透射边界高频失稳机理及其消除方法——SH波动

MECHANISM OF HIGH FREQUENCY INSTABILITY CAUSED BY TRANSMITTING BOUNDARY AND METHOD OF ITS ELIMINATION——SH WAVE

用有限元法求解近场波动问题,须选取人工边界条件以实现对无限域稳定、高效的数值模拟.该文探讨了SH波导有限元数值模拟中透射边界引发的高频失稳问题.从离散模型出发,分析了内节点与人工边界节点运动方程频散曲线之间的匹配关系,揭示了高频失稳的一种机理,即二者相互耦合所得计算方案支持自发从人工边界向计算区域内行进的高频波动.提出通过调整内节点运动方程以改变这一匹配关系,从而消除失稳的措施.理论分析与数值结果表明该措施能有效地消除高频振荡失稳.

To solve near-field wave problems by finite element method, absorbing boundary conditions were needed to simulate the unbound field robustly and efficiently. Taking numerical simulation of wave motion in SH waveguide as an example, high-frequency instability caused by transmitting boundary were discussed. Directly from discrete model, mechanism of instability was found by analyzing the matching relationship of motion equations of interior nodes and nodes on absorbing boundary. Results showed that instability was caused by high frequency wave, which was allowed to enter continuously from the absorbing boundary into the computational region without excitation. Thus an approach of eliminating such instability was proposed by adjusting the motion equations of interior nodes to change the matching relationship. Theoretical and numerical results showed that the present approach was efficient.