一类无界且带不平坦界面的声波导传播计算

Computation for a class of the unbounded acoustical waveguide with the curved interface

无界且带不平坦界面的声波导经局部正交变换和完美匹配层(PML)截断,波导计算问题可近似转化为有界且带有平坦界面的声波导的Helmholtz方程,由于利用PML进行截断,此方程为复偏微分方程,其特征函数系一般不具有正交性,故数值步进求解时,存在着局部基下坐标转换的困难.本文一方面运用共轭特征算子,通过其所对应的特征函数系与原特征函数系的正交性,给出了局部基下坐标转换的简便公式;另一方面,利用此简便公式,进行了声波导的步进计算,数值计算结果表明,所用方法切实可行.

The unbounded acoustical waveguide with the curved interface can be changed by the coordinate transform and terminated by the perfectly matched layer while the computation problem is then approximately turned to the nu- merical solution of the improved Helmholtz equation on the bounded waveguide with a flatted interface. It is ex- tremely difficult to compute the coordinates under the local bases when the equation is solved by some numerical marching methods as this one is an improved and complex Helmholtz equation （ICHE） whose eigenfunctions are not orthogonal. This paper is not only to reduce a simplified formula of computing the coordinates under the local bases by applying adjoint eigenoperator, but also to calculate the acoustical waveguide with marching methods by applying this simplified formula. The numerical results of simulation show that the treatment is relatively feasible and effi- cient.