To increase the flexibility of the non-dimensional lattice Boltzmann method (NDLBM), a non-uniform stretched mesh scheme was developed for coupled flow and heat transfer simulations. Mesoscopic scale governing equations and parameters are obtained through coordinate transformation between the non-uniform and uniform mesh spaces. Different from conventional single relaxation time closure models of the collision process, which need space interpolations and momentum adjustments, the present collision model is related to transformed relaxation time and force matrixes. Additional interpolations and adjustments are not necessary because the effects of local grids and properties are included in each component of the matrixes. The components of the relaxation time matrixes are directly expressed by mesoscopic governing parameters, discrete directions and local stretch gradients. Natural convection in an enclosure is simulated with meshes of various global stretch ratios and grid numbers. The non-uniform stretched mesh scheme can capture the temperature and velocity distributions as well as Nusselt numbers with negligible deviations from the uniform grids. Deviations increase slightly with global stretched ratios and appear at larger local velocity and grid size positions. Effects of the tilt angle and key governing parameters from conduction to convection regimes are illustrated and compare favorably with previous studies.

为了增加无量纲格子Boltzmann方法（NDLBM）的灵活性，开发了一种非均匀拉伸网格方案，用于耦合流动和传热模拟。通过非均匀网格空间和均匀网格空间之间的坐标变换，可以得到介观尺度控制方程和参数。与传统的碰撞过程单张弛豫时间闭合模型不同，该模型需要空间插值和动量调节，而本发明的碰撞模型与变换后的弛豫时间和力矩阵有关。不需要额外的插值和调整，因为矩阵的每个组件中都包含了局部网格和属性的影响。弛豫时间矩阵的分量直接由介观控制参数表示，离散方向和局部拉伸梯度。使用各种全局拉伸比和网格数的网格模拟围护中的自然对流。非均匀拉伸网格方案可以捕获温度和速度分布以及Nusselt数，与均匀网格的偏差可以忽略不计。偏差随整体拉伸比而略有增加，并出现在较大的局部速度和网格尺寸位置。示出了倾斜角和关键控制参数从传导到对流状态的影响，并与以前的研究进行了比较。非均匀拉伸网格方案可以捕获温度和速度分布以及Nusselt数，与均匀网格的偏差可以忽略不计。偏差随整体拉伸比而略有增加，并出现在较大的局部速度和网格尺寸位置。示出了倾斜角和关键控制参数从传导到对流状态的影响，并与以前的研究进行了比较。非均匀拉伸网格方案可以捕获温度和速度分布以及Nusselt数，与均匀网格的偏差可以忽略不计。偏差随整体拉伸比而略有增加，并出现在较大的局部速度和网格尺寸位置。示出了倾斜角和关键控制参数从传导到对流状态的影响，并与以前的研究进行了比较。