An efficient implicit direct forcing immersed boundary method for incompressible flows

A novel e cient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an e↵ective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressurecorrection projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature.