The PDE framework Peano applied to fluid dynamics: an efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids

Abstract

This paper presents the general purpose framework Peano for the solution of partial differential equations (PDE) on adaptive Cartesian grids. The strict structuredness and inherent multilevel property of these grids allows for very low memory requirements, efficient (in terms of hardware performance) implementations of parallel multigrid solvers on dynamically adaptive grids, and arbitrary spatial dimensions. This combination of advantages distinguishes Peano from other PDE frameworks. We describe shortly the underlying octree-like grid type and its most important properties. The main part of the paper shows the framework concept of Peano and the implementation of a Navier–Stokes solver as one of the main currently implemented application examples. Various results ranging from hardware and numerical performance to concrete application scenarios close the contribution.