标题： 基于非均匀网格的热对流插值补充格子玻尔兹曼模拟 显示英文标题

标题： Interpolation-supplemented lattice Boltzmann simulation of thermal convection on non-uniform meshes

摘要： 我们对一种插值补充格子玻尔兹曼方法（ISLBM）进行了系统评估，用于在非均匀网格上模拟浮力驱动的热对流。ISLBM通过在传输步骤中引入二次插值，扩展了标准格子玻尔兹曼框架，使得在保持算法简单性和并行可扩展性的同时，能够在固体边界附近灵活地进行网格细化。该方法应用于高雷诺数的二维侧加热腔体$10^6 \leq Ra \leq 10^8$，以及三维侧加热腔体$10^5 \leq Ra \leq 10^7$，普朗特数固定为$Pr=0.71$。基准结果表明，ISLBM能够准确捕捉温度和速度边界层，得到的努塞尔数和雷诺数与高保真参考数据高度一致。网格收敛研究表明，全局量接近三阶精度，局部场约为二阶精度。我们进一步将自研的LBM求解器与两个开源求解器进行了计算性能对比：基于谱元法的Nek5000和基于有限体积法的OpenFOAM。性能指标，包括每秒百万次格子更新（MLUPS）和无量纲时间单位的时钟时间（WCTpDT），表明ISLBM在大规模模拟中效率高出一到三个数量级。在GPU架构上，ISLBM保持了较高的计算性能：非均匀网格的吞吐量在MLUPS方面达到均匀网格的60%-70%，而WCTpDT的成本大约是其三倍。这些结果突显了基于插值的LBM方法在非均匀网格上高保真热对流模拟中的潜力，为未来扩展至湍流提供了坚实的基础。 显示英文摘要

摘要： We present a systematic evaluation of an interpolation-supplemented lattice Boltzmann method (ISLBM) for simulating buoyancy-driven thermal convection on non-uniform meshes. The ISLBM extends the standard lattice Boltzmann framework by incorporating quadratic interpolation during the streaming step, enabling flexible mesh refinement near solid boundaries while maintaining algorithmic simplicity and parallel scalability. The method is implemented for a two-dimensional side-heated cavity at high Rayleigh numbers $10^6 \leq Ra \leq 10^8$, and for a three-dimensional side-heated cavity at $10^5 \leq Ra \leq 10^7$, with the Prandtl number fixed at $Pr=0.71$. Benchmark results show that the ISLBM accurately captures thermal and velocity boundary layers, yielding Nusselt and Reynolds numbers in close agreement with high-fidelity reference data. Grid-convergence studies demonstrate nearly third-order accuracy for global quantities and about second-order for local fields. We further assess the computational performance of the in-house LBM solver against two open-source solvers: Nek5000 based on the spectral element method, and OpenFOAM based on the finite volume method. Performance metrics, including million lattice updates per second (MLUPS) and wall-clock time per dimensionless time unit (WCTpDT), indicate that the ISLBM offers one to three orders of magnitude higher efficiency in large-scale simulations. On GPU architectures, the ISLBM retains high computational performance: throughput on non-uniform meshes reaches 60 -- 70\% of that on uniform meshes in terms of MLUPS, while the cost in WCTpDT is about three times higher. These results highlight the potential of interpolation-based LBM approaches for high-fidelity simulations of thermal convection on non-uniform meshes, providing a robust foundation for future extensions to turbulent flows.