A unified and preserved Dirichlet boundary treatment for the cell-centered finite volume discrete Boltzmann method

A new boundary treatment is proposed for the finite volume discrete Boltzmann method (FVDBM) that can be used for accurate simulations of curved boundaries and complicated flow conditions. First, a brief review of different boundary treatments for the general Boltzmann simulations is made in order to primarily explain what type of boundary treatment will be developed in this paper for the cell-centered FVDBM. After that, the new boundary treatment along with the cell-centered FVDBM model is developed in detail. Next, the proposed boundary treatment is applied to a series of numerical tests with a detailed discussion of its qualitative and quantitative properties. From the results, it can be concluded that the new boundary treatment is at least first-order accurate for a variety of Dirichlet boundary conditions (BCs). It can handle both the velocity and density Dirichlet BCs in a unified way and further realize some BCs that the conventional lattice Boltzmann model fails to simulate. In addition, such a boundary treatment can incorporate different lattice models without changing its framework, and it can preserve the Dirichlet BCs up to machine accuracy in different situations. (C) 2015 AIP Publishing LLC.