Discrete-velocity Boltzmann model: Regularization and linear stability

Area of Science:

• Computational fluid dynamics
• Statistical physics

Background:

• Lattice Boltzmann (LB) methods are widely used for fluid dynamics simulations.
• Conventional LB schemes often use implicit collision models.
• Explicit collision models offer potential advantages in stability and control.

Purpose of the Study:

• To develop and analyze a discrete-velocity Boltzmann model with explicit collisions.
• To investigate the regularization of the collision term in LB models.
• To compare the proposed model with existing regularized LB schemes.

Main Methods:

• A nine-velocity discrete-velocity Boltzmann model with explicit collision definitions.
• Space and time discretization using the collide and stream method.
• Regularization of the collision term and linear stability analysis.
• Numerical experiments including double shear layer, lid-driven cavity flow, and wave propagation.

Main Results:

• The regularized model is equivalent to a specific two-relaxation-time LB model.
• The proposed scheme demonstrates controllable stability and dissipation properties.
• Numerical simulations validate the model's performance across various flow regimes and grid resolutions.

Conclusions:

• The discrete-velocity Boltzmann model with explicit, regularized collisions provides a flexible framework for LB simulations.
• Adjustable model parameters (collision cross sections) allow fine-tuning of stability and dissipation.
• This approach offers a viable alternative to conventional and other regularized LB methods.