Immersed Boundary Method with Pressure Boundary Condition for Moving Object of Infinitesimal Thickness

In this paper, the immersed boundary method (IBM) with the pressure boundary condition for the flow including moving objects of infinitesimal thickness is proposed and its effectiveness is discussed. In the original IBM, the pressure condition on the object boundary is not considered. Therefore, applying the original IBM to the very thin object, the pressure oscillations appear near the boundary because of the pressure jump between the front and the back of the object. In order to remove the pressure oscillations near the object boundary in the original IBM, the IBM with the pressure boundary condition was proposed. Because the IBM with the pressure boundary condition does not require the computational grid points inside the object, the applicability of this method to thin objects can be expected. In this paper, the present IBM with the pressure boundary condition is applied to the flow around a moving plate of infinitesimal thickness like a butterfly wing. As a result, by applying the present IBM, the pressure oscillations appeared in the original IBM was removed. However, in the present and original IBM, the oscillations of the time history of the drag coefficients appeared because the forcing points change by moving the virtual boundary beyond the computational grid. In order to reduce the influence by moving the virtual boundary beyond the computational grid in IBMs, we proposed a method combining the IBM with pressure boundary condition and the overset grid system. As a result, the oscillations of the drag coefficient were removed, and the pressure distributions around the plate were in good agreement with the reference result. From these results, we conclude that the present IBM combined with the overset grid system is effective for the analysis of the flow including the moving object of infinitesimal thickness.