[Электронный ресурс]. - Электрон. дан. (499 Кб) : диссертации на соискание ученой степени кандидата-физико математических наук (перевод на английский язык) / А.Н. Горбань. - Электрон. дан. (499 Кб). - [Б. м. : б. и.], 1997. - Б. ц.
Аннотация: The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ? of relaxation. This system of times contains: the time before the first entering of the motion into ?-neighbourhood of the limit set, the time of final entering in this neighbourhood and the time of stay of the motion outside the ?-neighbourhood of the limit set. The singularities of relaxation times as functions of (x0; k) under fixed ? are studied. A classification of different bifurcations (explosions) of limit sets is performed. The bifurcations fall into those with appearance of new limit points and bifurcations with appearance of new limit sets at finite distance from the existing ones. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The peculiarities of transition processes under perturbations are studied. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structural stable systems.
http://icm.krasn.ru/refextra.php?id=2806
Доп.точки доступа:
Gorban A.N.
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Numerical Integration of Stiff Systems with Low Accuracy
[Текст] : статья / А.Е. Новиков и др. // Mathematical Models and Computer Simulations. - 2010. - Vol.2, №.4. - С. 443-452
Доп.точки доступа:
Novikov, E.A.; Новиков, Евгений Александрович
Доп.точки доступа:
Novikov, E.A.; Новиков, Евгений Александрович
(2,1)-method for solving stiff nonautonomous problems
[Text] : статья / E. A. Novikov // Automation and Remote Control. - 2012. - Vol. 73, Iss. 1. - p. 191-197DOI 10.1134/S0005117912010183
. -
Аннотация: An L-stable (2,1)-method with second-order accuracy is developed for solving stiff nonautonomous problems. At each step, the right-hand side of the system, as well as Jacobian matrix decomposition are evaluated only once. Efficiency of the integration method is illustrated using ring modulator calculation as an example.
Полный текст на сайте правообладателя
Доп.точки доступа:
Новиков, Евгений Александрович
Аннотация: An L-stable (2,1)-method with second-order accuracy is developed for solving stiff nonautonomous problems. At each step, the right-hand side of the system, as well as Jacobian matrix decomposition are evaluated only once. Efficiency of the integration method is illustrated using ring modulator calculation as an example.
Полный текст на сайте правообладателя
Доп.точки доступа:
Новиков, Евгений Александрович
Parallel explicit Runge-Kutta method 2nd order: accuracy and stability control
[Text] : статья / E. A. Novikov, G. V. Vashchenko // Int. J. of Applied and Fundamental Research. Physical and Mathematical Science . - 2011. - № 1. - p. 101-102
Полный текст на сайте правообладателя
Доп.точки доступа:
Vashchenko, G.V.; Новиков, Евгений Александрович
Полный текст на сайте правообладателя
Доп.точки доступа:
Vashchenko, G.V.; Новиков, Евгений Александрович
The numerical modeling of a cesium cyclein the upper atmosphere by an l-stable method of second-order accuracy
[Текст] : статья / A.E. Novikov, E.A. Novikov // Вестник СибГАУ. - 2009. - Вып. 5(26). - С. 17-20
Кл.слова (ненормированные):
accuracy control -- L-stable method -- stiff problem -- cesium cycle -- chemical kinetics
Аннотация: An algorithm of right-hand side and Jacobian formation of differential equations of chemical kinetics is described. Numerical simulation of the cesium cycle in the upper atmosphere is conducted by means of the L-stable method of the second order of accuracy with the control accuracy. The results of the computation are presented.
Полный текст на сайте журнала
Доп.точки доступа:
Novikov, E.A.; Новиков, Евгений Александрович
Кл.слова (ненормированные):
accuracy control -- L-stable method -- stiff problem -- cesium cycle -- chemical kinetics
Аннотация: An algorithm of right-hand side and Jacobian formation of differential equations of chemical kinetics is described. Numerical simulation of the cesium cycle in the upper atmosphere is conducted by means of the L-stable method of the second order of accuracy with the control accuracy. The results of the computation are presented.
