By Dominik Schillinger, Quanji Cai, Ralf-Peter Mundani, Ernst Rank (auth.), Michael Bader, Hans-Joachim Bungartz, Tobias Weinzierl (eds.)
This complaints quantity collects evaluate articles that summarize study carried out on the Munich Centre of complicated Computing (MAC) from 2008 to 2012. The articles deal with the expanding hole among what can be attainable in Computational technology and Engineering because of fresh advances in algorithms, undefined, and networks, and what can really be completed in perform; additionally they research novel computing architectures, the place computation itself is a multifaceted procedure, with wisdom or ubiquitous parallelism because of many-core structures being simply of the demanding situations confronted. themes hide either the methodological points of complex computing (algorithms, parallel computing, facts exploration, software program engineering) and state-of-the-art functions from the fields of chemistry, the geosciences, civil and mechanical engineering, etc., reflecting the hugely interdisciplinary nature of the Munich Centre of complicated Computing.
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Thus, sophisticated methods to improve this accuracy are required. Here, immersed boundary methods such as Nitsche’s method are a promising approach. In this paper, we present a Cartesian grid implementation in Sundance including an extension of Nitsche’s method to flow simulations on moving geometries, in particular fluid-structure interaction and shape optimization problems. In the following section, we show the underlying equations of our fluid-structure scenarios and recall some basic methods for PDE constraint optimization.
For shape optimization, we present first simple scenarios with results in Sect. 9. Finally, we summarize results and give an outlook on future work in the conclusion (Sect. 10). Immersed Boundary Methods for Fluid-Structure Interaction and Shape. . 27 2 The Fluid-Structure Interaction Model and Optimization Methods The Fluid-Structure Interaction Model. v r/v rp C ff (momentum equation); @t r v D 0 (continuity equation) (1) (2) to model the fluid flow in connection with the structural dynamics equations s @2 u Cr @t 2 s C fs D 0; (structural dynamics) (3) where v denotes the flow velocities, p the fluid pressure, ff external forces acting on the fluid such as gravity forces, and the viscosity of the considered fluid.
Line or surface boundary integrals are computed analogously. However, we do not use precomputed weights here as (1) some boundary integrals involve normal vectors that are different for each subpart of the boundary inside a given cell, (2) boundary integrals are cheaper such that we can afford storing all quadrature points, (3) three-dimensional cases require the usage of data points in the vicinity but not directly on the boundary due to the approximation of the original triangulation within each cut cell.