We introduce an approach for solving the incompressible Navier-Stokes equations on a forest of Octree grids in a parallel environment. The methodology uses the p4est library of Burstedde et al. (2011) [15] for the construction and the handling of forests of Octree meshes on massively parallel distributed machines and the framework of Mirzadeh et al. (2016) [54] for the discretizations on Octree data structures. We introduce relevant additional parallel algorithms and provide performance analyses for individual building bricks and for the full solver. We demonstrate strong scaling for the solver up to 32,768 cores for a problem involving $\mathcal{O}(6.1\times {10}^8)$ computational cells. We illustrate the dynamic adaptive capabilities of our approach by simulating flows past a stationary sphere, flows due to an oscillatory sphere in a closed box and transport of a passive scalar. Without sacrificing accuracy nor spatial resolution in regions of interest, our approach successfully reduces the number of computational cells to (at most) a few percents of uniform grids with equivalent resolution. We also perform a numerical simulation of the turbulent flow in a superhydrophobic channel with unparalleled wall grid resolution in the streamwise and spanwise directions.

我们介绍了一种在并行环境中的Octree网格林中求解不可压缩的Navier-Stokes方程的方法。该方法使用Burstedde等人的p4est库。（2011年）[15]在大型并行分布式机器和Mirzadeh等人的框架上建设和处理Octree网格森林。（2016）[54]进行Octree数据结构的离散化。我们介绍了相关的附加并行算法，并为单个建筑砖块和完整的求解器提供了性能分析。我们针对涉及以下问题的求解器展示了多达32,768个核的强大扩展能力$\mathcal{Ø}（6.1\times {10}^8）$计算单元。我们通过模拟流过固定球体的流，封闭盒中由于振荡球体引起的流和无源标量的传输，说明了我们方法的动态自适应能力。在不牺牲感兴趣区域的精度或空间分辨率的情况下，我们的方法成功地将计算单元的数量减少到（最多）具有相等分辨率的均匀网格的百分之几。我们还对超疏水通道中的湍流进行了数值模拟，并在水流方向和展向方向上获得了无与伦比的壁栅分辨率。