An alternative lattice Boltzmann model for three-dimensional incompressible flow
In this work, an alternative lattice Boltzmann (LB) model for three-dimensional (3D) incompressible 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 designed 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 NavierStokes (NS) equations for incompressible 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 HeLuo 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.
lattice boltzmann model incompressible flow deviatoric stress hermite tensorial polynomials