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)