The linearized Boltzmann equation: Sound-wave propagation in a rarefied gas
The linearized Boltzmann equation: Sound-wave propagation in a rarefied gas
复制标题
线性玻尔兹曼方程：声波在稀薄气体中的传播
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
C. Siewert
中科院分区：
文献类型：
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作者：
R. Garcia;C. Siewert
摘要。用离散坐标法的一种解析方法（ADO法）对稀薄气体中的声波传播问题建立了简明而特别精确的解。分析和数值工作是基于线性化玻尔兹曼方程的严格形式（用于刚性球相互作用），与许多没有边界条件的其他作品（用于无限介质）形成对比，这里报告的解满足模拟扩散反射振动板的边界条件。此外，为了研究动力学模型的影响，我们开发了BGK模型、S模型、Gross-Jackson模型以及（新定义的）MRS模型和CES模型的解决方案。虽然开发的数值结果与现有的实验数据进行了比较，但本工作的重点放在用线性玻尔兹曼方程和五种考虑的动力学模型描述的声波传播问题的解决方案上。
Abstract.An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problem of sound-wave propagation in a rarefied gas. The analysis and the numerical work are based on a rigorous form of the linearized Boltzmann equation (for rigid-sphere interactions), and in contrast to many other works formulated (for an infinite medium) without a boundary condition, the solution reported here satisfies a boundary condition that models a diffusely-reflecting vibrating plate. In addition and in order to investigate the effect of kinetic models, solutions are developed for the BGK model, the S model, the Gross-Jackson model, as well as for the (newly defined) MRS model and the CES model. While the developed numerical results are compared to available experimental data, emphasis in this work is placed on the solutions of the problem of sound-wave propagation as described by the linearized Boltzmann equation and the five considered kinetic models.