An axisymmetric incompressible lattice Boltzmann model for pipe flow

In this paper an accurate axisymmetric lattice Boltzmann D2Q9 model is proposed to simulate the steady and pulsatile flows in circular pipes. Present model is derived from an incompressible D2Q9 model and some errors in a previous model [Halliday et al., Phys. Rev. E 64, 011208 (2001)] are revised. In the previous model, some terms relative to the radial velocity are missing and would lead to large error for constricted or expanded pipe flows. Present model is validated by cases of laminar steady flow through constricted tubes and 3D Womersley flow. Comparing with the previous model, our model is much more accurate for steady flow in constricted circular pipes. For 3D Womersley. flow, it is also observed that the present model can reduce the compressibility effect in previous model.