An Immersed Boundary Method For Solving Moving Boundary Problems

In this paper, a finite volume immersed boundary method based on extrapolation along the cell edgesfor incompressible Navier-Stokes equations is developed. Galerkin finite volume approximation isemployed for spatial discretization, and the dual-time scheme is chosen for time marching. Theflow-variables at the fictious point outside the solution domain are evaluated via extrapolation alongthe cell edges in conjunction with no-slip boundary condition. For multi-valued nodes, solutions aregiven in terms of the computation of flux, artificial dissipation and pressure, velocity gradient at thenodes in the vicinity of the wall associated with the wall boundary. A ‘sweeping with thebackward-edge of the wall boundary’ method is adopted to identify the ‘freshly cleared nodes’ whichemerge in boundary-moving cases and their values are constructed with the ‘matching the spoke-sidesin the influce domain’ method which can be easily implemented for moving wall boundaries withcomplex shape. In order to validate the present method, flows over a circular cylinder and an airfoil atlow Reynolds numbers are simulated repectively. The predictions show good agreement with thereference results.