| Abstract: | A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR (correction procedure or collocation penalty via reconstruction). The CPRapproach employs the differential form of the equation and accounts for the jumpsin flux values at the cell boundaries by a correction procedure. In addition to beingsimple and economical, it unifies several existing methods including discontinuousGalerkin, staggered grid, spectral volume, and spectral difference. To discretize the diffusion terms, we use the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG),and I-continuous approaches. The first three of these approaches, originally derivedusing the integral formulation, were recast here in the CPR framework, whereas theI-continuous scheme, originally derived for a quadrilateral mesh, was extended to atriangular mesh. Fourier stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried out. Finally, results for the Navier-Stokesequations are shown to compare the various schemes as well as to demonstrate thecapability of the CPR approach. |
