基于多原子ES-BGK模型的具有灵活普朗特数和比热比的格子玻尔兹曼格式
Lattice Boltzmann Scheme associated with flexible Prandtl number and specific heat ratio based on the polyatomic ES-BGK model
AI总结：
本文基于多原子ES-BGK模型提出一种可灵活调节普朗特数和比热比的格子玻尔兹曼格式，通过高斯分布参数和附加自由度实现调节，并推导Hermite系数公式，数值验证结果与解析解吻合良好。
摘要：
提出了一种具有灵活普朗特数和比热比的格子玻尔兹曼格式，该格式基于多原子椭球统计模型（ES-BGK）。普朗特数可以通过高斯分布的一个参数进行调节，比热比可以通过附加的自由度进行调节。为了构建所提出的格式，将高斯分布在Hermite多项式上展开，并推导了高斯分布Hermite系数的一般项公式。通过基准算例验证了所提出的格式。数值结果与解析解吻合良好。
英文摘要：
A lattice Boltzmann scheme associated with flexible Prandtl number and specific heat ratio is proposed, which is based on the polyatomic ellipsoidal statistics model(ES-BGK). The Prandtl number can be modified by a parameter of the Gaussian distribution and the specific heat ratio can be modified by additional free degrees. For the sake of constructing the scheme proposed, the Gaussian distribution is expanded on the Hermite polynomials and the general term formula for the Hermite coefficients of the Gaussian distribution is deduced. Benchmarks are carried out to verify the scheme proposed. The numerical results are in good agreement with the the analytical solutions.
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