光滑点插值法应用于流固耦合的比较研究

针对传统有限元法（FEM）固体模型刚度过硬导致低阶单元求解精度较低的问题，采用光滑点插值方法（S-PIM）. S-PIM得益于梯度光滑技术能软化固体模型刚度，基于容易剖分的线性背景网格能改善固体求解精度. 采用不同的光滑域构建方式可以得到不同的固体求解器，从而在不同程度上提高计算精度. 本研究以浸没光滑点插值法（IS-PIM）为基础，在流固耦合（FSI）模型中采用较成熟的半隐式特征分离法（CBS）作为流体求解器，分别采用有限元法、边基光滑点插值方法（ES-PIM）以及点基局部光滑点插值方法（NPS-PIM）作为固体求解器，比较不同固体求解器条件下的计算精度和效率. 结果表明，与边基光滑点插值方法和有限元法相比，在流固耦合模型中采用点基局部光滑点插值法可以得到更准确的固体模型刚度，也更有利于计算精度和计算效率的提高.

Comparative study of application of smoothed point interpolation method in fluid-structure interactions

The traditional finite element method (FEM) suffers the low accuracy problems for low order elements due to the overly stiffness problem in solid model. Thus, the smoothed point interpolation method (S-PIM) was employed. S-PIM has been proved to be able to soften solid stiffness through the gradient smoothing operation, and improve the accuracy of solving solid problems by using the linear background mesh, easily to be meshed. Different solid solvers can be got by different ways of constructing smoothing domains, improving the computational accuracy differently. In the framework of immersed smoothed point interpolation method (IS-PIM), the semi-implicit characteristic-based split (CBS) procedure was used as fluid solver in fluid-structure interactions (FSI) model, the performance of different solid solvers, including FEM, edge-based smoothed point interpolation method (ES-PIM) and the node-based partly smoothed point interpolation method (NPS-PIM), were compared to each other in terms of accuracy and efficiency. Results show that the NPS-PIM can get more accurate stiffness of solid model, and get better results in computational accuracy and computational efficiency comparing with ES-PIM and FEM.