Applications of high order hybrid DG/FV methods for 2D viscous flows

A concept of 'static reconstruction' and 'dynamic reconstruction' had been introduced for higher-order (third-order and higher) numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods had been developed for the scalar equations and Euler equations on triangular and Cartesian/triangular hybrid grids. In this paper, the hybrid DG/FV methods are extended to 2D Navier-Stokes equations on triangular and Cartesian/triangular hybrid grids. The BR2 scheme is employed to discretize the viscous terms. The numerical accuracy is validated by some typical test cases, including the Couette flow, laminar flows over a plate and a cylinder. The accuracy study shows that the hybrid DG/FV method achieves the desired order of accuracy, and they can capture the flow structure accurately. Qualitative analysis and numerical applications demonstrate that they can reduce the CPU time greatly than the traditional DG method with the same order of accuracy.