This work is developing simulation methods for unsteady flows of fluids in situations involving significant deformations of the computational domain. The methods in question are based on the finite element technique, using stabilized formulations, complex unstructured three-dimensional meshes, and iterative solution strategies. The parallel implementation is based on message-passing communication libraries and is portable across a wide range of machines. The two sets of problems under current investigation center on free-surface flows and on translating and rotating geometries, which can be modeled using the Shear-Slip Mesh Update Method (SSMUM).
In free-surface flows, the location of the interface is not known a priori and needs to be determined as part of the overall solution. The major challenges in this type of simulations are accurate representation of the interface in long-term time-integration, devising mathematical models and computational methods that take large variations in geometric scales into account, and keeping the computational cost at an acceptable level. Wave formation and break-up are also among the challenges. Mathematical models produced in this work are based on the Navier-Stokes equations of incompressible flows. Depending on the complexity of the interface and other conditions, work is being done on the development of two different methods. One approach is developing a stabilized space-time finite element formulation, which is an interface-tracking method with moving mesh. The other approach is working on a stabilized finite element/interface-capturing formulation with fixed meshes. The interface-capturing method is more flexible but yields less accurate representation of the interface compared to the interface-tracking method. The interface-tracking method has been successfully extended to three-dimensional and periodic flows. A model of the Olmsted Dam on the Ohio River is still being used as a test problem.
Work is continuing on the SSMUM for parallel, space-time computation of problems involving large regular mesh deformations. This technique connects, with structured mesh layers, regions of unstructured meshes, each rigidly attached to one of the moving boundaries. The connecting layers are designed to accept slip between the neighboring unstructured meshes and to accommodate such motion through limited remeshing. Because of the small size and structured nature of the layer mesh, its remeshing can be performed economically and in parallel. The SSMUM has been recently extended to three-dimensional geometries and applied to flows around a helicopter with a spinning main rotor.
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URL: http://www.msi.umn.edu/about/publications/annualreport/ar2000/depts/IT/Aerospace/behr.html |
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