Concepts for Efficient Flow Solvers Based on Adaptive Cartesian Grids

Ioan Lucian Muntean (), Miriam Mehl (), Tobias Neckel () and Tobias Weinzierl ()
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Ioan Lucian Muntean: TU München, Department of Computer Science
Miriam Mehl: TU München, Department of Computer Science
Tobias Neckel: TU München, Department of Computer Science
Tobias Weinzierl: TU München, Department of Computer Science

A chapter in High Performance Computing in Science and Engineering, Garching/Munich 2007, 2009, pp 535-549 from Springer

Abstract: Abstract This contribution describes mathematical and algorithmic concepts that allow for a both numerically and hardware efficient implementation of a flow solver. In view of numerical efficiency, this strongly suggests multigrid solvers on adaptively refined grids in order to minimize the amount of data to be computed for a prescribed accuracy as well as the number of iterations. In view of hardware efficiency, a minimization of memory requirements and an optimization of data structures and data access tailored to the memory hierarchy of supercomputing architectures is essential, since flow solvers typically are data intensive applications. We address both the numerical and the hardware challenge with a combination of structured but flexible adaptive hierarchical Cartesian grids with space-filling curves as traversal scheme and stacks as data structures. These basic concepts are applied to the two computationally demanding application areas turbulent flow simulations and fluid-structure interactions. We show the benefits of our methods for these applications as well as first results achieved at the HLRB2 and smaller clusters.

Date: 2009
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DOI: 10.1007/978-3-540-69182-2_42

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