Abstract
Three-dimensional global flow stability analysis generates very large complex generalized eigenvalue problem. Solution of the global flow stability problem delivers not only information about the growth rate of disturbances and respective frequencies. Eigenvectors of this system constitute physical modes space necessary in Low Dimensional Modeling of the flow and flow control design. Difficulties in solution of the eigenvalue problem limited till now the global stability to two-dimensional analysis, referred sometimes as bi-global. The 3D global stability solution (tri-global) are very rare and limited only to structured meshes. In the present study the solution procedure for unstructured 3D global flow stability problem with subspace iteration and domain decomposition is presented. The incompressible Navier-Stokes equation are discretized with the Finite Element Method in penalty formulation. The solution is demonstrated on well documented flow around the circular cylinder. With modest RAM and CPU requirements and decomposition of the computational domain into 8 subdomains (METIS software) the large eigenproblem having about 750 000 DOFs has been solved on 2 nodes (4CPU each) of PC cluster.
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References
Lehoucq, R., Salinger, A.: Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers (1999)
Zebib, A.: Stability of viscous flow past a circular cylinder. J. Engr. Math. 21, 155–165 (1987)
Morzyński, M., Thiele, F.: Numerical stability analysis of a flow about a cylinder. Z. Angew. Math. Mech. 71, T424–T428 (1991)
Abdessemed, N., Sherwin, S., Theofilis, V.: Linear Stability of the flow past a low pressure turbine blade. In: 36 th AIAA Fluid Dynamics Conference and Exhibit (2006)
Tezuka, A., Suzuki, K.: Three-Dimensional Global Linear Stability Analysis. of Flow Around a Spheroid (2006)
Burroughs, E., Romero, L., Lehoucq, R., Salinger, A.: Large scale eigenvalue calculations for computing the stability of buoyancy driven flows (2001)
Pawlowski, R., Salinger, A., Shadid, J., Mountziaris, T.: Bifurcation and stability analysis of laminar isothermal counterflowing jets. Journal of Fluid Mechanics 551, 117–139 (2006)
Theofilis, V.: Advances in global linear instability analysis of nonparallel and three-dimensional flows. Progress in Aerospace Sciences 39(4), 249–315 (2003)
Morzyński, M., Afanasiev, K., Thiele, F.: Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis. Comput. Meth. Appl. Mech. Enrgrg. 169, 161–176 (1999)
Meerbergen, K., Spence, A., Roose, D.: Shift-invert and Cayley transforms for detection of rightmost eigenvalues of nonsymmetric matrices. BIT Numerical Mathematics 34(3), 409–423 (1994)
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Morzyński, M., Thiele, F. (2008). 3D Global Flow Stability Analysis on Unstructured Grids. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_137
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DOI: https://doi.org/10.1007/978-3-540-68111-3_137
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