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Many modern discontinuous Galerkin (DG) methods for conservation laws makeuse of summation by parts operators and flux differencing to achieve kineticenergy preservation or entropy stability. While these techniques increase therobustness of DG methods significantly, they are also computationally moredemanding than standard weak form nodal DG methods. We present severalimplementation techniques to improve the efficiency of flux differencing DGmethods that use tensor product quadrilateral or hexahedral elements, in 2D or3D respectively. Focus is mostly given to CPUs and DG methods for thecompressible Euler equations, although these techniques are generally alsouseful for other physical systems including the compressible Navier-Stokes andmagnetohydrodynamics equations. We present results using two open source codes,Trixi.jl written in Julia and FLUXO written in Fortran, to demonstrate that ourproposed implementation techniques are applicable to different code bases andprogramming languages.

Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws