Oberseminar Numerische Mathematik / Scientific Computing
Matthias Meinke
Institute of Aerodynamics,RWTH Aachen University
Solution Adaptive Cartesian Mesh Methods for the Simulation of Flows with Moving Boundaries
Abstract:
The simulation of unsteady flows in or around geometries with moving boundaries is still a challenging problem. A general formulation of the grid generation for arbitrarily moving geometries is difficult to find. A method is presented which allows a fully automatic flow simulation in complex geometries with moving surfaces. This method is based on adaptively refined, hierarchical Cartesian meshes, in which a cut cell method is used for the formulation of boundary conditions. The cut cell method is implemented with the help of ghost cells, which can be freely positioned in space. A linear least-squares formulation is applied for the reconstruction of the gradients at cell centers, such that a fully conservative method is obtained also for viscous flows, [3]. The cut cell information is determined with a boundary surface representation in STL-format, which is typically provided by CAD software. Since the generation of the cut-cell information is computationally expensive for three-dimensional geometries, a more efficient method has been developed for the determination of the location of all moving boundaries within each time step. A level-set equation, [2], is solved, which allows a simple determination of the moving boundary location. To avoid an accumulation of errors during the level set integration, the level set is corrected with the STL-data after a certain number of time steps. A dual-mesh approach is used, in which the level set is solved only on a narrow band, which is independent from the CFD mesh. The hierarchical structure of the two meshes facilitates hereby the transfer of information from the level set to the CFD mesh where the cut cell information has to be determined. Results of flow simulations around an oscillating cylinder computed with this method will be presented.
References
[1] D. Hartmann, M. Meinke, and W. Schr¨oder. An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods. Comput. Fluids, 37:1103–1125, 2008.[2] D. Hartmann, M. Meinke, and W. Schr¨oder. Differential equation based constrained reinitialization for level set methods. J. Comput. Phys., 227:6821–6845, 2008.
[3] D. Hartmann, M. Meinke, and W. Schr¨oder. A general formulation of boundary conditions on Cartesian cut cells for compressible viscous flow. AIAA-Paper 2009-3878, 2009.
| Datum: | 08.02.10 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 032 im Erdgeschoss |