Study On Moving Interface Problems In Incompressible Viscous Flow Using Implicit Force Immersed Boundary Method

A new version of numerical method of fluid dynamics named immersed boundary method is presented, which is based on the Cartesian grid system and especially suitable for complex geometric boundary, unsteady moving boundary and fluid-solid interation probems. Compared with traditional numerical method of fluid dynamics, these are many advantages for immersed boundary method, such as a simple arithmetic, easy programming, easy to generate grid, natural parallel, easy to handle with boundary and highly computational effeciency.After reviewed the previous studies on immersed boundary method, an improved version of implicit force immersed boundary method on non staged grid is developed, which is solved by direct numerical simulation using approximate projection equation and especially suitable for simulating unsteady fluid problems with moving boundary. In simulating, the density force of immersed boundary is sought by implicit way, while the spatial terms, the temporal terms and the convective terms of imcomprossible Navier-Stokes equation are dispersed by second-order central scheme on the non staggered meshes, second-order Crank-Nicholson scheme, and the second-order Adams-Bashforth scheme respectively in this paper. Implicit force immersed boundary method has many advantages, which including no need to regerate grid every time, accurate imposition of no-slip boundary condtion and no limit on small time step. What's more, implicit force immersed boundary method can predigest the complexity of gird geometry, economize computing resources, and improve computing efficiency. Meanwhile, To solve macroeconomic forces simply, reduce memory requirement of computer and improve data processing speed, a general discrete format of solving the forces in immersed boundary using density force and velocity of immered boundary is presented as well.Immersed boundary method have developed quickly on hydrodynamics calculations in recent years, which have taken it to the point where it can successfully compute a number of fluid dynamics problems, such as biology and geology engineering. Yet, it is apparent that there is still a way to go before immersed boundary method can achieve full engineering status, For example, the application on naval architecture and ocean engineering. In order to expand the scope of immersed boundary method application areas,the paper focuses on the immersed boundary method methods to deal with moving boundary and numerieal simulation of the flow around a oscillating cylinder. Firsty, the improved implict force immersed boundary method is validated, which shows that the method has good numerical stability and accuracy. Then, flow past an in-line oscillatory circular cylinder is simulated; the result compared with other numerical simulation data is in good agreement. Finally, cylinder transversely forced oscillation in uniform flow is investigated, and that the lift, darg coeffeicient and vortex shedding patterns are analyzed. The numerical results demonstrate that implicit force immersed boundary method is a reliable and robust numerical approach to solve unsteady flow interacting with submerged moving rigid object, and the simulation results are of practical value.