A hybrid reconstructed discontinuous galerkin method for compressible flows on unstructured grids

A new reconstructed Discontinuous Galerkin (rDG) method based on a hybrid least-squares recovery and reconstruction, named P1P2(HLSr), is developed for solving the compressible Euler and Navier-Stokes equations on unstructured grids. Unlike the recoverybased DG method where a quadratic polynomial solution is recovered from the underlying linear DG solution and the reconstruction-based DG method where a quadratic polynomial solution is reconstructed from the underlying linear DG solution, the new hybrid rDG method obtains a quadratic polynomial solution from the underlying linear solution by using a hybrid recovery and reconstruction strategy. The developed hybrid rDG method combines the simplicity of the reconstruction-based DG method and the accuracy of the recovery-based DG method, and has the desired property of 2-exactness. A number of test cases are presented to assess the performance of the new P1P2(HLSr) method for a variety of ow problems. Numerical experiments demonstrate that this hybrid rDG method is able to achieve the designed optimal 3rd order of accuracy for both inviscid and viscous ows and outperform the rDG methods based on either Green-Gauss or least-squares reconstruction.