Entropic equilibrium for the lattice Boltzmann method: Hydrodynamics and numerical properties.

Area of Science:

• Computational fluid dynamics
• Thermodynamics
• Numerical analysis

Background:

• The entropic lattice Boltzmann (eLB) framework constructs equilibrium by minimizing a discrete entropy functional.
• The impact of this entropic equilibrium on solver properties is a subject of ongoing research and discussion.

Purpose of the Study:

• To rigorously analyze the hydrodynamics and numerics of the entropic equilibrium in the lattice Boltzmann method.
• To demonstrate the unconditional linear stability of the entropic equilibrium compared to conventional methods.

Main Methods:

• Analysis of hydrodynamics and numerics of the entropic equilibrium.
• Investigation of mechanisms maintaining unconditional linear stability, including adaptive propagation velocity and positive-definite dissipation rates.
• Development of a local correction to mitigate deviations in effective bulk viscosity.

Main Results:

• The entropic equilibrium demonstrates unconditional linear stability, a significant improvement over conventional polynomial equilibria.
• Key mechanisms for stability include adaptive propagation velocity of normal modes and positive-definite dissipation rates of hydrodynamic eigenmodes.
• A simple local correction effectively reduces deviations in the calculated effective bulk viscosity.

Conclusions:

• The entropic equilibrium provides a robust and unconditionally linearly stable framework for lattice Boltzmann solvers.
• Understanding the underlying mechanisms of stability offers insights into improving numerical accuracy and reliability in fluid simulations.
• The proposed local correction offers a practical method to enhance the accuracy of bulk viscosity calculations within this framework.