Development of a Novel Immersed Boundary-Lattice Boltzmann Method and Its Applications

Abstract

In recent years, the immersed boundary method (IBM) has been developed into a popular numerical technique in the community of computational fluid dynamics (CFD). On the other hand, as an alternative CFD tool, the lattice Boltzmann method (LBM) has gained wide range applications recently. Since the Cartesian mesh is employed in both IBM and LBM, an efficient solver can be generated by combining IBM with LBM, which is called IB-LBM. Some efforts have been made in this aspect and the achievement is obvious. However, there are still some shortcomings in this newly developed approach. In this work, two major improvements were made. Firstly, a new version of IB-LBM was proposed in order to strictly satisfy the non-slip boundary condition. In the conventional IB-LBM, the non-slip boundary condition is not enforced, and is only approximately satisfied at the converged state. To overcome this drawback, a boundary condition-enforced IB-LBM was developed. Applying the developed approach, the two-dimensional (2D) stationary and moving boundary flow problems, as well as particulate flow problems, were simulated. All the obtained numerical results are compared well with previous experimental and numerical results. In the application of IB-LBM, the non-uniform mesh is usually employed. To apply LBM on the non-uniform mesh, many variants of LBM can be chosen. A simple way is to use Taylor series expansion and least squared-based LBM (TLLBM). As compared to the standard LBM, the drawback of TLLBM is that additional memory is required to store the coefficients. Due to the limitation of virtual memory, it is not easy to apply TLLBM in three-dimensional (3D) simulations. To overcome this difficulty, an efficient LBM solver based on the one-dimensional interpolation was developed. As compared to TLLBM, much less coefficients are calculated. Combing with this efficient LBM solver, the new IB-LBM was easily extended to 3D simulation. The 3D flows around complex stationary and moving boundaries were simulated. The obtained numerical results are agreed well with the results and findings in the literature.