时空耦合谱元方法求解刚性圆柱体表面的声传播问题

Time-Space Coupled Spectral Element Method for Acoustic Wave Propagation on a Rigid Cylinder

以刚性圆柱体表面均匀分布若干单极子质量源的声传播问题为求解目标,在极坐标系中构建时空耦合模型。基于Least-Squares变分,在时间及空间方向同时采用Chebyshev谱元方法进行离散,将原来极坐标系中的问题转化到柱坐标系中进行求解,并通过数值实验验证了模型的正确性;进一步应用时空耦合模型求解刚性圆柱体表面声传播问题,在计算区域外边界采用C-E-M吸收边界条件。研究结果显示:时空耦合谱元模型通过时间及空间计算精度的匹配,能够获得高精度的数值解;增加时间及空间方向的单元数及单元内的插值阶数均能提高计算精度,且提高插值阶数的方法具有指数阶收敛特性;所构建的时空耦合模型能够稳定求解刚性圆柱体表面的声传播问题,将C-E-M吸收边界条件改写为第一类边界条件并应用于时空耦合模型依然有效。研究内容对构建高精度的计算气动声学求解方法具有指导意义。

A coupled time-space model is established in a polar coordinate to obtain the propagation characters from some monopole sources distributed evenly on a rigid cylinder. Following the least-squares variational principle, Chebyshev spectral element method is chosen to discretize both the time and space domains and the problem in polar coordinate is transformed into cylindrical coordinate. The validity of this model is verified by the numerical experiment, and the acoustic wave propagation on a rigid cylinder with C-E-M absorbing boundary condition on the edge of computational domain is revealed. The results show that a high-order accuracy can be obtained by the coupled time-space model via matching the numerical accuracy between time and space. The numerical accuracy can be improved by increasing the number of the elements or the interpolation order in each element of time and space. An exponential accuracy rate can be obtained with the increasing interpolation order. The acoustic wave propagation on the surface of a rigid cylinder can be simulated stably by this model, and the C-E-M absorbing boundary condition rewritten as the Dirichlet boundary condition still works well.