The spectral element scheme of multi-transmitting formula (MTF) which proposed by Xing and Li is developed and expanded to numerical simulation of SH-type wave motion in homogeneous linear medium. The spectral elements adjacent to the artificial boundaries are supposed to be rectilinear quadrilateral elements, in order that each node on the artificial boundary locates on a unique grid line pointing to the interior domain, hence the displacement of a particular artificial boundary node at a certain time can be inferred from displacements of nodes on the grid line at earlier times. Two numerical examples, the plane wave propagation with a certain angle (outer-source problem) and the free spread of a pulse wave originated from a point (inner-source problem), are employed for verification of this wave motion simulation procedure which combines the spectral element method with MTF boundary. The main parameters affecting reflection error of the MTF scheme, such as order of interpolation polynomial, artificial wave speed and transmitting order, are investigated in time domain via a series of initial-value problems. The results show that the order of interpolation poly-nomial influences the reflection error very little, while higher interpolation order may lead to better accuracy. For the choice of artificial wave speed, it is preferable to choose values equal or slightly greater than the physical wave speed, otherwise bigger reflection errors come about. Transmitting order exerts the most significant impact on reflection error, which would be reduced greatly with the increase of transmitting order of MTF, but the undesired drift instability may arise when transmitting order reaches three or two for inner-source and outer-source problems, respectively. Although the work combining MTF boundary with spectral element method is conducted on simulation of SH wave propagation in infinite homogeneous medium in this paper, it has laid the foundation of research on more complicated situations, such as issues of layered soil sites, propagation of P-SV wave or Rayleigh wave, etc.%将邢浩洁和李鸿晶提出的多次透射公式(multi-transmitting formula,MTF)的谱元格式应用于均匀介质中线弹性SH波动问题的谱元模拟.假定紧邻人工边界的一层谱单元为具有直线边界的四边形单元,以保证每个人工边界节点都唯一对应一条指向内域的离散网格线.人工边界节点在某时刻的位移由该离散网格线上的节点在前若干时刻的位移确定,按照MTF谱元格式进行计算.通过平面波以一定角度传播的外源问题算例和点源脉冲自由扩散的内源问题算例,验证了方法的可行性以及对实际复杂波动问题的适用性.通过不同类型初值问题算例,在时域内分析了插值多项式阶次、人工波速和透射阶次三个参数对反射误差的影响.结果表明:插值多项式阶次较高的格式会表现出更好的精度,但总体上对反射误差的影响较小;人工波速对反射误差具有显著影响,当人工波速小于介质物理波速时反射误差较大,而当人工波速等于或稍大于介质物理波速时反射误差处于较低水平;透射阶次对反射误差具有决定性影响,表现在不失稳的情形下提高透射阶次能够迅速降低反射误差,但内源问题从三阶MTF开始出现飘移失稳,外源问题从二阶MTF开始出现轻微的飘移失稳.
展开▼
