Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播

从群速度的角度推导了包含均匀稳定来流的二维波动方程的1阶吸收边界条件,基于Che-byshev谱元法提出了二维均匀稳定来流波动方程的求解方法.在空间上采用谱元方法,在时间上采用隐式Newmark积分法,从而获得了波动方程的离散形式.经具体算例验证表明:与1阶Clay-ton-Engquist-Majda吸收边界条件相比,所推导的吸收边界条件能更有效地削弱边界上的数值反射,避免解的失真,求解方法在空间上具有谱精度,在时间上达到了2阶精度.

Chebyshev Spectral Elements Method for 2-Dimensional Acoustic Propagation Problem in a Uniform Mean Flow with Absorbing Boundary Condition

In this study,the Chebyshev spectral elements approximation was applied to solve the acoustic propagation problem in the subsonic uniform mean flow.From the group velocity,the first-order Eliane-Dan-Thomas absorbing boundary condition was derived for the boundaries of the solution domain.In this approach,the discretization of the wave equation is based on the spectral elements in space and the implicit Newmark method in time marching.The numerical results with higher-order spectral accuracy in space and second-order accuracy in time agree well with the benchmark solutions.Compared with the first-order Clayton-Engquist-Majda absorbing boundary condition for the same wave problem,the first-order Eliane-Dan-Thomas absorbing boundary condition proposed here can effectively reduce the numerical reflection on boundaries and avoid solution distortion.