New Approach of Axisymmetric Compressible Finite-Volume Lattice Boltzmann Method for Numerical Simulation of Supersonic Inviscid Flow

A new approach of the axisymmetric compressible lattice Boltzmann method (LBM) has been developed for the numerical simulation of supersonic inviscid flow using the finite volume method. The circular function idea has been used for capturing the compressibility effect in the supersonic flow field. In this study, the axisymmetric LBM equations based on the circular function have been derived for the first time and presented in detail and appropriate axisymmetric boundary conditions have been applied for the 2-dimensional, 13-velocity, 2-energy-level lattices. For validation of developed code, two supersonic axisymmetric flows have been simulated around the hemisphere nose and 60 degrees blunt body. A comparison of the obtained results with some valid empirical data shows the accuracy of the developed numerical algorithm. Also, the results of 2D and axisymmetric simulations have been studied to evaluate the effects of the new derived axisymmetric formulation on flow macroscopic properties.