Essentially Entropic Lattice Boltzmann Model.

Area of Science:

• Computational fluid dynamics
• Hydrodynamics
• Thermodynamics

Background:

• The entropic lattice Boltzmann model (ELBM) is a kinetic theory for hydrodynamics.
• It ensures nonlinear stability through numerical enforcement of the H theorem, a discrete version of the second law of thermodynamics.
• This process typically involves iteratively solving a nonlinear equation to find the maximal discrete path length for zero dissipation.

Purpose of the Study:

• To develop an exact solution for determining the path length in ELBM simulations.
• To reduce the computational cost associated with ELBM.
• To resolve indeterminacy issues in ELBM when the entropic involution step does not exist.

Main Methods:

• An exact solution for path length was derived by assuming a negative entropy change criterion, transforming the problem into solving an inequality.
• A new framework for constructing Padé approximants via quadrature on convex functions was developed to solve this inequality.
• The formulation avoids complex mathematical library functions, significantly reducing computational demands.

Main Results:

• An exact solution for the path length in ELBM was obtained, simplifying the zero dissipation state determination.
• The method resolves indeterminacy issues in specific entropic involution scenarios.
• Computational cost is drastically reduced compared to traditional iterative methods.

Conclusions:

• The developed framework provides an efficient and exact method for ELBM path length calculation.
• This approach enhances the practicality of ELBM for complex hydrodynamic simulations.
• The study successfully simulated flow over a NACA-0012 airfoil at a high Reynolds number (2.88×10^6), demonstrating the method's efficacy.