Space- and time-parallel Navier-Stokes solver for 3D block-adaptive cartesian grids

Publisher Summary This chapter introduces a parallelization strategy for implicit solution methods for the Navier-Stokes equations based on domain decomposition in time and space and discusses in particular the use of parallel pre-conditioned conjugate gradient solvers. The discretization of the Navier-Stokes equations is based on a fully implicit, second order, three time levels scheme in time and a fully conservative, second order finite volume method in space using collocated variable arrangement and central differencing. The equations are solved by a segregated iterative approach with non-linearities and inter-equation coupling being resolved in a predictor-corrector scheme within outer iterations. The chapter describes the implementation of block-structured grids with non-matching block interfaces in a parallel environment. The parallelization method is applied to a direct numerical simulation of turbulent channel flow over a square rib, based on the mean velocity above the obstacle and the step height. The chapter analyzes the numerical efficiency of the method. The solution method using block-adaptive Cartesian grids presented is suitable for simulation of flows in rectangular geometries.