Direct numerical simulation of incompressible flows on parallel Octree grids

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., SIAM J. Sci. Comput., 33(3) (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., J. Comput. Phys., 322 (2016) [55] 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 O 6.1⇥ 108 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.