A reconstructed discontinuous Galerkin method for compressible turbulent flows on 3D curved grids

A third-order accurate reconstructed discontinuous Galerkin method, namely rDG(P1P2), is presented to solve the Reynolds-Averaged Navier-Stokes (RANS) equations, along with the modified one-equation model of Spalart and Allmaras (SA) on 3D curved grids. In this method, a piecewise quadratic polynomial solution (P2) is obtained using a least-squares method from the underlying piecewise linear DG(P1) solution. The reconstructed quadratic polynomial solution is then used for computing the inviscid and the viscous fluxes. Furthermore, Hermite Weighted Essentially Non-Oscillatory (WENO) reconstruction is used to guarantee the stability of the developed rDG method. A number of benchmark test cases based on a set of uniformly refined quadratic curved meshes are presented to assess the performance of the resultant rDG(P1P2) method for turbulent flow problems. The numerical results demonstrate that the rDG(P1P2) method is able to obtain reliable and accurate solutions to 3D compressible turbulent flows at a cost slightly higher than its underlying second-order DG(P1) method.