Документ взят из кэша поисковой машины. Адрес оригинального документа : http://hit-conf.imec.msu.ru/2006/Template.doc Дата изменения: Sat Jun 13 09:09:41 2015 Дата индексирования: Sat Apr 9 22:48:48 2016 Кодировка: koi8-r

Proceedings of ICHIT- 06

26 February - 5 March 2006, Moscow, Russia




здесь и ниже на русском или
английском языках


IGOR B. PALYMSKIY

Modern Academy for Humanities, Novosibirsk Branch , Novosibirsk, Russia,
630064
palymsky@hnet.ru


Abstract (РЕЗЮМЕ)
We explore the spectral characteristics of the numerical method for the
calculation of convectional We explore the spectral characteristics of the
numerical method for the calculation of convectional We explore the
spectral characteristics of the numerical method for the calculation of
convectional We explore the spectral characteristics of the numerical
method for the calculation of convectional We explore the spectral
characteristics of the numerical method for the calculation of convectional
flows. These spectral characteristics compare with


introduction (ВВЕДЕНИЕ)

At last time many workers have studied thermal Rayleigh-Benard convection
using numerical At last time many workers have studied thermal Rayleigh-
Benard convection using numerical time many At last time many workers have
studied thermal Rayleigh-Benard convection using numerical used spectral
methods with periodic boundary conditions. In At last time many workers
have studied thermal Rayleigh-Benard convection using numerical


Заголовок ПЕРВОГО УРОВНЯ

At last time many workers have studied thermal Rayleigh-Benard convection
using numerical At last time many workers have studied thermal Rayleigh-
Benard convection using numerical simulations were At last time many
workers have studied thermal Rayleigh-Benard convection using numerical At
last time many workers have studied thermal Rayleigh-Benard convection
using numerical conditions. In numerical simulations were derived secondary
stationary,
[pic]
where ? is a stream function, ? is the vortex, Q is the temperature
deviation from equilibrium profile (the total temperature being T = 1 - y
+ Q), ?f = fxx +fyy is the Laplace operator,

Ra = g?Н3dQ/?? is the Rayleigh number,

Pr = ?/? is the Prandtl number, g is the gravitational acceleration, ?, ?,
? are the coefficients of thermal expansion, kinematics viscosity and
thermal conductivity, respectively, H is the layer height and dQ is the
temperature difference on the horizontal boundaries.

Заголовок второго уровня

We briefly describe our special spectral-difference numerical algorithm and
testing [7]. Following a We briefly describe our special spectral-
difference numerical algorithm and testing [7]. Following a steps.
Fig.1 represents the spectral characteristics for

m = 1,2 and 3, Ra = 1000ћRa, Pr = 1, N = 65 and

M = 17, the time step ? is equal to 4ћ10-4. Here solid line is differential
problem, symbol ? - numerical method of present work and dash line - finite
difference numerical method [8], curves 1,2 and 3 are first, second and
third modes (m = 1,2 and 3), respectively.
[pic]
Figure 2
Instability boundary in spectral space

We can see from fig.1 and fig.2 that suggested We can see from fig.1 and
fig.2 that suggested We can We can see from fig.1 and fig.2 that suggested
more precision than finite-difference and We can see from We can see from
fig.1 and fig.2 that suggested We can see from fig.1 and fig.2 that
suggested precision than finite-difference.


CONCLUSION (ЗАКЛЮЧЕНИЕ)

The suggested numerical method exactly reproduce the spectral
characteristics of differential problem, it The suggested numerical method
exactly reproduce


REFERENCES (ЛИТЕРАТУРА)

1. Palymskiy I. B. Determinism and Chaos in the Rayleigh-Benard Convection
// Proceeding of the Second International Conference on Applied Mechanics
and Materials (ICAMM 2003), Durban, South Africa, 2003, p.139-144;
http://palymsky.narod.ru/
2. Sirovich L., Balachandar S. and Maxey M.R. Numerical Simulation of High
Rayleigh Number Convection // J. Scientific Computing, 1989, V. 4,

N. 2, p.219-236.
3. Paskonov V.M., Polezhaev V.I. and Chudov L.A. Chislennoe Modelirovanie
Protzessov Teplo- I Massoobmena, Nauka, Moscow, 1984.
4. Babenko K.I. and Rachmanov A.I. Chislennoe Issledovanie Dvumernoj
Konvektzii // Preprint 118 of Applied Mathematics Institute of RAS, Moscow,
1988, 20 p.


Igor Palymskiy is Professor of Modern University for Humanities,
Novosibirsk Branch, Mathematics Department. His main scientific interests
are Direct Numerical Simulation of Turbulent Flows and Flows with
Hydrodynamical Instabilities.