The Immersed Boundary Method In Compressible Flows And Its Applications

In the research of simulation for complex fluid, one of popular numerical algorithms is so called Immersed Boundary Method (IBM), which can overcome the grid generation difficulties, reduce the difficulties for treatment of multi-scale geometry, simplify the process of moving object simulation, and enhance the reusability of traditional body-fitted grid CFD code. For the reason of concerning with the simulations of compressible flow, the research of this kind of method mainly focuses on constructing immersed boundary conditions for compressible flow/reconstructing the immersed boundary, adaptive grid refinement technique, IBM using non-Cartesian grids such as the IBM for unstructured grids, simulation of high Reynolds number flow, numerical method for moving objects and so on. In this paper, ghost cell IBM on adaptive Cartesian grids has been developed. In order to increase the accuracy near the boundary, a radial basis function-based IBM for compressible Navier-Stokes equations has been presented. To overcome the low computing efficiency of overall Cartesian grids, an IBM based on unstructured girds finite volume method has also been given. Forevermore, IBM based on unstructured girds finite volume method has been used to study a flow control problem. Finally, a class of ghost cell IBM for moving objects has been studied. It primarily concerns five following aspects:Firstly, using adaptive Cartesian grid technique and the simplified process for the treatment of immersed boundary, combined with finite difference scheme with HLLC numerical flux, we studied all kinds of immersed boundary methods. The method developed here has been used to simulate and analyse diverse 2D and 3D flows.Secondly, based on the radial basis functions, a new IBM for compressible Navier-Stokes equations has been presented. The numerical calculations are performed on a non-uniform Cartesian grid. And a non-uniform grid finite difference scheme with MUSCL method is discussed.Thirdly, in order to obtain the flow characters of small scale part on the construction, simplify the difficulties of grid generations, and improve the reusability of traditional body-fitted grid CFD code, in this paper, an IBM based on unstructured girds finite volume method different from any other Cartesian grid IBMs has been presented.Fourthly, IBM based on unstructured girds finite volume method has been used to solve a new technique of flow control– flow deflector. It includes the effects of flow deflector, pneumatic parameters, flow characters, and the optimization of deflector geometry parameters.At last, a ghost cell IBM has been presented to deal with moving objects. Here we only consider the inviscid Euler equations. Forevermore, this method is used to simulate an inner weapon cabin, and some analysis on the flow characters is also given.