Numerical simulation of fluid flow in three dimensional domain based on two stage pressure-velocity correction method

In this paper a two stage pressure-velocity correction approach for immersed boundary method is proposed. The model is illustrated the interaction between incompressible viscous fluid and immersed bodies in three dimensional domain. A second correction step is added to the pressure value and the velocity vectors using Simplified Marker and Cell method (SMAC). This new scheme is applied on staggered grid using implicit finite difference methods in order to achieve second order accuracy. The algorithm is validated in comparison with a bench mark fluid solid structure case of laminar flow around a cylinder. The drag and lift coefficients are chosen to be the fundamental element to authenticate the new algorithm. Adding new stage of second pressure corrections did not affect the computations cost comparing with single correction stage methods. The preliminary results show there is a strong statistical correlation between Reynolds number and the error in pressure values. The stability of the developing method remain at the same level with other immersed boundary methods. Associated with conventional numerical optimization methods, the proposed approach achieve an acceptable degree of convergence rate per iteration and confirm decent performance. © 2015 by ASME.