用于变温 van der Waals 流体的二维离格 Boltzmann 模型
Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature
AI总结：
本文提出了一种变温液-汽系统的二维离格 Lattice Boltzmann 模型，采用全域 Hermite 多项式四阶展开与五阶投影格式，验证了四阶收敛性及 Galilean 不变性，并研究了平行壁面间的液-汽相分离过程。
摘要：
我们开发了一种用于变温液-汽系统的二维 Lattice Boltzmann 模型。我们的模型基于一个单粒子分布函数，该函数通过全域 Hermite 多项式展开。为了确保恢复热流体的流体力学方程，我们使用了四阶展开以及一组包含 25 个元素的动量向量，其笛卡尔投影是 Q = 5 阶 Hermite 多项式的根。由于这些向量是离格的，我们使用五阶投影格式来演化相应的分布函数集。我们使用基于 49 点模板的四阶格式来计算力项中的梯度算子，以确保液-汽相分离，并在壁面上使用漫反射边界条件。我们证明了在 van der Waals 流体中，在剪切波和纵波传播的背景下，相对于格子间距至少具有四阶收敛性。对于平面界面，在足够小的格子间距下可以看到四阶收敛性，同时发现伪速度对温度分布的影响小于 1.0%，即使当 T w ' 0.7 T c 时也是如此。我们通过考虑 Laplace 压力测试进一步验证了我们的格式。结果表明，相对于背景速度，Galilean 不变性保持到二阶。我们进一步研究了保持在恒定温度 T w（小于临界温度 T c）的两个平行壁面之间的液-汽相分离，并讨论了该过程的主要特征。
英文摘要：
We develop a two-dimensional Lattice Boltzmann model for liquid-vapour systems with variable temperature. Our model is based on a single particle distribution function expanded with respect to the full-range Hermite polynomials. In order to ensure the recovery of the hydrodynamic equations for thermal flows, we use a fourth order expansion together with a set of momentum vectors with 25 elements whose Cartesian projections are the roots of the Hermite polynomial of order Q = 5. Since these vectors are off-lattice, a fifth-order projection scheme is used to evolve the corresponding set of distribution functions. A fourth order scheme employing a 49 point stencil is used to compute the gradient operators in the force term that ensures the liquid-vapour phase separation and diffuse reflection boundary conditions are used on the walls. We demonstrate at least fourth order convergence with respect to the lattice spacing in the contexts of shear and longitudinal wave propagation through the van der Waals fluid. For the planar interface, fourth order convergence can be seen at small enough lattice spacings, while the effect of the spurious velocity on the temperature profile is found to be smaller than 1.0%, even when T w ' 0.7 T c . We further validate our scheme by considering the Laplace pressure test. Galilean invariance is shown to be preserved up to second order with respect to the background velocity. We further investigate the liquid-vapour phase separation between two parallel walls kept at a constant temperature T w smaller than the critical temperature T c and discuss the main features of this process.
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