透射边界高频失稳机理及稳定实现--P-SV波动

Mechanism of high frequency instability and stable implementation for transmitting boundary-P-SV wave motion

波动数值模拟的稳定性是获得可靠结果的前提.透射边界是一类具有高阶、高效等特点的人工边界,其引发的高频失稳是由内域格式和透射边界的不当耦合所致.本文针对P-SV波动有限元模拟中透射边界引发的失稳问题,基于GKS定理的群速度解释,通过对有限元和透射边界的频散分析揭示了数值失稳机理为透射边界和相邻内域格式支持了群速度指向内域的高频P波或SV波,波动能量将从边界进入内域引发数值失稳.同时,对比连续模型频散指出引发失稳的谐波是由有限元离散引入.本文采用修改的数值积分方法调整有限元刚度,以消除有限元中引发边界失稳的高频波动成分,从而稳定实现透射边界.理论分析和数值实验均表明本文稳定措施的有效性.

The stability of wave numerical simulation is the premise of obtaining reliable results.Transmitting boundary is a kind of artificial boundary with high order and high efficiency,but there exists high frequency instability induced by the improper coupling between the interior scheme and artificial boundary scheme.Aiming at the instability problem caused by transmitting boundary in the finite element simulation of P-SV wave motion,based on the group velocity interpretation of GKS theorem,the mechanism of instability is further clarified by the dispersion analysis of finite element and transmitting boundary scheme.The mechanism is that the interior scheme and artificial boundary scheme support high frequency P wave or SV wave whose group velocity points to interior domain,thus wave energy is allowed to enter interior domain spontaneously from artificial boundary to cause instability.At the same time,compared with the dispersion of the continuous model,it shows that the high frequency wave components leading to instability are introduced by the finite element discretization.In order to eliminate the above wave components,modified integration rules are used to change the stiffness of the finite element.Theory analysis and numerical experiments show that the proposed stabilization measures can ensure transmitting boundary to be implemented stably.