数值流形方法在流固耦合谐振分析中的应用

Application of numerical manifold method in fluid-solid interaction harmonic analysis

数值流形方法(流形法)是石根华博士利用现代数学中流形分析的有限覆盖技术建立起来的新的数值分析方法,统一解决了连续和非连续变形的力学问题,具有广阔的应用前景。本文将流形法应用于交界面耦合的流固振动分析,采用平面矩形数学网格,针对无粘、无旋、不可压缩流体和无阻尼的固体结构,提出分析流固耦合系统简谐振动的高阶流形法公式,其中,采用拉格朗日乘子法引入流场的已知边界条件。本文还初步研究了在特殊的无限远流场中采用解析解覆盖函数的实现技术。文中算例体现了流形法网格划分的方便性和计算的高精度,显示出流形法在数值解和解析解联合运用上的优势。

Numerical Manifold Method （NMM）, put forward by Shi Genhua, is capable of solving continuum and discontinuum problems and has bright future. This paper presents 2D high-order NMM equations of fluid-solid interaction harmonic analysis based on rectangular mathematical meshes, concerning inviscid, irrotational, incompressable fluid field and undamped structures. Definite boundary conditions are introduced via Lagrange multiplier method. One can select various polynomial orders of structure displacement and fluid pressure field by requirement. The given results of computing frequencies and harmonic response prove the validity of the approach, and indicate that high-order NMM has high precision and convenient preprocessing. The approach of using covers of analytic solution to simulate special infinite fluid field is also proposed in the paper, which can decrease greatly the number of meshes and unknowns to be solved, and converge quickly. The given example suggests that NMM should be very suitable for combination of numerical solution and analytic solution, and more convenient than other approaches.