Numerical Calculation Research On Discontinuous Galerkin Finite Element Method In Supersonic Flow

For the advantages of Discontinuous Galerkin Finite Element Method easy to construct high order accuracy explicit discrete numeric scheme and having stronger adaptability to the general rules of the grid,it gradually become an important part of the numerical simulation method of computational fluid dynamics.In the calculation process of using discontinuous Galerkin finite element method,the corresponding integral expression needs to be constructed as the starting point of numerical solving method,then the volume integral and surface integral will be introduced.Under normal circumstances,the value of these integral items will be acquired by using numerical integration method.When high-order discontinuous Galerkin finite element method needs to be used,the demand for numerical integration calculation accuracy will increase accordingly,and calculation amount will be too large,and as well the numerical integration calculation amount to a large extent determines the computational efficiency of discontinuous Galerkin finite element method.The process to establish one-dimensional and two-dimensional conservation law and high order equation strong solution and weak solution integral expression of DG method is deduced in this paper,and to solve the problem of large calculation amount,this paper emphasizes that an explicit semi-discretization of quadrature-free discontinuous Galerkin finite element method was structured by establishing the relationship between Lagrange interpolation polynomial basis function and Jacobi orthogonal polynomial basis function,and the scheme's effectiveness of onedimensional,two-dimensional linear and nonlinear problem,and the high order spatial derivative problems is verified by direct numerical simulation processing.Using this method,there's no need to calculate the integral items of each element by numerical integration and the high precision of discontinuous Galerkin finite element method can be achieved effectively,so the method has very significant meaning for structuring more efficient high-order discontinuous Galerkin finite element method.At the same time,this paper also discusses the structure thought of numerical flux and its influence on the results,as well as the aliasing error and filter stabilization,constructing limiter to eliminate nonphysical oscillations and other problems.