Полный текст на сайте журнала
Доп.точки доступа:
Novikov, E.A.; Новиков, Евгений Александрович
Singularities of Transition Processes In Dynamical Systems
[Electronic resource]. - Electronic text data : статья / A. N. Gorban. - Electronic text data // Electronic Journal of Differential Equations. - 1997. - Translation of Candidat (Ph.D) Thesis
Аннотация: The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ε of the relaxation. The singularities of relaxation times as functions of (x0,k) under fixed ε are studied. The classification of different bifurcations (explosions) of limit sets is performed. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Горбань, Александр Николаевич
Аннотация: The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ε of the relaxation. The singularities of relaxation times as functions of (x0,k) under fixed ε are studied. The classification of different bifurcations (explosions) of limit sets is performed. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Горбань, Александр Николаевич
Analyzing the behavior of the explicit Runge-Kutta methods at the singular point in the two-body problem
/ A.V. Vyatkin // Autom. Remote Control. - 2013. - Vol. 74, Is. 2. - P325-330, DOI 10.1134/S0005117913020173. - Cited References: 9. - This work was supported by the Russian Foundation for Basic Research, project no. 08-01-00621, and by the Russian President's Program, project no. NSh-3431.2008.9.
. - 6. - ISSN 0005-1179
РУБ Automation & Control Systems + Instruments & Instrumentation
Аннотация: The behavior of the explicit Runge-Kutta methods having the second, fourth and eighth orders of accuracy is analyzed at the singular point in the two-body problem. Numerical solutions are compared with their analytical counterpart. As the adequacy criterion for an approximate solution, the conservation law of the total mechanical energy is considered.
Доп.точки доступа:
Vyatkin, A.V.; Вяткин, Александр Владимирович
Аннотация: The behavior of the explicit Runge-Kutta methods having the second, fourth and eighth orders of accuracy is analyzed at the singular point in the two-body problem. Numerical solutions are compared with their analytical counterpart. As the adequacy criterion for an approximate solution, the conservation law of the total mechanical energy is considered.
Доп.точки доступа:
Vyatkin, A.V.; Вяткин, Александр Владимирович
Four-stage computational technology with adaptive numerical methods for computational aerodynamics
/ V.Shaydurov, T.Liu, Z.Zheng // AIP Conference Proceedings. - 2012. - Vol. 1487: 4th International Conference on Application of Mathematics in Technical and Natural Sciences: Memorial Volume devoted to Prof. Christo I. Christov, AMiTaNS 2012 (11 June 2012 through 16 June 2012, St. Constantine and Helena) . - pp. 42-48, DOI 10.1063/1.4758940
. -
Кл.слова (ненормированные):
four-stage computational technology -- heat-conducting gas -- high-order solvers -- Time-dependent Navier-Stokes equations
Аннотация: Computational aerodynamics is a key technology in aircraft design which is ahead of physical experiment and complements it. Of course all three components of computational modeling are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and high-performance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of computer architecture. Numerical algorithms are developed more conservative. More precisely, they are offered and theoretically justified for more simple mathematical problems. Nevertheless, computational mathematics now has amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and high-performance computers. A significant step in this direction was the European Project ADIGMA whose positive experience will be used in International Project TRISTAM for further movement in the field of computational technologies for aerodynamics. This paper gives a general overview of objectives and approaches intended to use and a description of the recommended four-stage computer technology. В© 2012 American Institute of Physics.
