This work reports on the performances of a fully-discrete hp-adaptive entropy stable discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations. The resulting code framework is denoted by SSDC, the first S for entropy, the second for stable, and DC for discontinuous collocated. The method is endowed with the summation-by-parts property, allows for arbitrary spatial and temporal order, and is implemented in an unstructured high performance solver. The considered class of fully-discrete algorithms are systematically designed with mimetic and structure preserving properties that allow the transfer of continuous proofs to the fully discrete setting. Our goal is to provide numerical evidence of the adequacy and maturity of these high-order methods as potential base schemes for the next generation of unstructured computational fluid dynamics tools. We provide a series of test cases of increased difficulty, ranging from non-smooth to turbulent flows, in order to evaluate the numerical performance of the algorithms. Results on weak and strong scaling of the distributed memory implementation demonstrate that the parallel SSDC solver can scale efficiently over 100,000 processes.

这项工作报告了全分立式hp的性能可压缩Naiver–Stokes方程的自适应熵稳定不连续并置Galerkin方法。生成的代码框架由SSDC表示，第一个S表示熵，第二个S表示稳定，DC表示不连续并置。该方法具有按部分求和的属性，允许任意的空间和时间顺序，并在非结构化高性能求解器中实现。所考虑的一类全离散算法是系统设计的，具有拟态和结构保留属性，可以将连续证明转移到全离散设置。我们的目标是为这些高阶方法的充分性和成熟度提供数值证据，以作为下一代非结构化计算流体动力学工具的潜在基础方案。为了评估算法的数值性能，我们提供了一系列难度增加的测试案例，从非平滑流到湍流。分布式内存实现的弱扩展和强扩展的结果表明，并行SSDC求解器可以有效扩展100,000个以上的进程。