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Entropic lattice Boltzmann representations required to recover Navier-Stokes flows
Brian Keating1, George Vahala, Jeffrey Yepez
1Department of Physics, William & Mary, Williamsburg, Virginia 23187, USA.
Summary
The entropic lattice Boltzmann scheme has two forms: one uses discrete Boltzmann H function, the other Tsallis entropy. Enforcing pressure tensor constraints proves the discrete Boltzmann form is necessary for Navier-Stokes equations.
Area of Science:
- Computational fluid dynamics
- Statistical mechanics
- Numerical analysis
Background:
- The lattice Boltzmann method (LBM) is a powerful numerical technique for fluid dynamics.
- Existing entropic LBM formulations diverge, one based on discrete Boltzmann H-function, another on Tsallis nonextensive entropy.
- Understanding the theoretical underpinnings of these formulations is crucial for accurate simulations.
Purpose of the Study:
- To investigate the theoretical basis of two entropic lattice Boltzmann schemes.
- To determine the conditions under which each entropic form is valid.
- To clarify the relationship between entropic LBM, statistical mechanics, and continuum fluid dynamics.
Main Methods:
- Theoretical analysis of entropy formulations in LBM.
- Derivation of entropic forms based on moment constraints.
- Three-dimensional numerical simulations of LBM schemes.
- Comparison of standard LBM, entropic LBM (Tsallis-like), and entropic LBM (discrete Boltzmann).
Main Results:
- Non-enforcement of pressure tensor moment constraints leads to Tsallis-like entropy forms.
- Imposition of pressure tensor moment constraints necessitates the discrete Boltzmann entropy form.
- Simulations demonstrate differences between standard and entropic LBM schemes.
- The number of phase-space velocities impacts simulation outcomes.
Conclusions:
- The discrete Boltzmann H-function is the theoretically sound entropic form for LBM when pressure tensor constraints are enforced for Navier-Stokes recovery.
- Tsallis-like entropy forms arise from relaxed moment constraints.
- Simulation results highlight the practical implications of theoretical choices in LBM.
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