Scopus,
РИНЦ
Доп.точки доступа:
Liu, T.; Zheng, Z.; Шайдуров, Владимир Викторович
Кл.слова (ненормированные):
four-stage computational technology -- heat-conducting gas -- high-order solvers -- Time-dependent Navier-Stokes equations
Аннотация: Computational aerodynamics is a key technology in aircraft design which is ahead of physical experiment and complements it. Of course all three components of computational modeling are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and high-performance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of computer architecture. Numerical algorithms are developed more conservative. More precisely, they are offered and theoretically justified for more simple mathematical problems. Nevertheless, computational mathematics now has amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and high-performance computers. A significant step in this direction was the European Project ADIGMA whose positive experience will be used in International Project TRISTAM for further movement in the field of computational technologies for aerodynamics. This paper gives a general overview of objectives and approaches intended to use and a description of the recommended four-stage computer technology. В© 2012 American Institute of Physics.
Scopus,
РИНЦ
Доп.точки доступа:
Liu, T.; Zheng, Z.; Шайдуров, Владимир Викторович
Fitted scheme of the finite element method for a convection-diffusion equation
[Text] / E.D. Karepova, V.V. Shaidurov // Russ. J. Numer. Anal. Math. Model. - 2000. - Vol. 15, Is. 2. - pp. 167-182, DOI 10.1515/rnam.2000.15.2.167. - Cited References: 8
. - ISSN 0927-6467
РУБ Engineering, Multidisciplinary + Mathematics, Applied
Аннотация: We consider the Galerkin piecewise linear finite element method for an ordinary convection-diffusion boundary value problem with a small parameter in front of the highest derivative. For the generation of a discrete linear algebraic system we use the special quadrature formulae that take into account the boundary layer character of the solution. It is proved that the resulting discrete problem is of epsilon(2) + h(2)-order of accuracy in the uniform discrete norm for small h and epsilon. The numerical example shows the advantage of the considered discrete scheme over two commonly used difference schemes.
Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaidurov, V.V.; Шайдуров, Владимир Викторович
Аннотация: We consider the Galerkin piecewise linear finite element method for an ordinary convection-diffusion boundary value problem with a small parameter in front of the highest derivative. For the generation of a discrete linear algebraic system we use the special quadrature formulae that take into account the boundary layer character of the solution. It is proved that the resulting discrete problem is of epsilon(2) + h(2)-order of accuracy in the uniform discrete norm for small h and epsilon. The numerical example shows the advantage of the considered discrete scheme over two commonly used difference schemes.
Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaidurov, V.V.; Шайдуров, Владимир Викторович
Метод второго порядка для решения аддитивных жестких задач
[Текст] / Е.А. Новиков // Компьютерное моделирование 2013 : труды международной научно-технической конференции. - Санкт-Петербург, 2013. - С. 39-44
Кл.слова (ненормированные):
stiff additive problem -- one-step scheme -- (m,k)-method -- error estimation
Аннотация: Is constructed the method of second order of accuracy for solution of additive stiff systems of ordinary differential equations. The inequalities for control of accuracy are obtained. The results of calculation are presented.
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Novikov E.A.
Кл.слова (ненормированные):
stiff additive problem -- one-step scheme -- (m,k)-method -- error estimation
Аннотация: Is constructed the method of second order of accuracy for solution of additive stiff systems of ordinary differential equations. The inequalities for control of accuracy are obtained. The results of calculation are presented.
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Novikov E.A.
Multispeed models in off-lattice Boltzmann simulations
[Text] : статья / A. Bardow, I. V. Karlin, A. A. Gusev // Physical review E. - 2008. - Vol. 77. - Ст. 025701, DOI 10.1103/PhysRevE.77.025701
. - ISSN 1539-3755
Аннотация: The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods. The approach is based on the general characteristic-based algorithm for off-lattice Boltzmann simulations that preserves all appealing properties of the standard lattice Boltzmann method while extending the method to unstructured grids. We show that the use of multispeed models indeed gives rise to major improvements in accuracy. The suggested approach thus renders truly large-scale off-lattice Boltzmann computations practical.
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Gusev, A.A.
Аннотация: The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods. The approach is based on the general characteristic-based algorithm for off-lattice Boltzmann simulations that preserves all appealing properties of the standard lattice Boltzmann method while extending the method to unstructured grids. We show that the use of multispeed models indeed gives rise to major improvements in accuracy. The suggested approach thus renders truly large-scale off-lattice Boltzmann computations practical.
