Moving immersed boundary method for fluid–solid interaction

A strongly coupled algorithm is presented for the incompressible fluid–rigid body interaction using the moving immersed boundary method. The pressure and the boundary force are treated as Lagrange multipliers to enforce the incompressibility and no-slip wall constraints. To compute the two unknowns from the velocity field, we adopt the fractional step algorithm and successively apply the two constraints. A Poisson equation and a moving force equation are derived for the pressure and the boundary force, respectively. As both coefficient matrices are formulated to be symmetric and positive-definite, the resulting linear systems are solved efficiently with the conjugate gradient solver. The strongly coupled nonlinear fluid–solid system is achieved by a fixed-point iteration. To improve the computational efficiency, we only iterate the moving force equation with the rigid body motion equation, and the time-consuming pressure Poisson equation is solved once the sub-iteration is finished. The proposed method is validated with various benchmark tests, and the results compare well with the literature