Kinetic energy preserving DG schemes based on summation-by-parts operators on interior node distributions

In this work, a kinetic energy preserving DG scheme in one space dimension using Gauss-Legendre nodes is presented. Stability problems will be demonstrated when using interface terms that are derived from the Lobatto nodes within the Gauss-Legendre skew-symmetric DG formulation. However, combined with correct interface terms, the skew-symmetric DG scheme constructed on Gauss-Legendre nodes is expected to yield higher accuracy compared to its Gauss-Lobatto counterpart. This advantage is demonstrated in the case of viscous compressible flow computation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)