A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids

A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier–Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi–Rebay II). The developed rDG(P₁P₂) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P₁P₂) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the direct numerical simulation (DNS) of compressible turbulent flows.