical results show that, FPM method is less sensitive to the kernel function and smooth length, and thus should have a wider range of applications and stronger robustness in engineering.