Research And Application Of Finite Volume Method Based On Comprssible Lattice Boltzmann Method

Recently, the Lattice Boltzmnn Method (LBM) is attracting a great ideal of attention, and has estabilished itself as an alternative approach to solve the fluid flow problems. However, LBM for compressible flow is still developing and little to application. In this work, we combine LBM with the traditional finite volume method (FVM), and propose a new scheme for compressible flows: FV-LBM scheme.Firstly, Similar to the Goduov scheme, in the present approach, LBM is used to evaluate the flux at the interface for local Riemann problem when solving Euler/Navier-Stokes equations by FVM. Two kinds of popular compressible Lattice Boltzmann models are applied in the new sheme, and some shock tube problems are performed to validate the proposed approach. From the sharper shock profile and higher computational efficiency, numerical results demonstrate that the proposeg scheme is superior the conventional Godunov scheme.In addition, based on the idea of flux vector splitting method (FVS), we divide the local distribution function on the two sides of the interface according to the directions of moving particle, and determine the distribution function crossing an interface. After the flux at the interface gotten, another LBM flux solver is proposed. By this method, some transonic and supersonic flow cases are simulated successfully.