Numerical validation of a consistent axisymmetric lattice Boltzmann model

Abstract

A recently derived axisymmetric lattice Boltzmann model is evaluated numerically. The model incorporates a spatially and temporally varying source term into the evolution equation for the momentum distribution function on a two-dimensional Cartesian lattice. The precise form of the source term is derived through a Chapman-Enskog analysis so that the additional axisymmetric contributions in the Navier-Stokes equations are furnished when written in the cylindrical polar coordinate system. The validity of the model is confirmed by simulating Hagen-Poiseuille flow. Numerical predictions for the drag coefficient in Stokes' flow over a sphere are presented and shown to be in excellent agreement with analytical results. At larger Reynolds numbers the numerical predictions are shown to approach an empirically derived formula for the drag coefficient.

Axisymmetric multiphase lattice Boltzmann method

“…The idea to model the 3D axisymmetric LBM with a 2D LBM supplemented with appropriate source terms has already been employed in a number of studies, for single-phase axisymmetric LBM models [4,5,17,18] and for the multiphase LBM as well [10,11]. Here we will develop an axisymmetric version of the Shan-Chen model [12,13].…”

“…(10) by means of a Chapman-Enskog (CE) expansion in the long-wavelength and long-time-scale limit. In order to derive such a model we start from the 2D LBM with the addition of appropriate space-and time-varying microscopic sources h i (see also [4,5,17,18]). We employ the following lattice Boltzmann equation:…”

Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

“…In the last two decades, LBE has been rapidly developed as an effective and promising numerical algorithm for computational fluid dynamics [4][5][6], which has also been applied to axisymmetric flows [7][8][9][10][11][12][13][14][15][16][17][18][19]. The straightforward way for LBE to simulate such flows is using a 3D LBE model with suitable curved boundary treatments [22][23][24].…”

“…In the literature, there are three categories of axisymmetric LBE models proposed for axisymmetric athermal flows [10][11][12][13][14][15][16], i.e., the coordinate transformation method (CTM), the vorticity-stream method (VSM) and the double-distribution-function (DDF) method. The main idea of CTM is that it transforms the axisymmetric Navier-Stokes equations (NSE) to the specific pseudo-Cartesian forms with some additional terms in these quasi-two-dimensional NSE.…”

“…However, Lee et al [11] found that some terms are missing in this model which would lead to large errors for simulating the constricted or expanded pipe flows. Later, Reis and Phillips [12,13] and Zhou [14] developed similar models based on the axisymmetric NSE. On the other hand, the VSM is another version of transformation method, it uses the relations between the vorticity, the stream function and the velocity, then the 3D axisymmetric NSE can be transformed to the vorticity-stream-function equations.…”