An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.

中文翻译：

---

混合非结构化网格上可压缩雷诺平均 Navier-Stokes 方程的有效边缘数据结构

为了实现混合网格上雷诺平均 Navier-Stokes 方程的基于非结构化顶点的有限体积算法，已经开发了一种有效的基于边的数据结构。在本方法中，通过考虑数据访问模式和缓存效率来定制数据结构以满足基于顶点的算法的要求。所需的数据在物理内存中以彼此靠近的方式进行打包和分配。因此，所提出的数据结构提高了缓存性能并缩短了计算时间。因此，与其他开源求解器相比，显式流求解器在 CPU 时间方面具有显着的加速。为了提高算法的鲁棒性，还基于 PETSc 库实现了一个完全隐式的版本。由于可压缩 Navier-Stokes 产生的代数方程和单方程 Spalart-Allmaras 湍流方程使用受限加性 Schwarz 预处理器结合 FGMRES Krylov 子空间算法以整体方式求解。为了进一步提高计算精度，使用基于多尺度度量的各向异性网格细化库 PyAMG 进行网格自适应。该数值算法针对经典基准问题进行了验证，例如超临界 RAE2822 翼型周围的跨音速湍流和 DLR-F6 机翼-机身-机舱-挂架配置。数据结构的效率通过在 CPU 时间上实现高达一个数量级的加速来证明。