论文标题
3D累积和中央矩的比较研究晶格玻尔兹曼方案具有插值边界条件，用于模拟高prandtl数量状态的热流量
A comparative study of 3D Cumulant and Central Moments lattice Boltzmann schemes with interpolated boundary conditions for the simulation of thermal flows in high Prandtl number regime
论文作者
论文摘要
当动量和热量的转移在不同的时间尺度上发生时，以高prandtl数字为特征的热流在数值上具有挑战性。为了说明非常低的导热率并遵守Courant-Friedrichs-Lewy条件，必须降低该方案的数值扩散。结果，数值人工制品主要由通常被称为摇摆的分散误差所占据主导地位。在这项研究中，我们通过应用新颖的碰撞内核，具有大量离散速度的晶格，即D3Q27和二阶边界条件，探讨了晶格玻尔兹曼方法框架的可能补救措施。首次利用基于累积的碰撞算子来模拟流体动力和热场。或者，使用中央力矩的碰撞运算符计算前流字段。已经检查了不同的放松策略，以说明高阶晶格引入的其他自由度。为了验证纯对流扩散问题所提出的内核，将数值模拟与高斯山丘的分析解决方案进行了比较。通过模拟平方指示器函数的对流和扩散来显示数值分散的结构。最后，进行了一项对牢固的圆柱体稳定强制热对流的研究，并与FEM溶液进行了比较。数值结果证实，必须以较大的离散速度从晶格中调整前流场的放松方案。在所有执行的基准测试中，两种松弛时间方法的有益效果已被证明是优越或至少与抗逆转核一样好。
Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity and obey the Courant-Friedrichs-Lewy condition, the numerical diffusion of the scheme has to be reduced. As a consequence, the numerical artefacts are dominated by dispersion errors commonly known as wiggles. In this study, we explore possible remedies in the framework of the lattice Boltzmann method by applying novel collision kernels, lattices with a large number of discrete velocities, namely D3Q27, and second-order boundary conditions. For the first time, the cumulant-based collision operator is utilised to simulate both the hydrodynamic and the thermal field. Alternatively, the advected field is computed using the central moments' collision operator. Different relaxation strategies have been examined to account for additional degrees of freedom introduced by a higher-order lattice. To validate the proposed kernels for a pure advection-diffusion problem, the numerical simulations are compared against an analytical solution of a Gaussian hill. The structure of the numerical dispersion is shown by simulating advection and diffusion of a square indicator function. Finally, a study of steady forced heat convection from a confined cylinder is performed and compared against a FEM solution. Numerical results confirm that the relaxation scheme of the advected field must be adjusted to profit from lattice with a larger number of discrete velocities. In all of the performed benchmarks, the beneficial effect of the two relaxation time approach has been shown to be superior or at least as good as counter-candidating kernels.
