An immersed boundary-lattice boltzmann flux solver in a moving frame to study three-dimensional freely falling rigid bodies

An immersed boundary-lattice Boltzmann flux solver (IB-LBFS) in a moving frame is proposed in this paper to study three-dimensional (3D) freely falling rigid bodies in unbounded domains. This solver includes the predictor and corrector steps. In the predictor step, the intermediate flow field is predicted on a moving Cartesian grid by 3D LBFS. In the corrector step, velocity correction is made by the implicit immersed boundary method to accurately satisfy the no-slip boundary condition. The motion of rigid body with six degrees of freedom is obtained by solving the governing ordinary differential equations. By enforcing the speed of the Cartesian grid the same as the translational velocity of the rigid body, the present solver is able to study a freely falling object in a large flow domain. It not only extends the applicability of fixed grid-based LBFS but also considerably reduces the number of grid points and computational efforts. In addition, the re-meshing process, which is commonly used in the conventional arbitrary-Lagrangian-Eulerian (ALE) approaches, is avoided. Several benchmarks, including an actively moving sphere, sedimentation of a particle and freely falling disks with finite aspect ratios, are studied to examine the reliability of the proposed solver. The obtained results compare well with theoretical and/or experimental data. After that, a numerical study of an infinitely thin disk falling in four different modes is carried out, which successfully demonstrate the capability of the proposed solver in capturing complex modes of a falling body.