透射边界条件在波动谱元模拟中的实现:一维波动

发布时间：2018-06-08 23:07

本文选题：波动数值模拟 + 谱元法　；参考：《力学学报》2017年02期

【摘要】：多次透射公式(multi-transmitting formula,MTF)是一种具有普适性的局部人工边界条件,但其在近场波动数值模拟中一般与有限元法结合.由于波动谱元模拟的数值格式与有限元格式有极大的不同,传统的MTF在谱元离散格式中无法直接实现.为了使物理概念清楚、精度可控的多次透射人工边界条件能够适应波动谱元模拟的需求,首先指出多次透射边界与谱元离散格式结合的基本问题,并分析了空间内插和时间内插两种方案的可行性.然后从空间内插角度出发,提出基于拉格朗日多项式插值模式的MTF谱元格式,并采用一种简单内插方法实现高阶MTF.最后通过一维波动数值试验检验这些MTF谱元格式的精度,并讨论其数值稳定性.结果表明:对于一、二阶MTF,几种格式的精度相当;对于三、四阶MTF,基于谱单元位移模式插值的格式精度最高.相反,随着插值多项式阶次的升高,不同MTF格式的稳定临界值逐步降低,但是所有格式均在人工波速大大超过物理波速时才可能发生失稳.
[Abstract]:Multi-transmissive formative MTF is a universal local artificial boundary condition, but it is generally combined with finite element method in numerical simulation of near-field wave. Because the numerical scheme of wave spectral element simulation is very different from the finite element scheme, the traditional MTF can not be realized directly in the spectral element discrete scheme. In order to make the physical concept clear and the precision controllable multiple transmission artificial boundary conditions can meet the needs of wave spectral element simulation, the basic problem of combining multiple transmission boundary with spectral element discrete scheme is pointed out. The feasibility of space interpolation and time interpolation is analyzed. Then, from the point of view of spatial interpolation, an MTF spectral element scheme based on Lagrange polynomial interpolation mode is proposed, and a simple interpolation method is used to realize higher order MTF. Finally, the accuracy and numerical stability of these MTF spectral element schemes are verified by one-dimensional wave numerical experiments. The results show that for the first and second order MTF, the accuracy of several schemes is the same, and for the third and fourth order MTF, the scheme based on spectral element displacement mode interpolation has the highest accuracy. On the contrary, with the increase of interpolation polynomial order, the stable critical value of different MTF schemes decreases gradually, but the instability of all schemes is likely to occur when the artificial wave velocity exceeds the physical wave velocity.
【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

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