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Gusev, A.A.
Convergence of a full multigrid algorithm for quadratic finite elements in a domain with a curvilinear boundary
[Text] / L. V. Gileva, V. V. Shaidurov // Russ. J. Numer. Anal. Math. Model. - 2009. - Vol. 24, Is. 5. - P425-438, DOI 10.1515/RJNAMM.2009.027. - Cited References: 11. - This analysis was partially supported by Grant 08-01-00621 of the Russian Foundation of Basic Research.
. - ISSN 0927-6467
РУБ Engineering, Multidisciplinary + Mathematics, Applied
Аннотация: In this paper, a full multigrid algorithm with a symmetric V-cycle for a grid problem obtained by discretization of a second-order elliptic equation with quadratic finite elements on triangles is studied. The multigrid complexity of the algorithm is proved. This means that the number of arithmetic operations required to achieve the order of accuracy of an approximate solution equal to that of the discretization error linearly depends on the number of unknowns. The rate of convergence is found to be higher than that for linear finite elements in spite of the higher order of accuracy.
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Гилева, Лидия Викторовна; Russian Foundation [08-01-00621]
Аннотация: In this paper, a full multigrid algorithm with a symmetric V-cycle for a grid problem obtained by discretization of a second-order elliptic equation with quadratic finite elements on triangles is studied. The multigrid complexity of the algorithm is proved. This means that the number of arithmetic operations required to achieve the order of accuracy of an approximate solution equal to that of the discretization error linearly depends on the number of unknowns. The rate of convergence is found to be higher than that for linear finite elements in spite of the higher order of accuracy.
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Гилева, Лидия Викторовна; Russian Foundation [08-01-00621]
Efficient simulations of detailed combustion fields via the lattice Boltzmann method
[Text] : статья / E. Chiavazzo [et al.] // International Journal of Numerical Methods for Heat & Fluid Flow. - 2011. - Vol. 21, Iss. 5. - p. 494-517, DOI 10.1108/09615531111135792
. - ISSN 0961-5539
Аннотация: Purpose – The paper aims to be a first step toward the efficient, yet accurate, solution of detailed combustion fields using the lattice Boltzmann (LB) method, where applications are still limited due to both the stiffness of the governing equations and the large amount of fields to solve. Design/methodology/approach – The suggested methodology for model reduction is developed in the setting of slow invariant manifold construction, including details of the while. The simplest LB equation is used in order to work out the procedure of coupling of the reduced model with the flow solver. Findings – The proposed method is validated with the 2D simulation of a premixed laminar flame in the hydrogen-air mixture, where a remarkable computational speedup and memory saving are demonstrated. Research limitations/implications – Because of the chosen detailed LB model, the flow field may be described with unsatisfactory accuracy: this motivates further investigation in this direction in the near future. Practical implications – A new framework of simulation of reactive flows is available, based on a coupling between accurate reduced reaction mechanism and the LB representation of the flow phenomena. Hence, the paper includes implications on how to perform accurate reactive flow simulations at a fraction of the cost required in the detailed model. Originality/value – This paper meets an increasing need to have efficient and accurate numerical tools for modelling complex phenomena, such as pollutant formation during combustion.
