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

IF 5.8 2区 工程技术 Q1 ENGINEERING, MECHANICAL
Ao Xu , Zheng Zhao , Ben-Rui Xu , Li-Sheng Jiang
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Abstract

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 106Ra108, and for a three-dimensional side-heated cavity at 105Ra107, 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.
非均匀网格上热对流的插值补格Boltzmann模拟
我们提出了一个系统的评价插值补充晶格玻尔兹曼方法(ISLBM)模拟浮力驱动的热对流在非均匀网格。ISLBM扩展了标准晶格玻尔兹曼框架,在流步骤中结合二次插值,在保持算法简单性和并行可扩展性的同时,在实体边界附近实现灵活的网格细化。该方法适用于高瑞利数106≤Ra≤108的二维侧加热腔体和105≤Ra≤107的三维侧加热腔体,Prandtl数固定为Pr=0.71。基准测试结果表明,ISLBM准确捕获了热边界层和速度边界层,得到的努塞尔数和雷诺数与高保真参考数据非常吻合。网格收敛研究表明,全局量的精度接近三阶,局部量的精度约为二阶。我们进一步评估了内部LBM求解器与两个开源求解器的计算性能:基于谱元法的Nek5000和基于有限体积法的OpenFOAM。性能指标,包括每秒百万次晶格更新(MLUPS)和每个无量纲时间单位(WCTpDT)的时钟时间,表明ISLBM在大规模模拟中提供了一到三个数量级的效率。在GPU架构上,ISLBM保持了很高的计算性能:就MLUPS而言,非均匀网格上的吞吐量达到均匀网格上的60%-70%,而WCTpDT的成本大约高出三倍。这些结果突出了基于插值的LBM方法在非均匀网格上高保真模拟热对流方面的潜力,为未来扩展到湍流提供了坚实的基础。
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来源期刊
CiteScore
10.30
自引率
13.50%
发文量
1319
审稿时长
41 days
期刊介绍: International Journal of Heat and Mass Transfer is the vehicle for the exchange of basic ideas in heat and mass transfer between research workers and engineers throughout the world. It focuses on both analytical and experimental research, with an emphasis on contributions which increase the basic understanding of transfer processes and their application to engineering problems. Topics include: -New methods of measuring and/or correlating transport-property data -Energy engineering -Environmental applications of heat and/or mass transfer
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