Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments

Abstract

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of $1000$. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.

arXiv comment23 pages, 8 figures

References in corpus (24)

• On pressure and velocity flow boundary conditions and bounceback for the lattice Boltzmann BGK model
• Simulation of non-ideal gases and liquid-gas phase transitions by lattice Boltzmann equation
• Lattice Boltzmann Simulation of Non-Ideal Fluids
• Lattice Boltzmann methods for multiphase flow and phase-change heat transfer
• A Lattice Boltzmann Model for Multi-phase Fluid Flows
• Recursive regularization step for high-order lattice Boltzmann methods
• Comprehensive comparison of collision models in the lattice Boltzmann framework: Theoretical investigations
• Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices
• Three-dimensional cascaded lattice Boltzmann method: improved implementation and consistent forcing scheme
• Consistent forcing scheme in the cascaded lattice Boltzmann method
• On the Three-dimensional Central Moment Lattice Boltzmann Method
• Multiphysics flow simulations using D3Q19 lattice Boltzmann methods based on central moments
• Lattice Boltzmann modeling and simulation of forced-convection boiling on a cylinder
• Lattice Boltzmann modeling and simulation of liquid jet breakup
• Impact of collision models on the physical properties and the stability of lattice Boltzmann methods
• Three-dimensional central-moments-based lattice Boltzmann method with external forcing: A consistent, concise and universal formulation
• Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations
• Improved three-dimensional color-gradient lattice Boltzmann model for immiscible multiphase flows
• A central-moment multiple-relaxation-time collision model
• Cross-platform programming model for many-core lattice Boltzmann simulations
• Achieving thermodynamic consistency in a class of free-energy multiphase lattice Boltzmann models
• Entropic multi-relaxation-time lattice Boltzmann model for large density ratio two-phase flows
• A quantitative comparison of physical accuracy and numerical stability of Lattice Boltzmann color gradient and pseudopotential multicomponent models for microfluidic applications
• Chromodynamic multi-relaxation time lattice Boltzmann scheme for fluids with density difference