Regularized lattice Bhatnagar-Gross-Krook model for two- and three-dimensional cavity flow simulations

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Fluid mechanics

Background:

• The standard single-relaxation time lattice Boltzmann equation (SRT-LBE) is widely used for fluid flow simulations.
• However, SRT-LBE can suffer from stability issues, particularly in complex flow scenarios like lid-driven cavities.
• Investigating enhanced versions of LBE is crucial for improving simulation accuracy and reliability.

Purpose of the Study:

• To evaluate the accuracy and performance of the regularized single-relaxation time lattice Boltzmann equation (R-SRT-LBE).
• To compare the R-SRT-LBE with the standard SRT-LBE in simulating two- and three-dimensional lid-driven cavities.
• To assess the trade-off between stability improvements and computational cost.

Main Methods:

• Implementation of the regularized single-relaxation time lattice Boltzmann equation.
• Numerical simulation of two- and three-dimensional lid-driven cavity flow problems.
• Comparative analysis of R-SRT-LBE and standard SRT-LBE for accuracy and stability.

Main Results:

• The regularized version demonstrates a significant improvement in numerical stability compared to the standard SRT-LBE.
• Accurate simulation results were achieved for both 2D and 3D lid-driven cavity flows using the R-SRT-LBE.
• The enhanced stability comes with only a moderate increase in computational overhead.

Conclusions:

• The regularized single-relaxation time lattice Boltzmann equation offers a more stable and accurate approach for simulating lid-driven cavity flows.
• R-SRT-LBE presents a viable alternative to standard methods, especially when stability is a concern.
• The findings support the broader application of regularized LBE methods in computational fluid dynamics.