## Massively parallel finite element computation of incompressible flows involving fluid-body interactions.(English)Zbl 0846.76048

We describe massively parallel finite element computations of unsteady incompressible flows involving fluid-body interactions. These computations are based on the deforming-spatial-domain/stabilized-space-time finite element formulation. Unsteady flows past a stationary NACA $$0012$$ airfoil are computed for Reynolds numbers $$1000$$, $$5000$$ and $$100 000$$. Significantly different flow patterns are observed for these three cases. The method is then applied to computation of the dynamics of an airfoil falling in a viscous fluid under the influence of gravity. All these computations were carried out on the Thinking Machines CM-200 and CM-5 supercomputers. The implicit equation systems arising from the finite element discretizations of these large-scale problems are solved iteratively by using the GMRES update technique with diagonal preconditioners.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 65Y05 Parallel numerical computation
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### References:

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