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An efficient multigrid FEM solution technique for incompressible flow with moving rigid bodies. (English) Zbl 1216.76037
Feistauer, M. (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18–22, 2003. Berlin: Springer (ISBN 3-540-21460-7/hbk). 844-853 (2004).
Summary: This paper uses the fictitious boundary method described in the authors’ paper [Challenges in Scientific Computing, Lect. Notes Comput. Sci. Eng. 35, 37–68 (2003; Zbl 1138.76388)] for the solution of incompressible flow with moving rigid bodies in complex geometries. The method is based on a special treatment of Dirichlet boundary conditions inside of a FEM approach in the context of a hierarchical multigrid scheme such that the flow can be efficiently computed on a fixed computational mesh while the solid boundaries are allowed to move freely through the given mesh. In this paper, we focus on the calculations of the drag and lift forces acting on the moving solid bodies which are not captured by the mesh. The comparison between the present and benchmark results for the flow around a circular cylinder with different Reynolds numbers is first presented, and then the result for a circular cylinder oscillating in a channel is given. The simulation results compared with corresponding reference results are found to be very reasonable and satisfactory.
For the entire collection see [Zbl 1046.65002].

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76T25 Granular flows
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
Software:
FEATFLOW
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