The Study Of Application Of Discontinuous Galerkin Method For Numerical Simulation Of Supersonic Flow

Due to advance of computer technology and computational demands of complex flows of engineering,the higher and higher requirements for computational fluid dynamics is proposed,and computational fluid dynamics is asked to put forward and develop computational methods that have higher precision and are more suitable for solving complex flow constantly.In recent years,as a numerical scheme with high precision and high resolution,because of its excellent characteristics,including computational stability,compact format,easy to deal with complex boundary conditions and parallel computing,and so on,discontinuous Galerkin(DG)finite element method has been widely developed and applied.How to effectively apply this method to calculation of fluid dynamics is the hot topic of issues that computational fluid dynamics focuses on recently.In this paper,discontinuous Galerkin finite element method is applied to solve typical equations and supersonic flow problems of fluid dynamics,and it is studied to its characteristics and application of numerical simulation of fluid mechanics.The main content includes the following aspects:1)The DG method is applied to solve some of one-dimensional and two-dimensional classical equations,including wave equation,Burgers equation,and we study the numerical characteristics of precision and discontinuous treatment for this method.By analyzing the results of the calculation,we confirm that DG method has some characteristics which are the high precision and the high resolution of discontinuity.2)The DG method is applied to the numerical simulation of one-dimensional and two-dimensional typical inviscid supersonic flow problems,including the Sod shock tube problem and the double Maher reflection problem,and it is further investigated to the characteristic of discontinuous treatment for this method.And the computation time and the maximum computable time step of DG method are studied by comparing with WENO method.3)The DG method is applied to the calculation of basic flow field of supersonic flat-plate boundary layer initially,and we analyze and study the issue of computation time and time step in the process of calculation.We compare the calculation results between viscous equation and inviscid equation,and it is studied to the influence of calculation of viscosity terms on the computation time of this method.