Lattice Boltzmann method for direct numerical simulation of turbulent flows

We present three-dimensional numerical simulations (DNS) of the Kida vortex flow, a prototypical turbulent flow, using a novel high-order lattice Boltzmann model. Extensive comparisons of various global and local statistical quantities obtained with an incompressible flow spectral element solver are reported. It is demonstrated that the lattice Boltzmann method is a promising alternative for DNS as it quantitatively capturesall the computed statistics of fluid turbulence

On the Three-dimensional Central Moment Lattice Boltzmann Method

A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal forces. For suitable choices of the orthogonal moment basis for the three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen velocity (D3Q15) lattice models, attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work; the corresponding source terms are specified to correctly influence lower order hydrodynamic fields, while avoiding aliasing effects for higher order moments. These are achieved by successively matching the corresponding continuous and discrete central moments at various orders, with the final expressions written in terms of raw moments via a transformation based on the binomial theorem. Furthermore, to alleviate the discrete effects with the source terms, they are treated to be temporally semi-implicit and second-order, with the implicitness subsequently removed by means of a transformation. As a result, the approach is frame-invariant by construction and its emergent dynamics describing fully 3D fluid motion in the presence of force fields is Galilean invariant. Numerical experiments for a set of benchmark problems demonstrate its accuracy.Comment: 55 pages, 8 figure

Lattices for the lattice Boltzmann method

A recently introduced theory of higher-order lattice Boltzmann models [Chikatamarla and Karlin, Phys. Rev.Lett. 97, 190601 (2006)] is elaborated in detail. A general theory of the construction of lattice Boltzmannmodels as an approximation to the Boltzmann equation is presented. New lattices are found in all threedimensions and are classified according to their accuracy (degree of approximation of the Boltzmann equation).The numerical stability of these lattices is argued based on the entropy principle. The efficiency and accuracyof many new lattices are demonstrated via simulations in all three dimensions

Elements of the lattice Boltzmann method II: kinetics and hydrodynamics in one dimension

Concepts of the lattice Boltzmann method are discussed in detail for the one-dimensional kinetic model. Various techniques of constructing lattice Boltzmann models are discussed, and novel collision integrals are derived. Geometry of the kinetic space and the role of the thermodynamic projector is elucidated

Grad's approximation for missing data in lattice Boltzmann simulations

Engineering applications of computational fluid dynamics typically require specification of the boundary conditions at the inlet and at the outlet. It is known that the accuracy and stability of simulations is greatly influenced by the boundary conditions even at moderate Reynolds numbers. In this paper, we derive a new outflow boundary condition for the lattice Boltzmann simulations from non-equilibrium thermodynamics and Grad's moment closure. The proposed boundary condition is validated with a three-dimensional simulation of a backward facing step flow. Results demonstrate that the new outlet condition significantly extends the simulation capability of the lattice Boltzmann method

Elements of the lattice Boltzmann method I: linear advection equation

This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems. The lattice Boltzmann method is introduced at the elementary level of the linear advection equation. Details are provided on lifting the target macroscopic equations to a kinetic equation, and, after that, to the fully discrete lattice Boltzmann scheme. The over-relaxation method is put forward as a cornerstone of the second-order temporal discretization, and its enhancement with the use of the entropy estimate is explained in detail. A new asymptotic expansion of the entropy estimate is derived, and implemented in the sample code. It is shown that the lattice Boltzmann method provides a computationally efficient way of numerically solving the advection equation with a controlled amount of numerical dissipation, while retaining positivity

Entropic lattice Boltzmann method for simulation of thermal flows

A new thermal entropic lattice Boltzmann model on the standard two-dimensional nine-velocity lattice is introduced for simulation of weakly compressible flows. The new model covers a wider range of flows than the standard isothermal model on the same lattice, and is computationally efficient and stable