{"title":"非均匀网格上热对流的插值补格Boltzmann模拟","authors":"Ao Xu , Zheng Zhao , Ben-Rui Xu , Li-Sheng Jiang","doi":"10.1016/j.ijheatmasstransfer.2025.127790","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>≤</mo><mi>R</mi><mi>a</mi><mo>≤</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>8</mn></mrow></msup></mrow></math></span>, and for a three-dimensional side-heated cavity at <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>5</mn></mrow></msup><mo>≤</mo><mi>R</mi><mi>a</mi><mo>≤</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>7</mn></mrow></msup></mrow></math></span>, with the Prandtl number fixed at <span><math><mrow><mi>P</mi><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>71</mn></mrow></math></span>. 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.</div></div>","PeriodicalId":336,"journal":{"name":"International Journal of Heat and Mass Transfer","volume":"255 ","pages":"Article 127790"},"PeriodicalIF":5.8000,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Interpolation-supplemented lattice Boltzmann simulation of thermal convection on non-uniform meshes\",\"authors\":\"Ao Xu , Zheng Zhao , Ben-Rui Xu , Li-Sheng Jiang\",\"doi\":\"10.1016/j.ijheatmasstransfer.2025.127790\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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 <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>≤</mo><mi>R</mi><mi>a</mi><mo>≤</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>8</mn></mrow></msup></mrow></math></span>, and for a three-dimensional side-heated cavity at <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>5</mn></mrow></msup><mo>≤</mo><mi>R</mi><mi>a</mi><mo>≤</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>7</mn></mrow></msup></mrow></math></span>, with the Prandtl number fixed at <span><math><mrow><mi>P</mi><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>71</mn></mrow></math></span>. 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.</div></div>\",\"PeriodicalId\":336,\"journal\":{\"name\":\"International Journal of Heat and Mass Transfer\",\"volume\":\"255 \",\"pages\":\"Article 127790\"},\"PeriodicalIF\":5.8000,\"publicationDate\":\"2025-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Heat and Mass Transfer\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0017931025011251\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Heat and Mass Transfer","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0017931025011251","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Interpolation-supplemented lattice Boltzmann simulation of thermal convection on non-uniform meshes
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 , and for a three-dimensional side-heated cavity at , with the Prandtl number fixed at . 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.
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