This paper reports the results of direct numerical simulation of the motion of a two-dimensional neutrally buoyant circular cylinder in a periodic lid-driven cavity by using multigrid fictitious boundary method (MFBM) coupled with finite element method. The MFBM is based on a regular rectangular grid. The flow is computed by a finite element solver and the solid cylinder is allowed to move freely through the computational mesh which can be chosen independently from the cylinder of size and number. The interaction between the fluid and the cylinder is taken into account by the MFBM in which an explicit volume based calculation for the hydrodynamic forces is integrated. The main advantage of the MFBM is that the solid cylinder can move freely through the computational mesh for the fluid part which has not to change in time. Comparisons with experimental results indicate that the present numerical method can capture complex flow-cylinder interaction phenomena, and obtain the detailed results of trajectories, translation and rotation of the free neutrally buoyant cylinder in a liddriven cavity flow.
Direct numerical simulation of solid-liquid flow is a difficult task since the domain occupied by the fluid is irregular and changes with motion of the particles. Also, the particles are advected by the fluid and exert forces at the fluid. The movement of both the interface and the solid particles is unknown in advance and must be determined as part of the solution, it can require a huge amount of time for the generation of a boundary-fitted mesh for each different position of the moving particles. Generally speaking, there are two ways to solve this problem. The first is a generalized ALE standard Galerkin finite element method (Hu, et al, 2001, Maury 1996) in which both the fluid and particle equations of motion are incorporated into a single coupled variational equation.
