Lattice Boltzmann method for thermal flow simulation on standard lattices.

Area of Science:

• Computational fluid dynamics
• Thermal flow simulation
• Lattice Boltzmann methods

Background:

• The consistent lattice Boltzmann model with energy conservation was recently introduced.
• Simulating thermal flows requires robust and accurate numerical methods.
• Standard lattices pose challenges for energy-conserving thermal flow models.

Purpose of the Study:

• To extend the consistent lattice Boltzmann model with energy conservation for thermal flow simulations.
• To develop a two-dimensional thermal model on a standard square lattice.
• To validate the model's performance in established thermal flow benchmarks.

Main Methods:

• Extension of the consistent lattice Boltzmann model with energy conservation.
• Development of a nine-velocity, two-dimensional thermal lattice model.
• Numerical simulation of thermal Couette flow.
• Numerical simulation of Rayleigh-Bénard natural convection.

Main Results:

• Successful extension of the consistent lattice Boltzmann model for thermal flows.
• Development of a functional two-dimensional thermal model on a square lattice.
• Validation of the model against thermal Couette and Rayleigh-Bénard problems, demonstrating accuracy.

Conclusions:

• The extended consistent lattice Boltzmann model is suitable for simulating thermal flows on standard lattices.
• The developed two-dimensional model accurately captures thermal phenomena in benchmark cases.
• This work provides a validated computational tool for thermal flow research.