Lattice Boltzmann model capable of mesoscopic vorticity computation

Area of Science:

• Computational Fluid Dynamics
• Mesoscopic Physics
• Numerical Analysis

Background:

• Standard lattice Boltzmann (LB) models offer second-order accuracy for strain-rate components.
• Existing LB models struggle to accurately compute vorticity and pressure gradients at the mesoscopic level.

Purpose of the Study:

• To design a multiple-relaxation time LB model capable of mesoscopic computation of velocity and pressure gradients.
• To achieve second-order accuracy for vorticity calculation within the LBM framework.

Main Methods:

• Development of a multiple-relaxation time LB model on a D3Q27 lattice.
• Detailed Chapman-Enskog analysis to derive constraints for isothermal Navier-Stokes equations.
• Analysis of nonequilibrium moments to enable mesoscopic computation of gradients.

Main Results:

• A novel LB model is designed, enabling second-order accurate mesoscopic vorticity computation.
• The model's accuracy is proven through asymptotic analysis.
• Successful validation in simulations of 3D decaying Taylor-Green flow, lid-driven cavity flow, and flow past a sphere.

Conclusions:

• Mesoscopic vorticity computation is achievable in LBM with sufficient degrees of freedom and model modifications.
• The developed model enhances the capabilities of LBM for fluid dynamics simulations.
• Mesoscopic vorticity computation is feasible even with a single relaxation parameter.