基于IPDG方法的超声速混合层流动数值模拟

为了满足超声速混合层高精度模拟需求，实现了基于内罚方法的间断伽辽金(IPDG)方法数值模拟。通过将黏性通量作为辅助变量使得Navier-Stokes方程降阶，并利用间断伽辽金方法进行空间离散，最后采用Newton-Krylov隐式方法对空间半离散方程进行时间推进。相对于有限体积法数值精度提高到了3阶。将该方法应用于对流马赫数为0.2的二维平面超声速混合层的数值模拟中，通过与实验数据的对比验证了方法的可靠性。数值结果显示了混合层中层流到湍流的发展过程。在此基础上，将基于数值解误差分布的自适应网格技术与IPDG方法结合起来，对比发现自适应网格数量减少了9倍，计算时间减少了8倍，大幅提高了方法的计算效率。 

Numerical simulations of supersonic mixing layers with IPDG method

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.