Journal of Visualization

, Volume 22, Issue 6, pp 1057–1070 | Cite as

Multi-relaxation time lattice Boltzmann simulations of oscillatory instability in lid-driven flows of 2D semi-elliptical cavity

  • Zhe Feng
  • HeeChang LimEmail author
Regular Paper


In this study, the multi-relaxation-time lattice Boltzmann method is applied to investigate the oscillatory instability of lid-driven flows in two-dimensional semi-elliptical cavities with different vertical-to-horizontal aspect ratios K in the range of 1.0–3.0. The program implemented in this study is parallelized using compute unified device architecture (CUDA), a parallel computing platform, and computations are carried out on NVIDIA Tesla K40c GPU. To carry out precise calculations, the CUDA algorithm is extensively investigated, and its parallel efficiency indicates that the maximum speedup is 47.6 times faster. Furthermore, the steady-oscillatory Reynolds numbers are predicted by implementing the CUDA-based programs. The amplitude coefficient is defined to quantify the time-dependent oscillation of the velocity magnitude at the monitoring point. The simulation results indicate that the transition Reynolds numbers correlate negatively with the aspect ratio of the semi-elliptical cavity and are smaller than those of the rectangular cavity at the same aspect ratio. In addition, the detailed vortex structures of the semi-elliptical cavity within a single period are also investigated when the Reynolds number is larger than the steady-oscillatory value to determine the effects of periodic oscillation of the velocity magnitude.

Graphic abstract


Lattice Boltzmann method Mass-conserved wall treatment Non-equilibrium extrapolation boundary condition Mass leakage CFD 



This work was supported by ‘Human Resources Program in Energy Technology’ of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20164030201230). In addition, this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2019R1I1A3A01058576).


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Copyright information

© The Visualization Society of Japan 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringPusan National UniversityBusanRepublic of Korea

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