Доп.точки доступа:
Chiavazzo, Eliodoro; Karlin, I.V.; Карлин, Илья Вениаминович; Gorban, A.N.; Горбань, Александр Николаевич; Boulouchos, Konstantinos
Аннотация: Purpose – The paper aims to be a first step toward the efficient, yet accurate, solution of detailed combustion fields using the lattice Boltzmann (LB) method, where applications are still limited due to both the stiffness of the governing equations and the large amount of fields to solve. Design/methodology/approach – The suggested methodology for model reduction is developed in the setting of slow invariant manifold construction, including details of the while. The simplest LB equation is used in order to work out the procedure of coupling of the reduced model with the flow solver. Findings – The proposed method is validated with the 2D simulation of a premixed laminar flame in the hydrogen-air mixture, where a remarkable computational speedup and memory saving are demonstrated. Research limitations/implications – Because of the chosen detailed LB model, the flow field may be described with unsatisfactory accuracy: this motivates further investigation in this direction in the near future. Practical implications – A new framework of simulation of reactive flows is available, based on a coupling between accurate reduced reaction mechanism and the LB representation of the flow phenomena. Hence, the paper includes implications on how to perform accurate reactive flow simulations at a fraction of the cost required in the detailed model. Originality/value – This paper meets an increasing need to have efficient and accurate numerical tools for modelling complex phenomena, such as pollutant formation during combustion.
Доп.точки доступа:
Chiavazzo, Eliodoro; Karlin, I.V.; Карлин, Илья Вениаминович; Gorban, A.N.; Горбань, Александр Николаевич; Boulouchos, Konstantinos
A 2.5-D electron Hall-MHD analytical model of steady state Hall magnetic reconnection in a compressible plasma
[Text] / D. B. Korovinskiy [et al.] // J. Geophys. Res-Space Phys. - 2011. - Vol. 116. - Ст. A05219, DOI 10.1029/2010JA015942. - Cited References: 45. - This work is supported by the Austrian Science Fund under projects I193-N16 and P21051-N16, by RFBR grant 09-05-91000-ANF-a, and by SPSU grant 11.38.47.2011. V. S. Semenov also thanks ISSI for hospitality and financial support.
. - ISSN 2169-9380
РУБ Astronomy & Astrophysics
Аннотация: A 2.5-D analytical electron Hall magnetohydrodynamic model of steady state magnetic reconnection in a collisionless compressible plasma with a constant electron temperature is developed. It is shown that as in the incompressible case, the solution of the Grad-Shafranov equation for the magnetic potential is a basis for the problem analysis. The formation of the double electric layers and layers of low-density plasma, mapping the magnetic separatrices, are investigated. It is found that the formation of depletion layers should not be governed by the out-of-plane magnetic field, but rather, the origin of these layers lies inside the electron diffusion region. The double electric layers are found to be thin separatrices-elongated sheets, whose cross sections are of the order of the electron diffusion region half width. These charged layers provide the presence of the strong electric field orthogonal to the in-plane projection of the magnetic field, which forces electrons to accelerate into the out-of-plane direction. Outside of the double electric layers, the condition of quasi-neutrality of the plasma is found to be fulfilled to high accuracy.
Доп.точки доступа:
Korovinskiy, D.B.; Semenov, V.S.; Erkaev, N.V.; Еркаев, Николай Васильевич; Divin, A.V.; Biernat, H.K.; Mostl, U.V.
Рубрики:
COLLISIONLESS RECONNECTION
CURRENT SHEET
CURRENT SYSTEM
FIELD
MAGNETOTAIL
REGION
ACCELERATION
DISSIPATION
CHALLENGE
CLUSTER
COLLISIONLESS RECONNECTION
CURRENT SHEET
CURRENT SYSTEM
FIELD
MAGNETOTAIL
REGION
ACCELERATION
DISSIPATION
CHALLENGE
CLUSTER
Аннотация: A 2.5-D analytical electron Hall magnetohydrodynamic model of steady state magnetic reconnection in a collisionless compressible plasma with a constant electron temperature is developed. It is shown that as in the incompressible case, the solution of the Grad-Shafranov equation for the magnetic potential is a basis for the problem analysis. The formation of the double electric layers and layers of low-density plasma, mapping the magnetic separatrices, are investigated. It is found that the formation of depletion layers should not be governed by the out-of-plane magnetic field, but rather, the origin of these layers lies inside the electron diffusion region. The double electric layers are found to be thin separatrices-elongated sheets, whose cross sections are of the order of the electron diffusion region half width. These charged layers provide the presence of the strong electric field orthogonal to the in-plane projection of the magnetic field, which forces electrons to accelerate into the out-of-plane direction. Outside of the double electric layers, the condition of quasi-neutrality of the plasma is found to be fulfilled to high accuracy.
