A three-dimensional fictitious domain method for the simulation of fluid structure interactions

The Distributed-Lagrange-Multiplier based Fictitious Domain (DLM/FD) method previously proposed by Yu [J. Comput. Phys. 207 (2005), 1-27] for the simulation of fluid/flexible-body interaction problems is extended from the 2D to the 3D case in this study. We first demonstrate that the Lagrange multiplier problem can be more efficiently solved with a direct-forcing scheme instead of the original Uzawa iterations without the sacrifice of the accuracy. The type of the interpolation function (i.e. smoothed delta function) for the transfer of the quantities between the Eulerian and Lagragian frames is shown not to affect the results significantly. Secondly, the fictitious domain method is implemented in the three-dimensional case. The new 3D codes are applied to the flapping of a 3D flexible plate in a uniform flow, and the deformation of tri-leaflets at opening stage.