Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics
Abstract
:1. Introduction
2. Equilibrium for DV Boltzmann Kinetic Model and the Euler Equations
3. Navier–Stokes Equations
4. Spurious Invariants
5. Nine Velocity DV Boltzmann Model for Lattice
- a.
- b.
- the collisions linking all three different energy states, they define transitions between the particle’s states with different kinetic energies, and evidently can not be excluded. We have four different reactions , , , . The corresponding contributions to the collision kernel are
- c.
- Broadwell type collision between the particles with the velocity magnitudes is defined by the reaction , the contributions to the collision kernel are
- d.
- the collisions between the particles with the velocity magnitudes and c, we have four different reactions , the contributions to the collision kernel are
6. Numerical Implementation and Test Problems
6.1. Shear Wave Decay
6.2. Taylor-Green Vortex
7. Results and Discussion
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
DV | discrete velocity |
LB | lattice Boltzmann |
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Ilyin, O. Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics. Mathematics 2021, 9, 993. https://doi.org/10.3390/math9090993
Ilyin O. Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics. Mathematics. 2021; 9(9):993. https://doi.org/10.3390/math9090993
Chicago/Turabian StyleIlyin, Oleg. 2021. "Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics" Mathematics 9, no. 9: 993. https://doi.org/10.3390/math9090993