A Reconstructed Discontinuous Galerkin Method Based on a Gas Kinetic Scheme for Compressible Flows on Arbitrary Grids

摘要

A reconstructed discontinuous Galerkin (RDG) Method based on a newly developedrngas-kinetic scheme is presented for the solution of the compressible Euler and Navier-Stokes equationsrnon arbitrary grids. The idea behind this approach is to combine the robustness of therngas-kinetic scheme with the accuracy of the DG methods in an effort to develop a more accurate,rnefficient, and robust method for numerical simulations of compressible flows in a wide range ofrnflow regimes. Unlike the traditional discontinuous Galerkin methods, where a Local DiscontinuousrnGalerkin (LDG) formulation is usually used to discretize the viscous fluxes in the Navier-Stokesrnequations, our RDG method computes the fluxes based on the time evolution of the Navier-Stokesrngas distribution function, which includes the contribution of both convective and dissipative terms.rnThe developed method is used to compute a variety of viscous flow problems on arbitrary grids.rnThe numerical results obtained by this RDG method are extremely promising and encouraging inrnterms of both accuracy and robustness, indicating its ability and potential to become not just arncompetitive but simply a superior approach than the current available numerical methods.