Alternative kinetic theory based lattice Boltzmann model for incompressible axisymmetric flows

Based on the axisymmetric Boltzmann equation, an incompressible lattice Boltzmann model for axisymmetric flows is proposed within the framework of the kinetic theory based model developed by Guo et al. (2009). While retaining the advantages of the Guo et al. (2009) model in terms of the solid physics basis and simple source terms involving no gradient calculations, the present model further improves the numerical stability, and reduces compressibility errors and computational requirements. Armed with the assumption that the fluid density is a constant and thus the fluid pressure has no direct relation with the density, the incompressibility conditions are realized by applying the Hermite expansion. Then, the present model employs a novel way of calculating the fluid pressure which is derived from the modified second-order moment equation. Additionally, based on the regularized lattice BGK (RLBGK) model, an extra relaxation parameter pertaining to the ghost mode is introduced to enhance the numerical stability of the present model. The accuracy and applicability of the present model are verified by both the Chapman-Enskog theoretical analysis and numerical validations. It is demonstrated via well-acknowledged test cases that the present model is accurate and reliable for incompressible axisymmetric flows, and is able to effectively reduce the compressibility errors vis-à-vis the Guo et al. (2009).