流-固耦合问题的精细积分求解法

Precise Integration Method for Solving Fluid-Solid Coupling Problems

为了解决流-固耦合动力学求解效率和精度低等问题,提出了增维精细积分法.根据有限元理论推导流-固耦合方程,将流-固耦合方程改写成状态空间形式,在矩阵仅增加1维的情况下将积分运算转化为代数运算,扩大了精细积分法的应用范围,从而得到增维矩阵的流-固耦合精细积分求解.同时,将增维精细积分法与Newmark法的计算结果进行对比,以验证其有效性.结果表明,由于不用求解矩阵H的逆矩阵,增维精细积分法避免了矩阵奇异带来的计算解的不稳定性.增维精细积分法与Newmark法的计算结果较吻合,且其在较大计算时间步长条件下的计算精度较高.

In order to solve the problem of poor efficiency and low accuracy in solving fluid-solid coupling problems, the method of increasing dimension precise integration is introduced. According to the finite ele- ment theory, fluid-solid coupling equation can be derived; then the equation is written in the form of state space. The dimension of augmented matrix only enlarges one, and the integration is transformed into alge- braic operation. It expands the scope of application of the precise integration method. The results show that because the inverse matrix of the iteration matrix/t need not be solved, the instability of the computa- tional solution caused by the singularity of the matrix is avoided. By comparing the results calculated by using the augmented precise integration method and the Newmark method, the results of the two ones are consistent, and in the case of a larger computation time step the proposed method does not affect the accu- racy of calculation.