GPU-Accelerated High-Fidelity Simulation of Turbulent Natural Convection

Document Type : Research Paper

Author
Alexander Nee
Research School of High-Energy Physics, National Research Tomsk Polytechnic University, Tomsk, Russia
10.22055/jacm.2026.48841.5540
Abstract
This paper presents the hybrid meso-macroscopic model for high-fidelity simulation of turbulent thermal flows. The two-relaxation lattice Boltzmann solver with the fourth order equilibrium distribution function representation was used to compute flow fields. Numerical integration of the energy equation was performed using a fourth-order Runge-Kutta method. In-house MATLAB and Julia codes were developed using CUDA tools. Turbulent natural convection of air was considered in a Rayleigh number range of 1010 ≤ Ra ≤ 1011 and aspect ratio range of 0.5 ≤ Ar ≤ 2. It was found that distribution of the second order statistics is mainly determined by convective plumes dynamics. The aspect ratio affects the level of heat stratification. Moreover, the horizontal distribution of temperature variance and turbulent kinetic energy with Ra = 1010 is altered to vertical distribution with Ra = 1011 when Ar = 2. The hybrid lattice Boltzmann scheme predicts the mean Nusselt numbers with error of no more than 1% and 4% when Ra = 1010 and Ra = 1011, respectively, compared to classical DNS techniques. The model performance achieves 1776 MLUPS and 1048.58 MLUPS with NVIDIA Tesla V100 when using single and double precision variables, respectively. This level of computational performance creates an opportunity for the real-time prediction of thermal turbulence characteristics.
Keywords
GPU computing
Thermal turbulence
High-performance computing
Hybrid LBM
Parallel simulation
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Barakos, G., Mitsoulis, E., Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions, International Journal for Numerical Methods in Fluids, 18, 1994, 727–739. 
[2]. Chen, H.-T., Huang, Y.-C., Chen, K.-X., Chang, J.-R., Yan, W.-M., Experimental and numerical study of inverse natural convection-conduction problem in a fully partitioned cavity, Numerical Heat Transfer, Part A: Applications, 85, 2024, 4204–4227.
[3]. Chen, H.-T., Huang, Y.-C., Rashidi, S., Chen, K.-X., Yan, W.-M., Numerical and experimental studies on heat transfer characteristics and ventilation for indoor vertical farming system, Thermal Science and Engineering Progress, 52, 2024, 102667.
[4] Paolucci, S., Direct numerical simulation of two-dimensional turbulent natural convection in an enclosed cavity, Journal of Fluid Mechanics, 215, 1990, 229–262.
[5] Fusegi, T., Hyun, J.M., Kuwahara, K., Three-dimensional simulation of natural convection in a sidewall-heated cube, International Journal for Numerical Methods in Fluids, 13, 1991, 857–867.
[6] Trias, F.X., Gorobets, A., Soria, M., Oliva, A., Direct numerical simulation of a differentially heated cavity of aspect ratio 4 with Rayleigh numbers up to 1011 – Part I: Numerical methods and time-averaged flow, International Journal of Heat and Mass Transfer, 53, 2010, 665–673. 
[7] Trias, F.X., Gorobets, A., Soria, M., Oliva, A., Direct numerical simulation of a differentially heated cavity of aspect ratio 4 with Rayleigh numbers up to 1011 – Part II: Heat transfer and flow dynamics, International Journal of Heat and Mass Transfer, 53, 2010, 674–683.
[8] Trias, F.X., Gorobets, A., Oliva, A., Pérez-Segarra, C.D., DNS and regularization modeling of a turbulent differentially heated cavity of aspect ratio 5, International Journal of Heat and Mass Transfer, 57, 2013, 171–182. 
[9] Trias, F.X., Gorobets, A., Pérez-Segarra, C.D., Oliva, A., Numerical simulation of turbulence at lower costs: Regularization modeling, Computers & Fluids, 80, 2013, 251–259. 
[10] Vasiliev, A., Sukhanovskii, A., Frick, P., Budnikov, A., Fomichev, V., Bolshukhin, M., Romanov, R., High Rayleigh number convection in a cubic cell with adiabatic sidewalls, International Journal of Heat and Mass Transfer, 102, 2016, 201–212. 
