(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
In this paper, a novel immersed boundary method is presented for simulating incompressible flows governed by Navier-Stokes equations. A virtual boundary is formed by the cell edges (for two-dimensional cases) in the vicinity of the immersed boundary. In the domain with the virtual boundary, the governing equations can be solved in the conventional way. Reconstructed velocity is imposed on the virtual boundary, which is determined via the interpolation along the direction normal to the wall and in conjunction with the no-slip condition for the actual boundary. For "freshly cleared nodes" on the virtual boundary encountered in moving-boundary problems, pressure at the previous time step is reconstructed by solving the local simplified momentum equation. In the test case for an analytical solution, the local accuracy of pressure is verified to be of the second order. In order to further validate the present method, various flows over the stationary and/or moving circular cylinder and NACA0012 airfoil have been simulated. The obtained results agree well with the available numerical or experimental data in the published literatures.