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In this paper, the immersed boundary method (IBM) with the pressure boundary condition is applied to a plate of infinitesimal thickness that the boundary is not along the grid and its effectiveness is discussed. In the original IBM, unphysical pressure oscillations appear near the object boundary, and as a result, it is difficult to correctly estimate the drag and the like. In the previous study, the present IBM has been applied to a plate of infinitesimal thickness whose boundary is along the computational grid and its effectiveness was shown. Therefore, in this paper, the present IBM is extended to be applicable to a plate of infinitesimal thickness whose boundary is not along the computational grid. Then, in order to validate the present IBM, the flow around a 2-dimensional flat plate of infinitesimal thickness of various attack angles is considered. As a result, unphysical pressure oscillations appear near the boundary in the original IBM, whereas in the present IBM, the oscillations do not appear at any attack angle. The drag and the lift coefficients in the present IBM are in good agreement with the reference results at any attack angle. Therefore, the IBM with the pressure boundary condition is very promising as a means to suppress unphysical pressure oscillations near the virtual boundary of an object of infinitesimal thickness in the original IBM. In addition, the present pressure estimation at the virtual grid point allows the IBM to be applied even when the virtual boundaries are not along the grid. From the above, it can be concluded that the present IBM is very promising as a Cartesian grid approach for a very thin object.

Computational Fluid Dynamics; Cartesian Grid Approach; Immersed Boundary Method; Incompressible Flow; Pressure Condition