[11] Sondak, D., Smith, T.M., Pawlowski, R.P., Condec, S., Shadid, J.N., High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard convection, Mechanics Research Communications, 109, 2020, 103614. 
[12] Kizildag, D., Trias, F.X., Rodríguez, I., Oliva, A., Large eddy and direct numerical simulations of a turbulent water-filled differentially heated cavity of aspect ratio 5, International Journal of Heat and Mass Transfer, 77, 2014, 1084–1094. 
[13] Dixit, H.N., Babu, V., Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, International Journal of Heat and Mass Transfer, 49, 2006, 727–739. 
[14] Sharma, K.V., Straka, R., Tavares, F.W., Natural convection heat transfer modeling by the cascaded thermal lattice Boltzmann method, International Journal of Thermal Sciences, 134, 2018, 552–564. 
[15] Frapolli, N., Chikatamarla, S.S., Karlin, I.V., Entropic lattice Boltzmann simulation of thermal convective turbulence, Computers & Fluids, 175, 2018, 2–19. 
[16] Wang, P., Zhang, Y., Guo, Z., Numerical study of three-dimensional natural convection in a cubical cavity at high Rayleigh numbers International Journal of Heat and Mass Transfer, 113, 2017, 217–228. 
[17] Wen, X., Wang, L.-P., Guo, Z., Zhakebayev, D.B., Laminar to turbulent flow transition inside the boundary layer adjacent to isothermal wall of natural convection flow in a cubical cavity, International Journal of Heat and Mass Transfer, 167, 2021, 120822. 
[18] Zhuo, C., Zhong, C., LES-based filter-matrix lattice Boltzmann model for simulating turbulent natural convection in a square cavity, International Journal of Heat and Fluid Flow, 42, 2013, 10–22. 
[19] Chen, S., Liu, H., Zheng, C., Numerical study of turbulent double-diffusive natural convection in a square cavity by LES-based lattice Boltzmann model, International Journal of Heat and Mass Transfer, 55, 2012, 4862–4870. 
[20] Lallemand, P., Lou, L.-S., Hybrid finite-difference thermal lattice Boltzmann equation, International Journal of Modern Physics B, 17, 2003, 41–47.
[21] Nee, A., Comparative Study of Hybrid Lattice Boltzmann and Vorticity-vector Potential Modelling of 2D and 3D Natural Convection Combined with Rosseland Radiation, Journal of Applied and Computational Mechanics, 8, 2022, 1467–1479. 
[22] Nee, A., Hybrid Lattice Boltzmann Scheme for Conductive-convective-radiative Heat Transfer, Journal of Applied and Computational Mechanics, 11, 2025, 1149–1161. 
[23] Nee, A., Evaluation of hybrid lattice Boltzmann models for laminar and turbulent natural convection, International Communications in Heat and Mass Transfer, 162, 2025, 108635. 
[24] Ginzburg, I., Verhaeghe, F., d’Humieres, D., Two-relaxation-time lattice Boltzmann scheme: About parameterization, velocity, pressure and mixed boundary conditions, Communications in Computational Physics, 3, 2008, 427–478.
[25] Feng, Y.-L., Guo, S.-L., Tao, W.-Q., Sagaut, P., Regularized thermal lattice Boltzmann method for natural convection with large temperature differences, International Journal of Heat and Mass Transfer, 125, 2018, 1379–1391. 
[26] Ampofo, F., Karayiannis, T.G., Experimental benchmark data for turbulent natural convection in an air filled square cavity, International Journal of Heat and Mass Transfer, 46, 2003, 3551–3572. 
[27] Kerr, R.M., Rayleigh number scaling in numerical convection, Journal of Fluid Mechanics, 310, 1996, 139–179.
[28] Trias, F.X., Soria, M., Oliva, A., Pérez-Segarra, C.D., Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4, Journal of Fluid Mechanics, 586, 2007, 259–293. 
[29] https://julialang.org/
[30] https://github.com/omlins/ParallelStencil.jl
Journal of Applied and Computational Mechanics
Volume 12, Issue 3
Summer 2026
Pages 1276-1287