风与柔性结构流固耦合作用的预处理方法研究

针对强耦合方法求解风与柔性结构流固耦合作用时,大量计算资源都耗费在对强耦合方程求解中这一弊端,本文研究了强耦合方程的预处理求解方法。在风与柔性结构流固耦合作用的强耦合整体方程的基础上,将时空离散和线性化后的类似结构方程看成是鞍点问题,首先推导得到了类似结构方程的预处理矩阵;再基于此推导出了强耦合整体方程的预处理矩阵。首先采用预处理方法对经典二维流固耦合问题进行了计算,验证了提出的预处理矩阵的正确性;然后对风与三维膜结构的流固耦合作用进行了分析,评估了所提出预处理方法的相关计算参数。计算结果表明,所提出的预处理方法可使强耦合整体方程的求解在计算精度和计算效率上都得到较大提升,证明本文提出的预处理方法适用于风与柔性结构的流固耦合分析。

Study on pre-treatment method of fluid-solid coupling of wind and flexible structures

Aiming at the disadvantages of a large number of computational resources in the solution of strong coupled equations for the coupled solution of wind and flexible structures by strong coupling method,this paper studies the preprocessing method for strong coupled equations.The linear elastic equation is introduced to deal with the deformation of the fluid domain,and the strong coupled global equation of fluid-solid coupling between wind and flexible structures is derived.The linear elastic equations with time-space discrete and linearized are regarded as the saddle point problem.The pre-processing matrix of the linear elastic equation is derived.Then the pre-processing matrix of the strongly coupled global equation is derived to simplify the solution.Firstly,the pre-processing method is used to calculate the classical two-dimensional fluid-solid coupling problem,and the correctness of the proposed pre-processing matrix is verified.Then the fluid-solid coupling between wind and three-dimensional membrane structures is analyzed,and the performance of the proposed pre-treatment method is evaluated.The calculation results show that the proposed pre-processing method greatly improves the efficiency of the strongly coupled equations,and proves the applicability of the pre-processing method for the fluid-solid coupling analysis of wind and flexible structures.