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The PDE framework Peano applied to fluid dynamics: an efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids. (English) Zbl 1301.76056

Summary: 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.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms
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