Moving immersed boundary method for fluid–solid interaction

Abstract

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.