The discontinuous Galerkin (DG) methods have attained increasing popularity for solving the incompressible Navier-Stokes (INS) equations in recent years. However, the DG methods have their own weakness due to the high computational costs and storage requirements. In this work, we develop a high-order hybrid reconstructed DG (rDG) method for solving the INS equations on arbitrary grids. To be specific, the inviscid term of the INS equations is discretized by applying the third-order hybrid rDG($P_1{P}_2$) method with a simplified artificial compressibility flux, while the viscous term of the INS equations is discretized by using the simple direct DG (DDG) method. A number of incompressible flow problems, in both steady and unsteady forms, for a variety flow conditions are computed to numerically assess the performance of the hybrid rDG($P_1{P}_2$) method, which confirm its ability to achieve the optimal third order of accuracy at a significantly reduced computational costs. Furthermore, a detailed comparison of a variety of different reconstructed strategies is performed and presented. Numerical results demonstrate that the hybrid rDG($P_1{P}_2$) method outperforms the rDG($P_1{P}_2$) method based on either the original least-squares reconstruction or the Green-Gauss reconstruction for solving the INS equations.

近年来，不连续的Galerkin（DG）方法在求解不可压缩的Navier-Stokes（INS）方程中越来越受欢迎。但是，由于高计算成本和存储要求，DG方法有其自身的缺点。在这项工作中，我们开发了一种用于求解任意网格上的INS方程的高阶混合重构DG（rDG）方法。具体而言，通过应用三阶混合rDG（）离散化INS方程的无粘性项。$P_{\mathrm{1个}}{P}_2$简化的人工可压缩通量的）方法，而INS方程的粘性项通过使用简单直接DG（DDG）方法离散化。计算了各种流动条件下的稳态和非稳态两种不可压缩的流动问题，以数值方式评估混合rDG（$P_{\mathrm{1个}}{P}_2$）方法，从而证实了其以显着降低的计算成本获得最佳三阶精度的能力。此外，对各种不同的重构策略进行了详细比较。数值结果表明，混合rDG（$P_{\mathrm{1个}}{P}_2$）方法胜过rDG（$P_{\mathrm{1个}}{P}_2$）方法，该方法基于原始最小二乘重构或Green-Gauss重构来求解INS方程。