Linear stability and isotropy properties of athermal regularized lattice Boltzmann methods

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Statistical physics

Background:

• Lattice Boltzmann (LB) methods are widely used for fluid dynamics simulations.
• Understanding stability and isotropy is crucial for LB scheme accuracy.
• Regularization techniques aim to improve LB scheme stability and accuracy.

Purpose of the Study:

• To propose a general methodology for analyzing stability and isotropy of LB schemes.
• To apply this methodology to regularized LB models.
• To compare the stability properties of different regularization approaches.

Main Methods:

• Linear stability analysis of 2D LB models (Bhatnagar-Gross-Krook, precollision regularization, recursive regularization).
• Analysis of eigenvectors to identify physical content of LB modes.
• Numerical simulations of shear and acoustic waves to confirm stability results.

Main Results:

• Recursive regularization demonstrates superior stability for the D2Q9 lattice, particularly at low viscosity.
• All regularized models exhibit mode filtering, enhancing stability.
• Anisotropic dissipation rates for physical wave modes in under-resolved conditions were observed in regularized models.

Conclusions:

• Recursive regularization is the most stable among the studied models for D2Q9 lattices.
• Mode filtering is a key factor for increased stability in regularized LB schemes.
• Anisotropic dissipation in under-resolved conditions is an inherent characteristic of these regularization methods.