A unified coupling scheme between lattice Boltzmann method and finite volume method for unsteady fluid flow and heat transfer

In this paper, a unified coupling scheme between the lattice Boltzmann method (LBM) and the finite volume method (FVM) is proposed for the unsteady fluid flow and heat transfer problems. Three improvements are achieved comparing to the existing coupling methods. Firstly, a generalized form of the reconstruction operator (RO) is derived for the information transfer from macroscopic parameters to LBM distribution functions. The existing RO for various LBM can all be derived from this generalized form. Secondly, an RO corresponding to the incompressible LBM is derived to deal with the incompressible flow, which can prevent the inconsistency between the incompressible FVM and the density change in the LBM. Thirdly, the time coupling scheme between LBM and FVM is proposed for the unsteady simulations. The LBM and FVM are solving sequentially and the information is transferred between the two methods at the intervals. The coupling scheme is validated by three numerical examples: the convection-diffusion of a Gaussian pulse, the unsteady flow past a circular cylinder and the start-up process of the natural convection in a square cavity. The numerical results agree well with the existing researches. The flow past a porous medium is also simulated to show the application of the coupling method. This method can give the detailed flow information and save the computational time. The proposed coupling scheme improves and expands the coupling scheme between LBM and FVM. It has the flexibility to simulate unsteady multiscale processes.