We discuss the efficient implementation of a high-performance second-order colocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex limiting technique introduced by Guermond et al. (SIAM J. Sci. Comput. 40, A3211--A3239, 2018). As such it is invariant-domain preserving, i.e., the solver maintains important physical invariants and is guaranteed to be stable without the use of ad-hoc tuning parameters. This stability comes at the expense of a significantly more involved algorithmic structure that renders conventional high-performance discretizations challenging. We demonstrate that it is nevertheless possible to achieve an appreciably high throughput of the computing kernels of such a scheme. We discuss the algorithmic design that allows a SIMD vectorization of the compute kernel, analyze the node-level performance and report excellent weak and strong scaling of a hybrid thread/MPI parallelization.

中文翻译：

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使用保持不变域的二阶有限元方案对可压缩欧拉方程进行大规模并行 3D 计算

我们讨论了用于求解非结构化网格上气体动力学的可压缩欧拉方程的高性能二阶共置型有限元方案的有效实现。求解器基于 Guermond 等人引入的凸限制技术。(SIAM J. Sci. Comput. 40, A3211--A3239, 2018)。因此，它保持不变域，即求解器保持重要的物理不变量，并保证在不使用临时调整参数的情况下稳定。这种稳定性是以更加复杂的算法结构为代价的，这使得传统的高性能离散化具有挑战性。我们证明，尽管如此，仍有可能实现这种方案的计算内核的高吞吐量。