Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows
Abstract
1. Introduction
2. Compressible Lattice Boltzmann Models
2.1. Discrete Kinetic Equations
2.2. Thermo-Hydrodynamic Equations
2.3. Lattices
2.4. Equilibrium
2.4.1. Equilibrium Construction
2.4.2. Computational Costs of Numerical Equilibrium
2.4.3. Numerical Equilibrium Accuracy
2.4.4. Equilibria Positivity
3. Extension of Operation Domain
3.1. Shifted Lattices
3.2. Lattices with Increased Temperature Range
4. Numerical Results
4.1. Supersonic Diamond Airfoil
4.2. Busemann Biplane
4.3. Supersonic NACA0012 Airfoil
4.4. Shock–Vortex Interaction
4.5. Richtmyer–Meshkov Instability
4.6. Transonic Onera M6 Wing
5. Conclusions and Outlook: Pruned Lattices and Entropic Guided Equilibrium Construction
5.1. Lattice Pruning
5.2. Entropic Guided Equilibrium
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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n | |||||||
---|---|---|---|---|---|---|---|
3 | 2 | ∞ | |||||
5 | 9 | ||||||
7 | |||||||
9 | |||||||
11 |
DdQ | DdQ | DdQ | |
---|---|---|---|
Polynomial | 1 | ||
Numerical | |||
Polynomial | 1 | ||
Numerical |
0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | |
1.000 | 1.047 | 1.023 | 1.059 | 1.062 | 1.070 | 1.067 |
Up | Analytical | |||||
ELBM | ||||||
Error | ||||||
Down | Analytical | |||||
ELBM | ||||||
Error |
Representative Velocity | Number of Velocities | ||
---|---|---|---|
0 | 0 | 1 | |
1 | 1 | 6 | |
2 | 2 | 12 | |
3 | 3 | 8 | |
4 | 2 | 6 | |
5 | 3 | 24 | |
6 | 4 | 24 | |
8 | 4 | 12 | |
9 | 3 | 6 | |
9 | 5 | 24 | |
10 | 4 | 24 | |
11 | 5 | 24 | |
12 | 6 | 8 | |
13 | 5 | 24 | |
14 | 6 | 48 | |
17 | 7 | 24 | |
18 | 6 | 12 | |
19 | 7 | 24 | |
22 | 8 | 24 | |
27 | 9 | 8 |
Representative Velocity | Number of Velocities | ||
---|---|---|---|
0 | 0 | 1 | |
1 | 1 | 6 | |
3 | 3 | 8 | |
4 | 2 | 6 | |
8 | 4 | 12 | |
9 | 3 | 6 |
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Frapolli, N.; Chikatamarla, S.; Karlin, I. Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows. Entropy 2020, 22, 370. https://doi.org/10.3390/e22030370
Frapolli N, Chikatamarla S, Karlin I. Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows. Entropy. 2020; 22(3):370. https://doi.org/10.3390/e22030370
Chicago/Turabian StyleFrapolli, Nicolò, Shyam Chikatamarla, and Ilya Karlin. 2020. "Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows" Entropy 22, no. 3: 370. https://doi.org/10.3390/e22030370
APA StyleFrapolli, N., Chikatamarla, S., & Karlin, I. (2020). Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows. Entropy, 22(3), 370. https://doi.org/10.3390/e22030370