基于无滑移边界条件的SPH方法研究

在回顾了SPH无滑移边界条件施加方法的基础上,针对Ellero等人提出的无滑移边界处理方法,结合两次导数求解粘性项,分析了利用该方法求解Poiseuille流模型时遇到的不稳定问题,包括数值误差引起的不稳定问题和边界粒子场变量更新方式引起的不稳定问题,提出了相应的解决方案并对其方法进行了一定的改进,获得了更加精确的计算结果。最后尝试了一种与改进边界处理方法等效的方法,并利用Poiseuille流模型进行了验证。

Study of no-slip boundary conditions for SPH method

Based on the reviewing of the implements of no-slip boundary conditions for SPH method, it combined the method brought by M. Ellero and viscosity solved by second derivative and analyzed the instability problems which were brought by numerical errors and different evolution methods of the boundary particles when M. Ellero's method was imposed on Poiseuille flow. And then it put forward corresponding resolve methods and some improvements of M. Ellero's method and got more accurate results. Finally, attempted an equivalent method to the improved method and validated by Poiseuille flow.