The Measure Against High Frequency Oscillating Instability of Multi-transmitting Formula
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摘要: 多次透射公式（MTF）物理概念简单，便于在计算机上实现时空解藕的高精度波动数值模拟。然而，MTF与其它局部人工边界条件类似，存在数值模拟失稳问题，如高频振荡便是可能出现的失稳现象。本文在分析MTF高频振荡失稳机理的基础上，提出了在波动有限元数值模拟中消除MTF高频振荡失稳的一种措施，即在整个有限元数值模拟区内施加与应变速率成正比的较小粘性阻尼；同时，讨论了这一稳定措施的有效性及其对数值计算精度的影响，并通过数值试验检验了这一稳定措施的可行性。结果表明，消除高频振荡失稳的措施行之有效，且只对波动有限元数值模拟中无意义的高频分量具有抑制作用，而对有意义的较低频段内的波动有限元数值模拟精度影响较小。Abstract: Multi-Transmitting Formula (MTF) based on one-dimensional description on general kinematic characteristics of one-way wave and direct numerical simulation has simple physical concepts, and it is easy to realize the high precision and decoupling wave motion numerical simulation on the computer. However, Multi-Transmitting Formula, similar as other local artificial boundary conditions, is also a local artificial boundary condition which existed numerical instability problems, in which high-frequency oscillation instability is one of the instability phenomenon. Through the discussion of the mechanism of high frequency oscillation instability of Multi-Transmitting Formula, we present a measure to eliminate high frequency oscillation instability in wave numerical simulation. Through numerical simulation, the feasibility of the stabilization measure is verified. The results show that this stabilization measure is effective and of significantly cutting effectiveness on high-frequency component that is meaningless for wave motion numerical simulation. However, its effect on the wave motion numerical simulation was too small to ignore in the lower frequency band.
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Key words:
- One-way wave /
- Viscous damping /
- Numerical simulation /
- The scattering problem /
- Source problem
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图 1 MTF数值模拟高频振荡失稳
Figure 1. High-frequency oscillation instability by MTF numerical simulation
图 2 归一化竖向近似脉冲力时程
Figure 2. Time-history of the normalized vertical approximate pulse force
图 3 竖向近似脉冲力作用下作用点处的位移反应时程
Figure 3. The displacement reaction of the point under the normalized vertical approximate pulse force
图 4 引入措施后竖向近似脉冲力作用下作用点处的位移反应时程
Figure 4. The displacement reaction of the point under the normalized vertical approximate pulse force which can eliminate high-frequency oscillation instability
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