Discontinuous Galerkin for Advection with Interface-Centered Reconstruction

摘要

The Recovery-based Discontinuous Galerkin (RDG) discretization has been shown to be the most accurate among contemporary DG schemes for diffusion on a Cartesian grid. It achieves the order of accuracy 3p + 2 for even p and 3p + 1 for odd p, where p is the order of the polynomial basis. However, the overall performance of a Navier-Stokes simulation, using RDG for viscous terms, is limited to 2p +1 due to the DG discretization for advection. We describe two different approaches to improve the accuracy of the DG discretization for advection. The first option is able to reach a maximal order of 4p + 3, albeit utilizing an enlarged computational stencil. The second one attains 3p +1 without enlarging the stencil. It is also computationally cheaper owing to the lower-order reconstruction.