In order to satisfy the high-precision simulation of supersonic mixing layers

discontinuous Galerkin finite element numerical method based on internal penalty method (IPDG) was realized. The viscous flux was introduced as an auxiliary variable to reduce the Navier-Stokes equation order

the discontinuous Galerkin method was used for spatial discretization and the Newton-Krylov implicit method was used for time marching. Compared with the finite volume method

the numerical accuracy of the method was improved to the third-order. The numerical simulation of the supersonic mixing layers developed in two-dimensional planar space with a convective Mach number of 0.2 was carried out

and the reliability of the method was verified by comparison with the experimental data. The numerical results clearly indicated the development of flow transition and vortices in the mixing layer. Meanwhile

the adaptive mesh technology based on numerical solution error distribution was combined with IPDG method.The comparison showed that the number of adaptive grids was reduced by 9 times

and the calculation time was reduced by 8 times

thus significantly improving the calculation efficiency of the method.