A Finite Volume Immersed Boundary Method And Its Application

A finite volume immersed boundary method (FVIB) is developed to simulate complex flows around moving boundaries. The discrete form of the governing equations does not involve any nodes outside solution domain. At each time-step, the flow variables are evaluated via linear interpolation along the wall normal direction in conjunction with the solid boundary conditions or via solving the local momentum equation in normal direction, and boundary conditions are enforced at the same time. In the artificial compressibility approach for incompressible N-S equations, Galerkin finite volume approximation is employed for spatial discretization and the dual time-stepping scheme is adopted in time integration. Steger-Warming flux splitting is used to construct non-reflecting far-field boundary conditions.Using the present FVIB method, flow equations can be solved on a fixed grid for moving boundary problems. Some critical issues associated with grid updating at each time-step, such as grid quality and interpolation error due to solution-transferring, can be removed. Compared to other immersed boundary methods such as DFD and HCIB, the FVIB developed in this thesis is easy to implement and is also suitable to the unstructured meshes. It is of considerable significance in numerical analysis and has a wide prospect in engineering applications for moving-boundary problems.In order to validate the present method for moving-boundary flow problems, two groups of flow phenomena have been simulated:(1) flows over a fixed circular cylinder, a harmonic in-line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a heaving-pitching airfoil. The predictions show good agreement with the published numerical results or experimental data.