|
Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 11, Pages 2017–2027
(Mi zvmmf4969)
|
|
|
|
This article is cited in 9 scientific papers (total in 9 papers)
Fast computation of optimal disturbances for duct flows with a given accuracy
A. V. Boikoa, Yu. M. Nechepurenkob, M. Sadkanec a Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian Academy of Sciences,
Institutskaya 4/1, Novosibirsk, 630090 Russia
b Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, Moscow, 119333 Russia
c Université de Bretagne Occidentale. Départment de Mathématiques, 6, Av. Le Gorgeu. CS 93837. 29238 Brest Cedex 3. France
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 $t\geq0$. 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.
Key words:
linearized viscous incompressible flow equations, optimal disturbances, matrix exponential, low-rank approximation, Lyapunov equations.
Received: 29.01.2010
Citation:
A. V. Boiko, Yu. M. Nechepurenko, M. Sadkane, “Fast computation of optimal disturbances for duct flows with a given accuracy”, Zh. Vychisl. Mat. Mat. Fiz., 50:11 (2010), 2017–2027; Comput. Math. Math. Phys., 50:11 (2010), 1914–1924
Linking options:
https://www.mathnet.ru/eng/zvmmf4969 https://www.mathnet.ru/eng/zvmmf/v50/i11/p2017
|
Statistics & downloads: |
Abstract page: | 238 | Full-text PDF : | 79 | References: | 41 | First page: | 2 |
|