适用于通用流体可压缩流动的含体积力与热源的格子玻尔兹曼一致模型

中文摘要 AI 辅助

本文在双分布函数格子玻尔兹曼框架内，提出了一种用于模拟通用流体可压缩流动的体积力与热源项的一致表述。所提方法通过引入偏移准平衡态，将外部强迫和体积加热纳入最近发展的非理想可压缩流体动力学动力学框架中。采用标准格子玻尔兹曼离散化，沿特征线进行二阶精确积分，并在最近邻格点上使用乘积形式平衡态，辅以必要的修正项。该表述确保在任意状态方程下一致地恢复纳维-斯托克斯-傅里叶方程（包括Korteweg应力张量），同时保持热力学和输运系数的独立可控性。该方法经过严格验证，并应用于两种不同流动状态：理想气体可压缩流动和非理想/多相可压缩流动，其中采用了一系列广泛的基准测试，包括非经典激波管、热库埃特流以及力驱动的泊肃叶和沃默斯利流。通过瑞利流和法诺流、焦耳-汤姆逊效应及节流过程，进一步展示了该框架利用强迫和加热捕获复杂热力学过程的能力。此外，该模型针对多相现象进行了验证，包括界面一致性和液-汽共存。结果表明，与解析解和参考数据高度一致，而时空网格细化研究确认了该方案预期的二阶精度。这确立了该模型作为在数值和物理源项存在下模拟通用流体高度可压缩流动的稳健高效基础。

英文摘要

This work presents a consistent formulation of body-force and heat-source terms within a double-distribution-function lattice Boltzmann framework for simulating compressible flows of generic fluids. The proposed approach extends a recently developed kinetic framework for non-ideal compressible fluid dynamics by incorporating external forcing and volumetric heating through shifted quasi-equilibrium states. The standard lattice Boltzmann discretization is applied with a second-order accurate integration along characteristics and product-form equilibria on nearest-neighbor lattices are employed, supplemented by necessary correction terms. This formulation ensures the consistent recovery of the Navier-Stokes-Fourier equations, including the Korteweg stress tensor, across arbitrary equations of state, while maintaining independently controllable thermodynamic and transport coefficients. The methodology is rigorously validated and applied for two different flow regimes, with ideal-gas compressible flows and non-ideal/multiphase compressible flows, respectively, where a broad hierarchy of benchmarks is employed, including non-classical shock tubes, thermal Couette flows, and force-driven Poiseuille and Womersley flows. The framework's ability to capture complex thermodynamic processes using forcing and heating is further demonstrated through Rayleigh and Fanno flows, Joule-Thomson effects, and throttling processes. Furthermore, the model is validated for multiphase phenomena, including interface consistency and liquid-vapor co-existence. The results demonstrate excellent agreement with analytical solutions and reference data, while spatio-temporal grid-refinement studies confirm the expected second-order accuracy of the scheme. This establishes the model as a robust and efficient foundation for simulating highly compressible flows of generic fluids in the presence of numerical and physical s...

发表机构

• ETH Zürich（苏黎世联邦理工学院）

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