Research On The Immersion Boundary Method Of Gas Dynamic Theory Format

Today,more and more complex flow field confronts the aircraft as the flight Mach number is higher and higher.Shock waves,expansion waves and shear layers may appear simultaneously in the flow field and the traditional NS-equation-based(Navier-Stokes-equation-based)numerical scheme is often powerless to capture all details of the flow.Thus more and more artificial modifications must be added to the scheme,such as artificial viscosity,entropy fix,etc.In recent years,some scholars discarded the continuum model and proposed the GKS(Gas-Kinetic Scheme)on a more essential basis—the mesoscopic particle model.Due to the advantage of the basic model,GKS is robust,positivity-preserving and satisfies the entropy condition spontaneously.It combines the high precision with the high resolution while its computational efficiency is not lower than the traditional NS-equation-based scheme.It is a numerical scheme of limited applicability but worth to be extended.The IB method(Immersed-Boundary method)is a kind of boundary technique which has been very popular these years.In IB method,the mesh doesn't have to fit the solid boundary,which significantly reduces the complexity of the mesh generation.It is especially applicable for simulations with one or more complex and moving objects.To expand the application range of the GKS and enrich the content of the IB method,the paper combined the above techniques for the first time.First,the paper proposed the IB-GKS method based on the idea of a class of IB method called the continuous forcing approach.In this method,a force will be exerted by the Lagrangian point on the surrounding finite control volumes to fulfill the no-slip boundary condition.Unlike the traditional IB method,the force not merely acts as a force source term to the cell,but also influences the flux at the interface of the cell through the GKS flux solver.The force is calculated by an implicit way and the flow penetration is eliminated thoroughly.This method can be applied to simulations of incompressible viscous flow with complex and moving boundaries.Then,the paper modified the other class of IB method called the direct forcing approach and applied it to GKS.In the presented direct-forcing-based IB-GKS method,the flow variables are interpolated to ghost cells inside the solid body to fulfill the boundary condition.The ghost cell is identified through how the connection between cells is cut off by the boundary segment.The paper modified the construction of the ghost cell,which would make the method more reasonable when there are steps or sharp corners in the flow field.This method can be used to simulate viscous flows from subsonic to supersonic with stationary complex boundaries.Through the simulation of the Stokes' first problem,the paper testified the second-order temporal accuracy of the presented continuous-forcing-based IB-GKS method.The order of the spatial accuracy for this method is 1 in the L? sense and 1.24 in the 2L sense.Then,the paper investigated the incompressible flows around a stationary circular,two circular cylinders in tandem and an oscillating cylinder to further testify the continuous-forcing-based IB-GKS method.After that,the validity of the proposed direct-forcing-based IB-GKS method is verified by simulations of incompressible flow around a circular cylinder,supersonic and high Reynolds number flow around a circular cylinder,subsonic and transonic flows round a NACA0012 airfoil.By comparison with numerous other numerical and experimental results,the good capability of the presented two methods in handling complex or moving boundaries,incompressible or compressible flow is demonstrated.Combining GKS with the IB method to conduct the numerical simulation is applicable and meaningful.