Haiqiong Xie

A comparative study of lattice Boltzmann models for incompressible flow

Abstract For incompressible flow, a comparative study on the four lattice Boltzmann (LB) models, the standard model, the He–Luo model, Guo’s model, and the present model, is performed. Theoretically, the macroscopic equations derived from the involved LB models are compared by the Chapman–Enskog analysis. Then, the analytical framework proposed in M. Junk’s work is applied to investigate the finite difference stencils and the equivalent moment systems pertaining to the concerned LB models. Conclusions are drawn from the theoretical derivations that the truncated error terms, which differ among the concerned LB models, have effects on the accuracy of the modeled deviatoric stress. Moreover, the cavity flow in two dimensions is adopted as a benchmark test to confirm the theoretical demonstrations. The resulting velocity fields from the present model are more in line with the reference solutions in the region of high deviatoric stress than other three LB models, which is consistent with the theoretical expectations and is further confirmed by the comparisons of the truncation error terms. In addition, we also conclude from the numerical tests that the present model has the advantage of better convergence efficiency but suffers from the worse stability.

Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow*

We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model.

An alternative lattice Boltzmann model for three-dimensional incompressible flow

a b s t r a c t In this work, an alternative lattice Boltzmann (LB) model for three-dimensional (3D) in- compressible flow is proposed. The equilibrium distribution function (EDF) of the present model is directly derived in accordance with the incompressibility conditions by applying the Hermite expansion. Moreover, an alternative formula for pressure computation is de- signed from the second order moment of the distribution function. The present 3D LB model inherits the advantageous features of Guos LB model: the density is a constant, the fluid pressure is independent of density and the Navier-Stokes (N-S) equations for incompress- ible flow can be derived. Two benchmark tests, flow over a backward-facing step and the lid-driven cavity flow, are applied to validate the present model. Accurate results for these tests are obtained with the present model, and further comparisons with the previous LB models (the standard LB model, the He-Luo model and Guos LB model) demonstrate that the present model provides better accuracy in the region of high deviatoric stress and such advantage is further enhanced by using the D3Q27 lattice.