A class of DG/FV hybrid schemes for conservation law IV: 2D viscous flows and implicit algorithm for steady cases

• A class of high-order DG/FV hybrid schemes for 2D viscous flows is proposed.
• An implicit algorithm based on Newton/Gauss–Seidel iteration is developed.
• The DG/FV hybrid schemes are more efficient than the same order DGM.
• The implicit algorithm improves the convergence history significantly.

The DG/FV hybrid schemes developed in the authors’ previous work were extended to solve two-dimensional Navier–Stokes equations on arbitrary grids. For the viscous term, the well-known BR2 approach was employed. In addition, to accelerate the convergence of steady flows, an efficient implicit method was developed for the DG/FV schemes. The Newton iteration was employed to solve the nonlinear system, while the linear system was solved with Gauss–Seidel iteration. Several typical test cases, including Couette flow, laminar flows over a flat plate and a NACA0012 airfoil, steady and unsteady flows over a circular cylinder, and a mixing layer problem, were simulated to validate the accuracy and the efficiency. The numerical results demonstrated that the DG/FV hybrid schemes for viscous flow can achieve the desired order of accuracy and the present implicit scheme can accelerate the convergence history efficiently. Moreover, in the same framework, the DG/FV hybrid schemes are more efficient than the same order DG schemes.