基于预处理方法的风与膜结构流固耦合效应研究

Study on fluid-structure interaction of wind and membrane structures based on preconditioning

采用强耦合整体方法求解风与膜结构的流固耦合作用在精度和稳定性方面都具有优势,但求解强耦合整体方程时的巨大机时耗费成为了限制其应用的主要问题之一。本文提出采用预处理的方法处理Newton-Raphson方法线性化后的强耦合整体方程,以改善矩阵的条件数,提高计算效率和精度。强耦合整体方程中采用了线弹性有限元模型处理流体域的变形,结合强耦合整体方程,在雅可比矩阵中使用块状结构,推导了指定边界条件的线弹性模型预处理矩阵以及强耦合整体方程的预处理矩阵。基于广义极小残余法(generalized minimum residual,简称GMRES),给出了采用预处理的强耦合整体方法的求解步骤。最后将该方法应用于风与膜结构的流固耦合分析,比较了采用预处理前后的相关参数变化,结果表明采用预处理方法后计算精度和效率大大提高,计算时间节约40%以上。结果表明预处理方法在强耦合整体方法中的采用是稳定有效的。

The monolithic strongly coupled method has an edge in accuracy and stability in computing fluid-struc- ture interaction of wind and membrane structures. However, huge computational cost is among the restrictions for its application. A preconditioner is proposed to deal with the linear equations produced by employing Newton-Raph- son method, to improve the condition number of coefficient matrix, and enhance the computation efficiency and ac- curacy. Linear-elastic model is employed to manage the fluid deformation. Combined with monolithic strongly cou- pled equations, block structures are adopted in Jacobian matrix, and preconditioning matrix of linear-elastic model with prescribed boundary conditions and monolithic strongly coupled equations. Based on generalized minimum re- sidual, GMRES for short procedures for monolithic strongly coupled method with preconditioner is presented. Final- ly, the method is applied to fluid-structure interaction of wind and membrane structures. Comparisons are made be- tween results with preconditioner and without preconditioner. The results show that preconditioner can greatly im- prove computational accuracy and efficiency, with computational time saving over 40%. Preconditioner in solving monolithic strongly coupled equations is effective and robust.