Extended Lattice Boltzmann Model

Abstract

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model remains valid also for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

References in corpus (9)

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• Lattice Boltzmann method for thermal flow simulation on standard lattices
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Cited by in corpus (6)

• Extended Lattice Boltzmann Model for Gas Dynamics
• Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues
• Particles on Demand for flows with strong discontinuities
• Multi-scale semi-Lagrangian lattice Boltzmann method
• Detonation modeling with the Particles on Demand method
• Towards nonlinear thermohydrodynamic simulations via the Onsager-Regularized Lattice Boltzmann Method