Axisymmetric and Three-Dimensional Lattice Boltzmann Models and Their Applications in Fluid Flows

Abstract

The lattice Boltzmann Method (LBM) has attracted significant interest in the CFD community. The axisymmetric flows are not able to be solved by 2D standard LBM directly. Here a general method was suggested to derive axisymmetric lattice Boltzmann D2Q9 models through inserting different source terms into the 2D lattice Boltzmann equation (LBE). The axisymmetric models were used to study the steady and unsteady blood flows through constricted tubes and elastic vascular tubes. A 3D multi-block LBM solver was also used to study the blood flow through an asymmetric tube. An axisymmetric D2Q9 model considering the swirling effect and buoyancy force was proposed to simulate the benchmark problems for melt flows in Czochralski crystal growth. Compared with the previous axisymmetric model, present axisymmetric model seems more stable. A revised axisymmetric D2Q9 model was also applied to investigate gaseous slip flow (i.e., Kn in range (0.01, 0.1) ) with slight rarefaction through long microtubes. Our LBM is also found to be more accurate and efficient than DSMC when the slip flow in microtube was simulated. A recent curved non-slip wall boundary treatment for isothermal LBE (Guo, et al., 2002) was successfully extended to handle the 2D and 3D thermal curved wall boundary for thermal LBE and proved to be of second-order accuracy.