吸收边界条件在全空间瞬变电磁计算中的应用

Application of Absorbing Boundary Condition in Whole-Space Computation of Transient Electromagnetic Response

吸收边界条件对于全空间瞬变电磁计算的稳定性和精确性是至关重要的.将Laplace方程应用于巷道中,避免了对巷道内空气电阻率的设置;将廖氏边界条件进行必要的修正,导出了适用于扩散方程的新的吸收边界条件;计算了新边界条件的应用效果和巷道底板内低阻薄板的响应特征.结果表明:巷道边界两侧瞬变场的扩散速度明显改变;应用Dirichlet边界条件使边界处的磁场约在0.05 ms后发生畸变,并对计算区域内部磁场产生影响,而新吸收边界条件采用N=4阶精度并取控制系数为β=0.9时,计算的磁场值与理论值具有相同的衰减规律,该方法能较好的反映出薄板的位置及倾斜角度.新的吸收边界条件适用于全空间瞬变电磁场的有限差分计算.

The absorbing boundary condition（ABC） was very important to the stability and accuracy of calculating whole-space transient electromagnetic response. The Laplace equation was used in the laneway to avoid setting the air resistivity. A new ABC was derived by modifying Liao＇s ABC, which was suitable to the electromagnetic diffusion equation. The application effect of new ABC and the response characteristics of sheet conductive body located in the floor of laneway were studied. The results show that the diffusion velocity of magnetic field in two sides of laneway boundary was obviously different. The magnetic field at boundary started to distort at 0.05 ms using the Dirichlet boundary condition and the internal magnetic field was gradually influenced by this distortion, while the magnetic field value calculated by the new ABC has a same attenuation law to analytical solution by choosing the order N= 4 and control coefficient β=0.9 in the new ABC. The location and oblique angle of sheer conductive body can easily be identified. The new ABC is suitable to the whole-space finite difference computation.