动水压力波高阶双渐近时域平面透射边界Ⅱ:计算性能  

High-order doubly asymptotic time-domain plane transmitting boundary for hydrodynamic pressure Ⅱ. Computational performance

作　　者：王翔[1] 金峰[1] 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《水利学报》2011年第8期986-994,共9页Journal of Hydraulic Engineering

基　　金：国家自然科学基金重点项目(90510018);国家自然科学基金重大研究计划(90715041)

摘　　要：为了阐明动水压力波高阶双渐近平面透射边界在时域内的计算性能,本文从时域求解、稳定性、收敛性、计算精度和计算效率等方面对其进行了研究和验证。为了提高计算效率,通过空间模态解耦将原时域高阶透射边界的求解转化为一系列单模态透射边界的求解。常微分方程系数矩阵的广义特征值分析表明,本文发展的高阶双渐近边界是渐近稳定的。高阶双渐近边界的等价频域动力刚度表达的误差范数分析显示,连分式逼近的计算误差会随着阶数的增加迅速下降,计算结果快速收敛于准确解。刚性坝算例表明,在计算精度相当的情况下,高阶双渐近透射边界与远置Sommerfeld边界方法相比在计算效率上有数量级的提高,并且还具备长期计算误差发展稳定的特点。上述研究和验证算例揭示了本文发展的高阶双渐近时域平面透射边界所具备的优良计算性能,可以考虑将其进一步应用到大坝水库动力相互作用分析中。To illustrate the computational performance of high-order doubly asymptotic time-domain plane transmitting boundary for hydrodynamic pressure, some research and verification are done on its solution method in time domain, stability, convergence, computational accuracy and computational efficiency. First, to improve the computational efficiency, the original high-order boundary is converted into a series of single-mode transmitting boundaries by employing the modal decoupling in space. Second, the study on the eigenvalues of coefficient matrices of the ordinary differential equation indicates the presented high-order doubly asymptotic boundary is asymptotic stable. Third, the analysis of error norm for the equivalent dynamic stiffness expression in frequency domain of the high-order doubly asymptotic boundary presented in this paper shows that the computational error of the continued-fraction approximation will decay rapidly as its order increases and the computational results converge into the exact solution quickly. Forth, the numerical example on a rigid dam shows the high-order doubly asymptotic boundary has an improvement in order of magnitude in the aspect of computational efficiency compared with the method locating the Sommerfeld boundary at a distance under a close computational accuracy and a characteristic of a stable long-time computational error level. The above research and numerical example reveal the excellent computational performance owned by the high-order doubly asymptotic time-domain plane transmitting boundary developed in this paper. It is probable to apply it to the dynamic interaction analysis of dam and reservoir further.

关 键 词：透射边界 双渐近 动水压力 高阶边界 比例边界有限单元法 

分 类 号：TV131.1[水利工程—水力学及河流动力学]