A cascaded lattice Boltzmann (LB) approach based on central moments and multiple relaxation times to simulate thermal convective flows, which are driven by buoyancy forces and/or swirling effects, in the cylindrical coordinate system with axial symmetry is presented. In this regard, the dynamics of the axial and radial momentum components along with the pressure are represented by means of the 2D Navier-Stokes equations with geometric mass and momentum source terms in the pseudo Cartesian form, while the evolutions of the azimuthal momentum and the temperature field are each modeled by an advection-diffusion type equation with appropriate local source terms. Based on these, cascaded LB schemes involving three distribution functions are formulated to solve for the fluid motion in the meridian plane using a D2Q9 lattice, and to solve for the azimuthal momentum and the temperature field each using a D2Q5 lattice. The geometric mass and momentum source terms for the flow fields and the energy source term for the temperature field are included using a new symmetric operator splitting technique, via pre-collision and post-collision source steps around the cascaded collision step for each distribution function. These result in a particularly simple and compact formulation to directly represent the effect of various geometric source terms consistently in terms of changes in the appropriate zeroth and first order moments. Simulations of several complex buoyancy-driven thermal flows and including rotational effects in cylindrical geometries using the new axisymmetric cascaded LB schemes show good agreement with prior benchmark results for the structures of the velocity and thermal fields as well as the heat transfer rates given in terms of the Nusselt numbers.

中文翻译：

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基于中心矩的级联格子玻尔兹曼方法，用于轴对称热流，包括旋流效应

提出了一种基于中心矩和多个弛豫时间的级联晶格玻尔兹曼 (LB) 方法来模拟在具有轴对称的圆柱坐标系中由浮力和/或旋流效应驱动的热对流。在这方面，轴向和径向动量分量与压力的动力学通过具有几何质量和动量源项的二维 Navier-Stokes 方程表示为伪笛卡尔形式，而方位角动量的演变和温度场均由具有适当局部源项的对流扩散型方程建模。基于这些，制定了涉及三个分布函数的级联 LB 方案，以使用 D2Q9 点阵求解子午面中的流体运动，并使用 D2Q5 晶格分别求解方位角动量和温度场。流场的几何质量和动量源项以及温度场的能量源项使用新的对称算子分裂技术包括在每个分布函数的级联碰撞步骤周围的预碰撞和后碰撞源步骤中。这导致了一个特别简单和紧凑的公式，以根据适当的零阶和一阶矩的变化来一致地表示各种几何源项的影响。