An axisymmetric incompressible lattice BGK model for simulation of the pulsatile flow in a circular pipe

Abstract

Applying the idea of Halliday et al., through inserting the 'source' term into the two-dimensional lattice Boltzmann equation to recover the incompressible Navier-Stokes equation in the cylindrical coordinates, an axisymmetric incompressible Lattice-BGK D2Q9 model was proposed here to simulate the pulsatile flows in a circular pipe. The pulsatile flows in a circular pipe with 1 <Re<2000 (Reynolds number is based on pipe's diameter), Womersley number 1 <α<25 were investigated and compared with the exact analytical solutions. The excellent agreements between numerical and the analytical solution validate our model. The effect of schemes to implement pressure gradient and the model's spatial accuracy were also discussed. To show the performance of the proposed model, the same problems were also simulated by Halliday's axisymmetric model which derived from standard LBM and the three-dimensional incompressible LBGK model. It is observed that the present model reduces the compressibility effect in Halliday's model and is much more efficient than the LBGK D3Q19 model for an axisymmetric pulsatile flow problem. Copyright © 2005 John Wiley & Sons, Ltd.