Galilean-Invariant Lattice-Boltzmann Models with H-Theorem

Abstract

We demonstrate that the requirement of galilean invariance determines the choice of H function for a wide class of entropic lattice Boltzmann models for the incompressible Navier-Stokes equations. The required H function has the form of the Burg entropy for D=2, and of a Tsallis entropy with q=1-2/D for D>2, where D is the number of spatial dimensions. We use this observation to construct a fully explicit, unconditionally stable, galilean invariant, lattice-Boltzmann model for the incompressible Navier-Stokes equations, for which attainable Reynolds number is limited only by grid resolution.

4 pages

References in corpus (4)

• Role of the H theorem in lattice Boltzmann hydrodynamic simulations
• Entropic lattice Boltzmann methods
• Family of additive entropy functions out of thermodynamic limit
• Detailed Balance and H-Theorems for Dissipative Particle Dynamics

Cited by in corpus (28)

• Lattice Boltzmann simulations of soft matter systems
• Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation
• The nonextensive parameter and Tsallis distribution for self-gravitating systems
• What should a statistical mechanics satisfy to reflect nature?
• Lattice Boltzmann scheme for relativistic fluids
• Preferential attachment growth model and nonextensive statistical mechanics
• Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization
• Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number
• On the Three-dimensional Central Moment Lattice Boltzmann Method
• A fully relativistic lattice Boltzmann algorithm
• Three Dimensional Lattice-Boltzmann Model for Electrodynamics
• Kinetic Theory of Turbulence Modeling: Smallness Parameter, Scaling and Microscopic Derivation of Smagorinsky Model
• Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations
• Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg
• Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
• What does the nonextensive parameter q stand for in self-gravitating systems ?
• Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach
• The effects of the nonextensivity on the dimerization process and nematic ordering
• Lattice Boltzmann model for weakly compressible flows
• Semi-automatic construction of Lattice Boltzmann models
• Essentially entropic lattice Boltzmann model: Theory and simulations
• Nonextensive Thermostatistical Approach to the Thermoluminescence Decay
• Nonlinear waves in a hot, viscous and nonextensive quark gluon plasma
• Lattice Boltzmann Model for Numerical Relativity
• Entropy production in the cyclic lattice Lotka-Volterra model
• A Partial Entropic Stabilization of Lattice Boltzmann MHD
• A Partial Entropic Lattice Boltzmann MHD Simulation of the Orszag-Tang Vortex
• A generalized molecular theory for nematic liquid crystals formed by non-cylindrically symmetric molecules