Fast computation of optimal disturbances for duct flows with a given accuracy |
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Authors: | A V Boiko Yu M Nechepurenko M Sadkane |
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Institution: | 1.Khristianovich Institute of Theoretical and Applied Mechanics,Siberian Branch of Russian Academy of Sciences,Novosibirsk,Russia;2.Institute of Numerical Mathematics,Russian Academy of Sciences,Moscow,Russia;3.Départment de Mathématiques,Université de Bretagne Occidentale.,Brest Cedex 3,France |
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Abstract: | This work is devoted to the numerical analysis of small flow disturbances, i.e. velocity and pressure deviations from the
steady state, in ducts of constant cross sections. The main emphasis is put on the disturbances causing the most kinetic energy
density growth, the so-called optimal disturbances, whose knowledge is important in laminar-turbulent transition and robust
flow control investigations. Numerically, this amounts to computing the maximum amplification of the 2-norm of a matrix exponential
exp{tS} for a square matrix S at t ≥ 0. To speed up the computations, we propose a new algorithm based on low-rank approximations of the matrix exponential
and prove that it computes the desired amplification with a given accuracy. We discuss its implementation and demonstrate
its efficiency by means of numerical experiments with a duct of square cross section. |
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