基于玻尔兹曼方程的声多极源
Acoustic multipole sources from the Boltzmann equation
摘要：
通过在动力学理论的玻尔兹曼方程中加入一个粒子源项，可以用一个特定的粒子速度分布来表示在整个流体中出现和消失的粒子。从这个修正的Boltzmann方程出发，通过流体力学的守恒方程导出波动方程，得到了波动方程中的多极源项，这些多极源项由Boltzmann方程中的粒子源项给出。在动量方程的欧拉水平上，波动方程中出现了一个偶极子源项和一个偶极子源项。在Navier-Stokes水平上，还出现了一个量级可以忽略的四极项。
英文摘要：
By adding a particle source term in the Boltzmann equation of kinetic theory, it is possible to represent particles appearing and disappearing throughout the fluid with a specified distribution of particle velocities. By deriving the wave equation from this modified Boltzmann equation via the conservation equations of fluid mechanics, multipole source terms in the wave equation are found. These multipole source terms are given by the particle source term in the Boltzmann equation. To the Euler level in the momentum equation, a monopole and a dipole source term appear in the wave equation. To the Navier-Stokes level, a quadrupole term with negligible magnitude also appears.
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