Progress of current seamless virtual boundary method

In this paper, a current virtual boundary method, i.e., a seamless virtual boundary method (VBM) is presented. In the seamless VBM, the forcing term is added not only to the grid points near the boundary but also to the grid points inside the boundary, in order to remove unphysical oscillations near the boundary. The development of seamless VBM can be applied to solve for heat transfer and moving boundary problems in both the Cartesian and the curvilinear coordinates, and the lattice Boltzmann equation. A series of the method is validated in the typical test problems. Therefore, it is concluded that the present method is a very versatile numerical approach for solving the incompressible Navier–Stokes equations.