To calculate the acoustic problems of relative uniform motion between the acoustic source and the fluid, we propose a boundary element method (BEM) strategy that can calculate various forms of relative uniform motion in subsonic conditions in a unified framework and is simple to implement. The acceleration algorithm for the BEM, like the fast multipole method (FMM), in the relative motionless state between the source and the fluid can be directly used without major modifications to the program. We propose a two-step transformation method to unify the wave equations of different relative motion forms into the classical form. In the first step, we transform the wave equations for various forms of relative motion into the equation where the convective terms are present only in the source part. Then, in the second step, we propose an acoustic-analogy Lorentz (a-a Lorentz) transformation to apply Lorentz covariance further to eliminate the convection term and establish the wave equation with classical form in a-a Lorentz space. We implement the boundary integration in the transformed a-a Lorentz space and derive a transformation method to transform discretized geometry and boundary conditions in the original space to the a-a Lorentz space. The problem that the boundary conditions are difficult to apply when solving the boundary integral equation (BIE) after the time-space coordinate transformation is solved. Numerical validations for the proposed method are performed by comparing with analytical results over a wide range of relative velocities. The results show that the proposed method can efficiently compute such problems with high accuracy and concise formulation.

为了计算声源与流体之间相对匀速运动的声学问题，我们提出了一种边界元法（BEM）策略，可以在统一的框架中计算亚音速条件下各种形式的相对匀速运动，并且易于实现。边界元法的加速算法与快速多极法（FMM）一样，在源与流体相对静止状态下，可以直接使用，无需对程序进行较大修改。我们提出了一种两步变换方法，将不同相对运动形式的波动方程统一为经典形式。第一步，我们将各种形式的相对运动的波动方程转换为对流项仅出现在源部分的方程。然后，在第二步中，我们提出了声学类比洛伦兹（aa Lorentz）变换，进一步应用洛伦兹协方差来消除对流项，并在aa洛伦兹空间中建立经典形式的波动方程。我们在变换后的aa洛伦兹空间中实现了边界积分，并导出了将原始空间中的离散几何和边界条件变换到aa洛伦兹空间的变换方法。解决了时空坐标变换后求解边界积分方程（BIE）时边界条件难以适用的问题。通过与大范围相对速度的分析结果进行比较，对所提出的方法进行了数值验证。结果表明，该方法能够有效地计算此类问题，且精度高且公式简洁。