PARALLEL SPECTRAL ELEMENT METHOD FOR 3D LOCAL-SITE GROUND MOTION SIMULATIONS OF WAVE SCATTERING PROBLEM
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摘要: 针对平面波入射下三维局部场地的波动散射问题, 利用解析法实现了考虑非均匀分布谱元节点的自由场计算, 将其作为谱元波动数值模拟的输入波场. 利用高阶谱元方法模拟内域节点的运动, 采用多次透射边界(MTF)模拟边界节点的运动, 同时基于消息传递接口(MPI)技术完成跨节点的并行计算, 进而实现基于谱元法的三维散射波动问题并行模拟, 最后基于典型数值算例验证了方法的精度及稳定性表现. 结果表明: 本方法对于不同偏振方向入射体波下的局部场地三维散射问题均具有较高的模拟精度. 直至3阶MTF, 在满足内域计算稳定的前提下, 取MTF人工波速接近介质剪切波速即可实现长持时稳定计算, 而无需其他消除高频振荡的附加措施. 取较小的消飘因子即可消除MTF的低频飘移失稳且基本不影响模拟精度. 本方法在平面波入射下区域性三维地震动数值模拟分析中具有较好的应用前景.Abstract: For the wave scattering problem of 3D regional sites under plane wave incidences, the free field considering non-uniform distributed nodes of the spectral element method (SEM) is derived by using analytical method, which is used as the input wave filed for wave motion simulations based on the SEM. The motions of interior nodes are computed using the high-order SEM, and the motions of the boundary surface nodes are obtained by applying the multi-transmitting formula (MTF). In addition, a parallel computation across nodes is realized by using the Message Passing Interface (MPI) technique. Then, the parallel simulations of 3D wave scattering problems base on SEM are achieved. Finally, the accuracy and stability performance of the proposed method are validated by some typical numerical examples. The results show that the presented method can achieve high simulation accuracy for the 3D local site scattering problem under plane wave incidence in different polarization directions. Up to the third order MTF, under the condition that the stability of the internal domain computation is ensured, a long-time stable calculation results can be obtained when the artificial wave velocity of the MTF is taken to be close to the shear wave velocity of the corresponding boundary nodes, and no other additional treatments are needed to eliminate the high-frequency oscillations. The low-frequency drift instability of the MTF can be easily eliminated by applying quite small modification parameters, and the simulation accuracy is generally unaffected by it. The method of this paper has promising application prospect in the numerical simulations of regional 3D ground motion under plane wave incidences.
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图 1 三维平面波斜入射示意图
Figure 1. Schematic diagram of oblique incidence of three-dimensional plane wave
图 2 不同体波入射时的振动方向规定
Figure 2. Regulation of vibration direction under different body wave incidence
图 6 不同平面波入射时3个观测点的位移时程与解析解对比
Figure 6. Comparison of displacement time histories and analytical solutions of three observation points under plane wave incidence
6 不同平面波入射时3个观测点的位移时程与解析解对比 (续)
6. Comparison of displacement time histories and analytical solutions of three observation points under plane wave incidence (continued)
图 10 垂直入射SV波时测线1沿x分量的位移时程
Figure 10. Displacement time history of line 1 in the x component under vertical incident SV wave
图 11 2阶MTF, 施加不同小量时均匀半空间模型观测点B的位移时程
Figure 11. Displacement time history of point B of the homogeneous halfspace model when different γ values are applied (second-order MTF)
图 12 3阶MTF, 施加不同小量时均匀半空间模型观测点B的位移时程
Figure 12. Displacement time history of point B of the homogeneous halfspace model when different γ values are applied (third-order MTF)
图 13 半球形盆地模型, 施加不同小量时测点B的位移时程
Figure 13. Displacement time history of point B of the hemisperical basin model when different γ values are applied
13 半球形盆地模型, 施加不同小量时测点B的位移时程 (续)
13. Displacement time history of point B of the hemisperical basin model when different γ values are applied (continued)
图 14 长持时计算时
Figure 14. Displacement time history of observation point B of different model under long duration calculation
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