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

Abstract

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