High-Order Immersed-Boundary Method for Incompressible Flows

In this work, a high-order numerical approach based on the immersed-boundary method to simulate viscous incompressible flows involving arbitrary boundaries is described. The idea is to combine compact finite difference schemes and a high-order direct forcing approach of the sharp-interface immersed-boundary method. In this approach, a particular challenge is to solve the pressure Poisson equation using the compact stencil. This issue is addressed by introducing an efficient approach based on high-order corrections to the right-hand side of the Poisson equation (that is, the source term) while retaining the second-order short stencil for the Laplace operator. The two-dimensional implementation is described, for which third-order global convergence is achieved when an immersed boundary is present.