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Flow Around a Submarine

In this problem we simulate flow around a Los Angeles-class submarine. We use a stabilized finite element method together with an unstructured mesh to solve this problem. The images below on the left appeared on the cover page of the Slide Book of the ARPA High Performance Computing Software PI Meeting, San Diego, California, September 27-29, 1993. The top image shows the streamlines and the pressure distribution on the surface of the submarines, while the bottom image shows the stream ribbons color-coded with the axial velocity.
The Reynolds number based on the free-stream velocity and the hull length is one billion. A Smagorinsky turbulence model was used in this unsteady computation, which was restarted from a steady-state solution at Reynolds number one million. We employed a spatial mesh consisting of 71,035 nodes and 345,129 tetrahedral elements. This resulted in 466,688 coupled equations that were solved iteratively. A similar simulation was performed later at higher resolution. The flow solver and flow visualization software (based on Visual3 library) were developed by the T*AFSM.

The flow simulation for the submarine is part of an effort by the T*AFSM researchers, partially funded by the Advanced Research Projects Agency, for the development of scalable libraries for fluid mechanics applications.


1. T.J.R. Hughes, T.E. Tezduyar and A.N. Brooks, "Streamline Upwind Formulations for Advection-Diffusion, Navier-Stokes, and First-order Hyperbolic Equations", Proceedings of the Fourth International Conference on Finite Element Methods in Fluid Flow, University of Tokyo Press, Tokyo (1982).

2. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1991) 1-44.

3. T.E. Tezduyar, M. Behr and T.J.R. Hughes, "High Performance Finite Element Computation of Fluid Dynamics Problems", Computational Fluid Dynamics Review 1995 (eds. M. Hafez and K. Oshima), John Wiley & Sons (1995) 300-321.

4. T.E. Tezduyar, M. Behr and T.J.R. Hughes, "Finite Element Methods", Section 19.3 in Handbook of Fluid Dynamics and Fluid Machinery, John Wiley & Sons (1996).