A fractional-step lattice Boltzmann flux solver for axisymmetric thermal flows
A fractional-step lattice Boltzmann flux solver for axisymmetric thermal flows
复制标题
DOI：
10.1080/10407790.2015.1096682
复制
发表时间：
2016-01
期刊：
影响因子：
--
通讯作者：
Y. Wang;C. Shu;C. J. Teo;L. M. Yang
中科院分区：
文献类型：
--
作者：
Y. Wang;C. Shu;C. J. Teo;L. M. Yang
摘要 本文提出了一种分数步格子玻尔兹曼通量求解器，用于有效模拟旋转壁的轴对称热流。求解器中引入了预测器和校正器步骤。在预测器步骤中，排除轴对称效应，中间流动变量通过格子玻尔兹曼通量求解器（LBFS）进行预测，该求解器应用有限体积方法对标准格子玻尔兹曼方法（LBM）恢复的保守方程进行离散化。细胞界面处 LBFS 的通量通过局部应用具有三个分布函数的格子玻尔兹曼 (LB) 模型来重建。这三个分布函数分别用于计算轴向和径向速度、方位角速度和内能。在校正步骤中，通过考虑轴对称效应来校正中间流动变量。该方法既保留了LBM的简单性，又消除了轴对称LB模型中复杂的推导过程。通过应用模拟环空中的自然对流、瑞利-贝纳德对流、垂直高环空中的混合对流以及晶体生长中的惠勒基准问题来检验所提出的求解器的可靠性。获得的数值结果与已发表的数据非常吻合。
ABSTRACT A fractional-step lattice Boltzmann flux solver is proposed in this work for effective simulation of axisymmetric thermal flows with rotating walls. The predictor and corrector steps are introduced in the solver. In the predictor step, excluding axisymmetric effects, the intermediate flow variables are predicted by the lattice Boltzmann flux solver (LBFS), which applies the finite-volume method to discretize the conservative equations recovered by the standard lattice Boltzmann method (LBM). The fluxes of the LBFS at the cell interfaces are reconstructed by local application of the lattice Boltzmann (LB) model with three distribution functions. These three distribution functions are used respectively for calculating axial and radial velocities, azimuthal velocity, and internal energy. In the corrector step, the intermediate flow variables are corrected by considering the axisymmetric effects. The present method not only retains the simplicity of the LBM but also eliminates the complicated derivation process in the axisymmetric LB model. The reliability of the proposed solver is examined by its application to simulate natural convection in an annulus, the Rayleigh-Benard convection, mixed convection in a vertical tall annulus, and Wheeler’s benchmark problem in crystal growth. The numerical results obtained agree well with the published data.