Transient fluid–solid interaction with the improved penalty immersed boundary method

Abstract In the present paper, the penalty immersed boundary method is improved to resolve the transient fluid–solid interaction problems. The Eulerian finite-element method is chosen as the fluid solver, and the conservation of the total energy is solved to ensure the correct results for discontinuous problems. The penalty immersed boundary method is adopted to couple the fluid and the submerged solid body, which is improved by considering both the normal and tangential relative velocities of the solid surface with an upwind scheme when updating the penetrated depth. With the present model, the simulated results of a 1-dimensional moving piston problem in the ideal gas are compared with the exact solution and the results from the Abaqus to validate the capability of the present method in dealing with shocks. Then, several 3-dimensional problems are simulated and analyzed, including a bubble–sphere interaction problem, and three high-speed water entry problems. The results are compared with experiments and show good agreements.