A hybrid adaptive-gridding immersed-boundary lattice Boltzmann method for viscous flow simulations

Robust use of adaptive mesh refinement (AMR) techniques in the immersed-boundary (IB) lattice Boltzmann method (LBM) framework is seldom reported, but indeed expected owing to its foreseeable broad applicability and computational efficiency. This study is aimed at developing a highly hybrid computational framework that seamlessly incorporates the AMR algorithm in the IB-LBM approach, so that challenging problems, including the case of an obstacle that moves through a flowing fluid, can be numerically investigated. Owing to the feedback forcing based IB model, the advantages, such as simple mechanics principle, explicit interpolations, and inherent satisfaction of no-slip boundary condition for solid surfaces, are fully exhibited. Additionally, the "bubble" function is employed in the local mesh refinement process so that, for newly generated nodes belonging to a region with overlapping coarse and fine cells, the solution of second-order accuracy can be obtained only through the spatial interpolation but no temporal interpolation. With simulation interests in both steady and unsteady flows around a single cylinder and bi-cylinders, a number of test cases performed in this study have demonstrated the usefulness and effectiveness of the present hybrid AMR-IB-LBM approach.