An efficient unified iterative scheme for moving boundaries in lattice Boltzmann method

The lattice Boltzmann equation (LBE) is an efficient kinetic method for particulate flows. Two key issues should be addressed in the implementation of LBE for such systems, i.e., how to treat the curved surface of a solid particle on a uniform Cartesian grid, and how to initialize the state of a fresh node coming from the moving particle. These two key issues are usually considered separately in previous studies. In this work, we propose an efficient unified iterative scheme (UIS) to treat both the issues simultaneously. On one hand, the present method provides a consistent treatment for both the boundary nodes and fresh nodes, on the other hand, to enforce the no-slip boundary condition and decrease the inconsistency between the constructed distribution functions and those evolutionary ones, an enforced iteration (EI) is employed. To describe the inconsistency quantitatively, the inconsistency degree is defined. Simulations of several typical problems are conducted, and the numerical accuracy, computational efficiency and ability to treat moving boundaries are validated. Compared with the combination method, the inconsistency degree around the moving body and spurious force fluctuation are suppressed significantly due to the improved consistency.