Essentially entropic lattice Boltzmann model: Theory and simulations.

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis
• Statistical Mechanics

Background:

• The entropic lattice Boltzmann model (ELBM) ensures numerical stability by solving a nonlinear entropy evolution equation.
• Existing ELBMs involve iterative solutions, leading to computational overhead and complexity.

Purpose of the Study:

• To derive closed-form analytic solutions for the entropic lattice Boltzmann model.
• To demonstrate the accuracy and simplicity of the analytic solution compared to iterative methods.
• To extend the analytic solution for heat transfer problems by removing Prandtl number limitations.

Main Methods:

• Derivation of closed-form analytic solutions for the nonlinear entropy evolution equation.
• Comparison of analytic solutions with iterative solutions using test cases.
• Extension of the analytic solution for the Ellipsoidal Statistical (ES)-Bhatnagar-Gross-Krook model.

Main Results:

• The analytic solution is shown to be equivalent to the standard lattice Boltzmann model near equilibrium.
• Analytic solutions exhibit minimal deviation from iterative solutions across test cases.
• The extended analytic solution removes Prandtl number limitations for heat transfer.

Conclusions:

• The derived analytic solution offers a computationally efficient and simpler alternative to iterative entropic lattice Boltzmann models.
• The method enhances the applicability of lattice Boltzmann models to heat transfer problems.
• This work provides a robust and accessible framework for entropic lattice Boltzmann simulations.