Accurate Mesh Generation of Undulating Interface Based on Truegrid and the Ground Motion Simulation
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摘要: 利用谱元法的规则六面体单元进行网格剖分时，界面起伏较大处会出现阶梯状网格而导致模拟时产生数值散射。为消除阶梯状网格对起伏界面地震动模拟计算的影响，本文基于TrueGrid软件编写了应用程序，提出了起伏界面处六面体单元网格剖分方式，通过该程序可快速建立起伏界面处均匀的六面体网格模型。本文采取了删除四纵列拐角单元、删除一纵列拐角单元以及构造单元过渡环3种剖分方式，解决两个方向上（x-z与y-z方向）单元二合一过渡后拐角处产生扭曲单元的问题。将阶梯状网格经二合一处理后变为斜面网格，并投影至起伏界面，使得网格完全贴合起伏界面，改善了用台阶状网格近似描绘起伏界面的问题。将3种模型通过谱元法进行数值模拟计算验证了该剖分方式的正确性,对比结果发现删除拐角处一纵列单元方式与设置过渡环的方式均可使用，删除四纵列拐角单元方式不推荐使用，本文提出的方案有助于提高谱元法处理起伏界面问题的灵活性。Abstract: When the regular hexahedral element of the spectral element method is used for meshing, a stepped grid will appear where the interface fluctuates greatly, which leads to numerical scattering during simulation. In order to eliminate the influence of the stepped grid on the ground motion simulation calculation of the undulating interface, an application program is written based on the TrueGrid software, and a method of meshing hexahedral element at the undulating interface is proposed. By using this program, a uniform hexahedral mesh model at the undulating interface can be quickly established. This paper adopts three meshing methods: deleting four-column corner elements, deleting one-column corner elements, and constructing element transition rings to solve the problem of twisting elements at the corners after the two-in-one transition of the elements in the two directions (x-z and y-z directions). The stepped grid is transformed into an inclined grid after two-in-one processing, and projected to the undulating interface, so that the grid fits the undulating interface completely, and the problem of using a stepped grid to approximate the undulating interface is improved. Numerical simulations of the three models verify the correctness of the subdivision method. Comparing the results, it is found that both the method of deleting one column of elements at the corner and the method of setting a transition ring are effective,but the method of deleting four columns of corner elements is not recommended. The schemes proposed in this paper can help to improve the flexibility of the spectral element method to deal with undulating interface problems.
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Key words:
- Mesh generation /
- Hexahedral element /
- Spectral element method /
- Numerical simulation
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图 5 起伏界面上与下的阶梯状网格完成单元二合一处理后变为斜面网格示意图
Figure 5. The stepped mesh above and below the undulating interface become inclined grids using two-in-one unit method
图 6 台阶状网格处使用单元二合一的方式处理过程示意图
Figure 6. process of using two-in-one unit method on stepped mesh
图 7 起伏界面上与下的阶梯状网格完成单元二合一处理后变为斜面网格的模型示意图
Figure 7. The stepped mesh above and below the undulating interface become inclined grids using two-in-one unit method
图 14 研究区域第四系沉积地层地形
Figure 14. Topographic map of quaternary sedimentary strata in the study area
图 18 均匀介质中3种剖分方式在测点位置一处四纵列单元的模拟时程曲线结果对比
Figure 18. Comparison of the simulation time history curves of three mesh generation methods in a uniform medium with four rows of elements at the test point one
图 19 非均匀介质中3种剖分方式在测点位置一处四纵列单元的模拟时程曲线结果对比
Figure 19. Comparison of the simulation time history curves of three mesh generation methods in a four-row unit at a test point in heterogeneous medium
图 20 非均匀介质中直接使用台阶状网格在测点位置一处四纵列单元的模拟时程曲线结果对比
Figure 20. Comparison of simulation time history curve results of four rows of units at a test point directly using stepmesh in non-uniform medium
图 21 3种剖分方式在测点位置二的时程曲线对比
Figure 21. Comparison of the time history curves of the three mesh generation methods at the second test point
表 1 模型基本参数
Table 1. Basic parameters of the model
模型尺寸/m 总步长/步 格点间距/m 时间步长/s 震源时间函数主频/Hz 震源时间函数 6 000×5 000×1 100（长×宽×深） 4 000 100 0.001 4 主频为4 Hz的Ricker子波 
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