2011/11/30 by Alexander N. Gorban, A. N. Gorban, D. Packwood +1
Engineering · Mathematics · Physics and Astronomy · #Boltzmann constant #Boltzmann equation #Boltzmann's entropy formula #Bounded function #Classical mechanics #Detailed balance #Dissipation #Distribution function #Entropy (arrow of time) #Fluid Dynamics and Turbulent Flows #H-theorem #Joint quantum entropy #Lattice Boltzmann Simulation Studies #Lattice Boltzmann methods #Mach number #Mathematical analysis #Mathematics #Maximum entropy thermodynamics #Mechanics #Model Reduction and Neural Networks #Non-equilibrium thermodynamics #Physics #Quantum #Quantum mechanics #Statistical physics #Thermodynamics #physics.comp-ph
paper · pdf · doi:10.1103/physreve.86.025701
published as Physical Review E 86, 025701(R) (2012) · v2 minor misprint corrections
arxiv created 2011/11/30 · openalex publication_date 2012/08/24 · arxiv updated 2013/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the possibility of modifying collisions in the lattice Boltzmann method to keep the proper entropy balance. We demonstrate that in the space of distributions operated on by lattice Boltzmann methods which respect a Boltzmann type H theorem, there exists a vicinity of the equilibrium where collisions with entropy balance are possible and, at the same time, there exists a region of nonequilibrium distributions where such collisions are impossible. In particular, for a strictly concave and uniformly bounded entropy function with positive equilibria, we show that proper entropy balance is always possible sufficiently close to the local equilibrium and it is impossible sufficiently far from it, where additional dissipation has to appear. We also present some nonclassical entropies that do not share this concern. The cases where the distribution enters the region far from equilibrium typically occur in flows with low viscosity and/or high Mach number flows and in simulations on coarse grids.