An immersed boundary method for incompressible flows using volume of body function

A simple and effective immersed boundary method using volume of body (VOB) function is implemented on unstructured Cartesian meshes. The flow solver is a second-order accurate implicit pressure-correction method for the incompressible Navier-Stokes equations. The domain inside the immersed body is viewed as being occupied by the same fluid as outside with a prescribed divergence-free velocity field. Under this view a fluid-body interface is similar to a fluid-fluid interface encountered in the volume of fluid (VOF) method for the two-fluid flow problems. The body can thus be identified by the VOB function similar to the VOF function. In fluid body interface cells the velocity is obtained by a volume-averaged mixture of body and fluid velocities. The pressure inside the immersed body satisfies the same pressure Poisson equation as outside. To enhance stability and convergence, multigrid methods are developed to solve the difference equations for both pressure and velocity. Various steady and unsteady flows with stationary and moving bodies are computed to validate and to demonstrate the capability of the current method.