Lattice Boltzmann approach for complex nonequilibrium flows

Area of Science:

• Computational physics
• Fluid dynamics
• Nonequilibrium thermodynamics

Background:

• Grad's extended hydrodynamic approach offers a more comprehensive description of fluid behavior than classical hydrodynamics.
• Simulating nonequilibrium flows is computationally challenging, especially across different Knudsen number regimes.
• Lattice Boltzmann methods provide a powerful framework for simulating complex fluid dynamics.

Purpose of the Study:

• To develop and validate a lattice Boltzmann realization of Grad's extended hydrodynamic approach.
• To accurately model nonequilibrium fluid flows from the hydrodynamic to the ballistic regime.
• To assess the method's performance in benchmark flow configurations.

Main Methods:

• Utilized higher-order isotropic lattices within the lattice Boltzmann framework.
• Implemented a higher-order regularization procedure to align with Grad's theory.
• Applied the method to simulate flow across parallel plates and in three-dimensional porous media.

Main Results:

• The lattice Boltzmann realization demonstrated excellent agreement with analytical and numerical solutions.
• Accurate prediction of mass flow was achieved across the full range of Knudsen numbers.
• The method successfully captured flow behavior from the hydrodynamic to the ballistic motion regime.

Conclusions:

• The presented lattice Boltzmann method is a robust and accurate tool for simulating nonequilibrium flows.
• This approach effectively bridges the gap between classical hydrodynamics and kinetic theory.
• The validated method holds promise for applications in microfluidics and rarefied gas dynamics.