Extended volumetric scheme for lattice Boltzmann models

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Mesoscopic physics

Background:

• Lattice Boltzmann (LB) methods are widely used for simulating fluid dynamics.
• Standard LB models can face numerical stability issues, especially in high Reynolds number flows.
• Multispeed LB models offer advantages but can be complex to stabilize.

Purpose of the Study:

• To propose an extended volumetric scheme for lattice Boltzmann models.
• To enhance numerical stability and remove nonlocal advection in multispeed LB models.
• To maintain macroscopic hydrodynamic recovery and numerical accuracy.

Main Methods:

• Development of an extended volumetric scheme for LB models.
• Implementation of the scheme in multispeed LB simulations.
• Analysis of the scheme's impact on Courant-Friedrichs-Lewy number and numerical stability.
• Comparison with standard LB methods for macroscopic hydrodynamics recovery.

Main Results:

• The proposed scheme effectively removes nonlocal advection in multispeed LB models.
• It recovers the same macroscopic hydrodynamics as standard LB methods without additional treatments.
• The scheme achieves an effectively reduced Courant-Friedrichs-Lewy number.
• Numerical stability is significantly enhanced for high Reynolds number simulations.

Conclusions:

• The extended volumetric scheme offers a robust solution for stabilizing LB simulations, particularly for high Reynolds number flows.
• This advancement is crucial for extending the applicability of LB methods in complex fluid dynamics problems.
• The scheme provides a stable and accurate alternative for multispeed LB model development.