Graduate School of Computational Engineering

Adaptive Multigrid Methods for Fluid-Structure Interaction Optimization

Strong fluid structure coupling is a part of many technical systems. In recent years, encouraging progress has been made concerning the numerical simulation of Fluid-Structure Interaction (FSI) problems. The aim of this project is to combine methods for PDE constrained optimization, adaptivity and FSI simulation to develop an efficient adaptive multigrid method for Fluid-Structure Interaction optimization. Thus we go for an adjoint based Trust-Region SQP method that allows adaptive refinement of both, spatial and temporal grids.


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Multilevel methods for the optimization of fluid-structure interaction problems based on adaptive discretizations and reduced order models

Many problems arising in engineering applications (aerodynamics, civil engineering,…) involve the interaction of fluid flows with the elastic deformation of structures. While the numerical simulation of fluid-structure-interaction (FSI) problems is nowadays quite well understood, the efficient optimization of such problems with derivative based optimization methods is still in its beginning. On the one hand the Eulerian-Lagrangian-coupling of fluid and structure makes the derivation, analytical foundation and numerical implementation of adjoint-based techniques for the derivative computation involved. Moreover, rigorous analytical existence and uniqueness results for FSI-problems are even in 2D limited. On the other hand, the computational complexity of FSI-problems requires highly efficient optimization methods in order to solve optimization problems with reasonable effort.

The aim of this project is the extension of adaptive multilevel optimization techniques based on adaptive discretization, reduced order models and error estimation, which have been developed in the group of the supervisor, to the optimization of FSI-problems. This includes the development of the optimization method including error control criteria, the construction of suitable reduced order models and the convergence analysis under suitable assumptions. Moreover, the algorithm shall be implemented based on existing codes of the working group and be tested on demonstrator problems. The work builds on previous/current work of Sarah Essert within GSC CE, who has derived and implemented adjoint-based derivative computations for FSI-problems.

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