Research And Application Of Immersed Boundary Method For Compressible Flow

Based on the idea of diffuse interface immersed boundary method for incompressible viscous flow,this thesis proposes a diffuse interface immersed boundary method for compressible viscous flow,and describes in detail how to modify and update all flow variables.In order to verify the feasibility and effectiveness of the proposed method,this work numerically simulates the flow over a classic complex composited airfoils.In natural and practical engineering applications,the moving boundary problem is common,so this work also uses this method to perform numerical simulation of the moving boundary problem,including rotating and oscillating cylinders,harmonic oscillating airfoil,and tandem rotating double cylinders and other cases.Flows over rotating and oscillating cylinders verify the ability of the proposed method to solve the moving boundary problem.Through the simulation of the harmonic oscillation of NACA0012 airfoil at low Reynolds number,the characteristics and trend of dynamic stall are obtained.The simulations of double cylinders under different rotation modes and different rotation velocities show that the upstream cylinder promotes the lift coefficient of the downstream cylinder,while the drag coefficient has no effect.At the same time,this thesis also develops an immersed boundary method for Neumann boundary condition.In the diffuse interface immerse boundary method,the processing of Neumann boundary conditions is far more complicated than the Dirichlet boundary condition.In order to overcome this difficulty,in the correction step,for the temperature field,given the Neumann(heat flux)boundary condition,this work uses the idea of adding an epitaxial auxiliary layer combined with the concept of implicit velocity correction to perform temperature correction.Through this process,the variable correction update with Neumann boundary conditions is successfully resolved.In order to verify the algorithm,this work numerically simulates some classic examples,including the flow around a cylinder from subsonic to supersonic,and the NACA0012 airfoil under different Mach numbers,angles of attack,and Reynolds numbers.The calculated results are in good agreement with the existing data in the literature.The comparison of examples shows the ability of the current developed method to simulate compressible flows with Neumann boundary condition.