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Pseudoentropic derivation of the regularized lattice Boltzmann method
Andreas Krämer1,2, Dominik Wilde1,3, Knut Küllmer1,3
1Institute of Technology, Resource and Energy-efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany.
Physical Review. E
|October 3, 2019
Summary
The regularized lattice Boltzmann method (RLBM) enhances fluid turbulence simulations on underresolved grids, outperforming conventional LBM. RLBM suppresses spurious vortices effectively, though KBC excels at resolving small-scale vortices.
Area of Science:
- Computational fluid dynamics
- Numerical methods for turbulence
- Statistical mechanics
Background:
- The lattice Boltzmann method (LBM) is crucial for simulating fluid turbulence.
- Stable simulations require collision operators that prevent deviations from local equilibrium.
- Existing methods include multirelaxation time, entropic, quasiequilibrium, regularized, and cumulant schemes.
Purpose of the Study:
- To derive the regularized lattice Boltzmann method (RLBM) within a unified theoretical framework.
- To compare RLBM with the entropic multirelaxation time LBM (KBC) by Karlin, Bösch, and Chikatamarla.
- To investigate the role of pseudoentropy maximization in these LBM schemes.
Main Methods:
- Derivation of RLBM by expanding entropy around a global equilibrium.
- Comparison with KBC, derived by expanding entropy around a local equilibrium.
- Numerical simulations of 2D shear layers and 3D Taylor-Green and Kida vortices.
Main Results:
- RLBM ensures stable simulations on underresolved grids (e.g., 16x16), unlike conventional LBM.
- RLBM effectively suppresses spurious vortices in 2D shear layers compared to KBC.
- KBC demonstrates superior performance in resolving small-scale vortices in 3D simulations, achieving a higher effective Reynolds number.
Conclusions:
- RLBM offers enhanced stability and spurious vortex suppression for large-scale turbulent structures.
- KBC excels in resolving finer turbulent scales, indicating a trade-off between the methods.
- Both RLBM and KBC can be derived from maximizing a quadratic Taylor expansion of the entropy function.
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