Enhancement of coupled immersed boundary–finite volume lattice Boltzmann method (IB–FVLBM) using least–square aided “ghost–cell” techniques

In this paper, a new hybrid numerical approach is presented that couples “ghost cell” based immersed boundary (IB) method with the finite volume lattice Boltzmann method (FVLBM). In the implementation process, the grid cells are classified into three types, i.e., “fluidcell”, “solidcell” and “ghostcell”, where the “ghostcell” is the first layer of “solidcell” near the “fluidcell”. As the wall boundary condition is reflected in the “ghostcell”, the high–accuracy reconstruction of variables in it will be the key point of present approach. Then, a FVLBM scheme is used to update the distribution function in the “fluidcell”, and a least square interpolation based formulation is derived to construct the distribution functions in it. Further, the bounce–back scheme embedded in the streaming–collision lattice Boltzmann method will be employed as the wall boundary condition. Besides, for the class of moving boundary problems, the construction of the distribution function in the “freshcell” is also considered. A number of typical benchmarking incompressible viscous fluid flows over both stationary and moving objects are simulated to justify the present method, using obstacles ranging from a stationary and a translating circular cylinders, a rotationally oscillating cylinder, to two more complex flows around an oscillating cylinder in the stationary fluid and in the free–stream. Besides, the temporal and spatial accuracy also are testified by the simulation of Taylor–Couette flow. The obtained accurate simulation results demonstrate the capability of the present hybrid IB–FVLBM for computer simulations of both stationary and moving boundary problems in the incompressible flow regime.