三维斜流线性完全耦合层吸收边界条件

Three Dimensional Linear PML Absorbing Boundary Conditions with an Oblique Mean Flow

采用傅里叶与拉普拉斯变换方法分析了三维斜流背景下声波、涡波与熵波的色散关系;根据各物理波的色散轨迹特征,结合频率变化的时空坐标变换方法,给出了一组时间与空间坐标变换关系式,并将三维斜流线性欧拉方程变换至新坐标系;采用复数变换方法,引入阻尼,分别构建了x层、y层、z层及角层的完全耦合层(PML)吸收边界条件,给出了吸收项的施加原则;最后通过三维脉冲声波、对称涡环与周期性点声源在斜时均流中的传播问题验证了该吸收边界条件的正确性。研究结果表明:所提出的坐标变换关系能够有效解决各物理波相位速度与群速度不一致的问题;在斜背景流下,该PML吸收边界条件能较好地吸收物理波,有效抑制边界反射,可用于气动声学计算。

For three dimensional linear Euler equations in the case ot oblique mean lIow, the dis- persion relations of acoustic, vortex and entropy wave were first analyzed by using Fourier and La- place transform method. Then the hypothesis for changed frequency was employed, a proper space- time transformation was presented for deriving three dimensional linear Euler equations in trans- formed coordinates. A complex change was applied to the new equations and a damping parameter was introduced. A three linear PML absorbing boundary conditions in the case of oblique mean flow for x layer, y layer, z layer and corner layer were derived. In addition, the importance of added ab- sorption term was emphasized. Finally, the effectiveness of linear PML absorbing boundary condi- tions was validated by computing the computational aeroacousties benchmark problems. The results prove that： the presented space-time transformation can solve the problem of direction inconsistence in group and phase velocity of physical wave; in the case of oblique mean flow, the proposed PML ab- sorbing boundary conditions can absorb the physical wave with little or no reflection. Therefore, it also can be applied to aeroacoustic computation.