Development of Finite Volume-Lattice Boltzmann Method Based on Circular Function idea in Simulation of Inviscid Compressible Flow in Curvilinear Grid System

In this research, a finite volume-Lattice Boltzmann Method (FVLBM) for simulation of inviscid compressible flows in 1-D and 2-D structured curvilinear coordinate system is presented. In this simulation, LBM, with new method of Circular Function idea instead of expansion or correction of Maxwelian function was implemented for evaluation of equilibrium distribution functions, moreover, in order to capture discontinuities in the flow field, 3rd order MUSCL scheme was implemented for approximation of convective term. Since in lattice Boltzmann method time step is extremely limited by relaxation time (Knudsen number), we improved performance of FVLBM with a third-order IMEX Rung-Kutta scheme for temporal discretization of BGK-model for archiving greater time step and lower CPU time. Consequently, the present work can be used widely for simulation of actual engineering problems in aerodynamics. Various gas dynamics benchmark problems and applied engineering unsteady problems in curvilinear coordinate grid is solved for validation. The numerical results of the presented method are compared with experimental dates and the results of FVM Euler solutions; there is good agreement between the results of the present method and those of the references.