Implicit temperature-correction-based immersed-boundary thermal lattice Boltzmann method for the simulation of natural convection.
Implicit temperature-correction-based immersed-boundary thermal lattice Boltzmann method for the simulation of natural convection.
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DOI：
10.1103/physreve.87.063304
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发表时间：
2013-06
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通讯作者：
Takeshi Seta
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作者：
Takeshi Seta
本文将隐式校正方法应用于两个同心水平圆柱体之间和包含圆柱体的方形框内的自然对流问题的浸入边界热晶格玻尔兹曼方法（IB-TLBM）。Chapman-Enskog多尺度展开式证明了温度方程中存在一个从动力学方程源项出发的额外项。为了消除多余的项，我们重新定义了晶格玻尔兹曼方程中的温度项和源项。当弛豫时间小于1时，温度和源项的新定义提高了热晶格玻尔兹曼方法的精度。为了使用重新定义的温度计算流体与刚性固体之间的热相互作用，需要隐式修正方法。对两个同心圆柱体之间的热传导进行了仿真，结果表明，随着构成边界的拉格朗日点数目的增加，所提出的lb - tlbm在每个边界点处的误差减小。我们推导了边界温度滑移与弛豫时间之间的理论关系，并证明了IB-TLBM需要较小的弛豫时间以避免浸入边界周围的温度畸变。该方法计算的流线、等温线和平均努塞尔数与以往涉及自然对流的数值研究结果吻合较好。所提出的IB-TLBM通过为每个拉格朗日节点提供足够的离散区域，提高了温度和速度边界条件的准确性，并减少了流线在物体表面的渗透。
In the present paper, we apply the implicit-correction method to the immersed-boundary thermal lattice Boltzmann method (IB-TLBM) for the natural convection between two concentric horizontal cylinders and in a square enclosure containing a circular cylinder. The Chapman-Enskog multiscale expansion proves the existence of an extra term in the temperature equation from the source term of the kinetic equation. In order to eliminate the extra term, we redefine the temperature and the source term in the lattice Boltzmann equation. When the relaxation time is less than unity, the new definition of the temperature and source term enhances the accuracy of the thermal lattice Boltzmann method. The implicit-correction method is required in order to calculate the thermal interaction between a fluid and a rigid solid using the redefined temperature. Simulation of the heat conduction between two concentric cylinders indicates that the error at each boundary point of the proposed IB-TLBM is reduced by the increment of the number of Lagrangian points constituting the boundaries. We derive the theoretical relation between a temperature slip at the boundary and the relaxation time and demonstrate that the IB-TLBM requires a small relaxation time in order to avoid temperature distortion around the immersed boundary. The streamline, isotherms, and average Nusselt number calculated by the proposed method agree well with those of previous numerical studies involving natural convection. The proposed IB-TLBM improves the accuracy of the boundary conditions for the temperature and velocity using an adequate discrete area for each of the Lagrangian nodes and reduces the penetration of the streamline on the surface of the body.