透射边界条件在波动谱元模拟中的实现:二维波动
发布时间：2019-05-11 18:03
【摘要】：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.
[Abstract]:The spectral element scheme of multiple transmission formula (multi-transmitting formula,MTF) proposed by Xing Haojie and Li Hongjing is applied to the spectral element simulation of elastic SH wave problem in the middle line of homogeneous media. It is assumed that a layer spectral element adjacent to the artificial boundary is a Quadrilateral element with a straight line boundary to ensure that each artificial boundary node has a unique discrete grid line pointing to the inner domain. The displacement of the artificial boundary node at a certain time is determined by the displacement of the node on the discrete grid line at the previous time, and calculated according to the MTF spectral element scheme. The feasibility of the method and its applicability to complex wave problems are verified by an example of exogenous problem propagated by plane wave at a certain angle and an example of internal problem of free diffusion of point source pulse. Through the examples of different types of initial value problems, the effects of interpolation order, artificial wave velocity and transmission order on reflection error are analyzed in time domain. The results show that the format with higher interpolation order will show better accuracy, but it has little effect on the reflection error as a whole. The reflection error is larger when the artificial wave velocity is less than the medium physical wave velocity, while the reflection error is lower when the artificial wave velocity is equal to or slightly greater than the medium physical wave velocity. The transmission order has a decisive effect on the reflection error. Increasing the transmission order without instability can reduce the reflection error rapidly, but the internal problem begins to appear drift instability from the third order MTF. The external problem begins with the slight drift instability of the second order MTF.
【作者单位】： 南京工业大学土木工程学院;
【基金】：国家自然科学基金资助项目(51278245)
【分类号】：O241.82
，
本文编号：2474723
[Abstract]:The spectral element scheme of multiple transmission formula (multi-transmitting formula,MTF) proposed by Xing Haojie and Li Hongjing is applied to the spectral element simulation of elastic SH wave problem in the middle line of homogeneous media. It is assumed that a layer spectral element adjacent to the artificial boundary is a Quadrilateral element with a straight line boundary to ensure that each artificial boundary node has a unique discrete grid line pointing to the inner domain. The displacement of the artificial boundary node at a certain time is determined by the displacement of the node on the discrete grid line at the previous time, and calculated according to the MTF spectral element scheme. The feasibility of the method and its applicability to complex wave problems are verified by an example of exogenous problem propagated by plane wave at a certain angle and an example of internal problem of free diffusion of point source pulse. Through the examples of different types of initial value problems, the effects of interpolation order, artificial wave velocity and transmission order on reflection error are analyzed in time domain. The results show that the format with higher interpolation order will show better accuracy, but it has little effect on the reflection error as a whole. The reflection error is larger when the artificial wave velocity is less than the medium physical wave velocity, while the reflection error is lower when the artificial wave velocity is equal to or slightly greater than the medium physical wave velocity. The transmission order has a decisive effect on the reflection error. Increasing the transmission order without instability can reduce the reflection error rapidly, but the internal problem begins to appear drift instability from the third order MTF. The external problem begins with the slight drift instability of the second order MTF.
【作者单位】： 南京工业大学土木工程学院;
【基金】：国家自然科学基金资助项目(51278245)
【分类号】：O241.82
，
本文编号：2474723
本文链接：https://www.wllwen.com/kejilunwen/yysx/2474723.html
