Discontinuous Galerkin Finite Element Method On Hybrid Grids And Finite Element/Finite Volume Mixed Method

With the rapid development of computer science and Computational Fluid Dynamics(CFD) technology,numerical simulation has become one of the main research tools for aerodynamic performance evaluation of components and/or vehicle before the wind tunnel tests and through the detail aerodynamic design,due to their great characteristics on high efficiency and economy.However,CFD still faces some challenges in practice applications,for example,the ability of heat flux and skin friction prediction over complex geometries has a long way to go.The main purpose of this work is to improve the accuracy of heat flux prediction for hypersonic flows over complex configurations.Firstly,a Discontinuous Galerkin(DG) finite element method (FEM) is presented for arbitrary elements,including hexahedron,prism and tetrahedron.Secondly,a mixed method of DG-FEM and finite volume method(FVM) on hybrid grids is proposed,based on the zone-decomposition approach.Then the present method is validated by some typical hypersonic cases,and finally,is applied to some complex configurations.The computational results,including flow patterns and heat flux distributions,show good agreements with experimental data,and the comparison on CPU time and store memory demonstrates its higher efficiency.This dissertation is organized as following:Chapter one is the Introduction,in which the development history of CFD applications of finite element methods and finites volume methods is reviewed briefly, and the current status of applications of finite element methods,finite volume methods, as well as grid generation techniques are summarized,and finally,the main work of this paper is introduced briefly.The second chapter introduces the numerical methods in details.Based on the Runge-Kutta(RK) DG finite element method proposed by Shu and Cockburn,two dimensional and three dimensional DG finite element methods are constructed on hybrid grids for viscous flows through local coordinate transformation.Meanwhile,the limiters for various types of non-orthogonal elements are proposed,and an implicit scheme for DG finite element method is developed also.Furthermore,in order to remedy the deficiencies of memory requirement and calculation efficiency of pure DG-FEMs,a mixed finite element/finite volume scheme is proposed.The DG-FE solver runs only in the zone of boundary layer,whereas the FV solver runs in the outer computational domain.In Chapter 3,the RKDG finite element method is validated by some typical test cases,including some traditional one-dimensional cases(Sod,Shu and Lax's problems and the shock wave collision),2D supersonic flow over front step in a tube at Mach number 3,and the double Mach reflection case with strong inclined shock wave movement.The numerical results demonstrate that this method has good capability to capture shock waves and contact-discontinuity with high resolution,and there are no obvious non-physical oscillations in the flow field.In chapter 4,the DG finite element scheme for non-orthogonal elements is validated.Supersonic viscous flow over 2-D cylinder,the fourth class of shock wave interaction,and hypersonic viscous flow over a 3-D blunt spherical head are simulated. The numerical results agree with experimental data very well,which demonstrates the excellent ability of heat flux prediction of present method.Chapter 5 discusses the validation of the mixed FE/FV scheme.Hypersonic viscous flow over the blunt spherical head and a blunt cone at 20 degrees angle of attack are simulated on various types of grids(structured and hybrid grids).The present mixed FE/FV algorithm offers the flow structure and the heat flux distribution as good as those by the DG-FE solver.Furthermore,the mixed FE/FV algorithm reduces the requirements of computer resource greatly and increases the computational efficiency.In chapter 6,the present mixed FE/FV solver is applied to heat flux prediction over complex geometries.The numerical results show good agreement with those of wind tunnel testing,which indicates its potential ability in engineering applications.Chapter 7 is the conclusion of the dissertation.