Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness of DG methods significantly, they are also computationally more demanding than standard weak form nodal DG methods. We present several implementation techniques to improve the efficiency of flux differencing DG methods that use tensor product quadrilateral or hexahedral elements, in 2D or 3D, respectively. Focus is mostly given to CPUs and DG methods for the compressible Euler equations, although these techniques are generally also useful for other physical systems, including the compressible Navier-Stokes and magnetohydrodynamics equations. We present results using two open source codes, Trixi.jl written in Julia and FLUXO written in Fortran, to demonstrate that our proposed implementation techniques are applicable to different code bases and programming languages.

许多现代守恒定律的不连续伽辽金 (DG) 方法利用部分算子求和和通量差分来实现动能守恒或熵稳定性。虽然这些技术显着提高了 DG 方法的稳健性，但它们在计算上也比标准弱形式节点 DG 方法要求更高。我们提出了几种实现技术来提高通量差分 DG 方法的效率，这些方法分别在 2D 或 3D 中使用张量积四边形或六面体元素。重点主要集中在可压缩欧拉方程的 CPU 和 DG 方法上，尽管这些技术通常也可用于其他物理系统，包括可压缩纳维-斯托克斯和磁流体动力学方程。我们使用两个开源代码（用 Julia 编写的 Trixi.jl 和用 Fortran 编写的 FLUXO）展示结果，以证明我们提出的实现技术适用于不同的代码库和编程语言。