Abstract
In the present study, we use the immersed-boundary technique to simulate two and three-dimensional viscous incompressible flows interacting with moving solid boundaries. For both stationary and moving boundary problems, we apply the solid body forcing within the solid node and provide a procedure to implement the forcing nodes between the non-stationary fluid and solid body. The accuracy of numerical scheme is first examined by decaying vortex test, and the results show that these are second-order accurate with respect to the L2 norm and the L∞ norm. Further test problems are simulated to examine the validity of the present immersed-boundary technique such as 2-D flow over an asymmetrically-placed cylinder, in-line oscillating cylinder in fluid at rest, and 3-D simulation of a sphere settling under gravity. In addition to one moving object, two spheres sedimenting in a closed container filled with a viscous fluid are investigated. There must be a collision model to prevent the spheres penetrating into each other. All the computed results are in generally good agreement with experimental measurements. This indicates the capability of the present implementation in solving flows with moving solid objects. The above implementations and techniques are all constructed on the software of PETSc, which is associated with a parallel solver. By using the parallel solver, we can enhance the capability of computational power for two- and three-dimensional fluid-solid interaction simulations. The scalability results show that the speedup performance for two-dimensional and three-dimensional test cases are almost the same, except when the number of processors increases to 32 where two-dimensional case has better performance. However, the overall scalability for both cases deviates from the theoretical values. There is still much room for improving the parallel efficiency.