一种基于多项式外推的局部透射边界位移解(外行波为非平面波情形)

A new approach for solution of local artificial transmitting boundary

一般情况下,通过人工边界向外透射的波动常为非平面波。对于近场非平面波在人工边界上的透射问题,不能采用简单的平面波透射方法。本文针对近场非平面波在人工边界上的透射特点,分析了非平面波沿人工边界法向视波速的变化规律及其近场失稳机制,推导了适合近场非平面波的、人工边界点位移解的不等步距线性外推公式。

As a wave motion generated by a dynamic source transmits outward through the artificial boundary, its corresponding normal apparent wave velocity usually changes from point to point along the artificial boundary. In this paper the variation of the normal apparent wave velocity along the artificial boundary is analyzed and its effects on the stability of the displacement solution is studied. In the analysis, a piecewise local plane wave motion is used to approximate the non-plane wave motion and a linear extrapolation formula with unequal step for the displacement solution at the node along the boundary is developed. It is concluded that with this method both precision and stability of the displacement solution for the near-source wave motion can be remarkably improved.