Discontinuous Galerkin method for 3-D RANS equations

The application of discontinuous Galerkin method(DGM) was investigated to simulate 3-D compressible turbulence flow field.DGM was used to solve the Reynolds-averaged Navier-Stokes equations closed by S-A turbulence model.Roe scheme was adopted as numerical flux of inviscid terms at the element interface.An efficient algorithm was developed to evaluate the gradients in the viscous terms for high-order accurate DGM.In the algorithm the gradient of conservative variables in the computational space is treated as auxiliary unknowns of mixed formulation,which were solved to the same order of accuracy as the conservative variables without need of quadrature.The 3-D turbulence flow field in compressor cascade NACA64 was simulated and numerical results agree well with the experimental data,which demonstrates the accuracy and capability of DGM in the simulation of turbulence flow in turbomachinery.