Доп.точки доступа:
Korovinskiy, D.B.; Semenov, V.S.; Erkaev, N.V.; Еркаев, Николай Васильевич; Divin, A.V.; Biernat, H.K.; Mostl, U.V.
Some adaptive numerical technology for computational aerodynamics
/ V. Shaydurov, T. Liu // Procedia Eng. - 2013. - Vol. 61: 25th International Conference on Parallel Computational Fluid Dynamics, ParCFD 2013 (20 May 2013 through 24 May 2013, Changsha) Conference code: 101818. - P16-22, DOI 10.1016/j.proeng.2013.07.086
. -
Кл.слова (ненормированные):
Four-stage computational technology -- Heat-conducting gas -- High-order solvers -- Time-dependent Navier-Stokes equations
Аннотация: All three components of computational aerodynamics are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and high-performance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of the computer architecture. Numerical algorithms developed more conservative. Nevertheless, computational mathematics now amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and high-performance computers. This paper gives a general overview of objectives and approaches of international Project TRISTAM and a description of the four-stage computer technology in the field of computational aerodynamics. © 2013 The Authors.
Scopus
Держатели документа:
Beihang University, 37# Xueyuan Road, Haidian District, Beijing, 100191, China
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Liu, T.; Шайдуров, Владимир Викторович
Кл.слова (ненормированные):
Four-stage computational technology -- Heat-conducting gas -- High-order solvers -- Time-dependent Navier-Stokes equations
Аннотация: All three components of computational aerodynamics are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and high-performance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of the computer architecture. Numerical algorithms developed more conservative. Nevertheless, computational mathematics now amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and high-performance computers. This paper gives a general overview of objectives and approaches of international Project TRISTAM and a description of the four-stage computer technology in the field of computational aerodynamics. © 2013 The Authors.
Scopus
Держатели документа:
Beihang University, 37# Xueyuan Road, Haidian District, Beijing, 100191, China
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Liu, T.; Шайдуров, Владимир Викторович
Solving the linear interval tolerance problem
/ S. P. Shary // Mathematics and Computers in Simulation. - 1995. - Vol. 39, Is. 1-2. - P53-85
. - ISSN 0378-4754
Аннотация: For the interval linear system Ax = b, the linear tolerance problem is considered that requires inner evaluation of the tolerable solution set ???(A, b) = {x ? Rn {divides} (?A ? A)(Ax ? b)} formed by all point vectors x such that the product Ax remains within b for all possible A ? A. Along with the simple incompatibility criterion, we develop comprehensive solvability theory for the linear tolerance problem that not only settles whether ??? is empty or not, but also enables modification of the problem to ensure its desired properties. To conclude, we advance several numerical methods of various accuracy and complexity for construction of an interval solution to the linear tolerance problem around a given center. В© 1995.
Scopus
Держатели документа:
Computer Center, Siberian Department, Russian Academy of Sciences, Akademgorodok, 660036 Krasnoyarsk, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shary, S.P.; Шарый С.П.
Аннотация: For the interval linear system Ax = b, the linear tolerance problem is considered that requires inner evaluation of the tolerable solution set ???(A, b) = {x ? Rn {divides} (?A ? A)(Ax ? b)} formed by all point vectors x such that the product Ax remains within b for all possible A ? A. Along with the simple incompatibility criterion, we develop comprehensive solvability theory for the linear tolerance problem that not only settles whether ??? is empty or not, but also enables modification of the problem to ensure its desired properties. To conclude, we advance several numerical methods of various accuracy and complexity for construction of an interval solution to the linear tolerance problem around a given center. В© 1995.
Scopus
Держатели документа:
Computer Center, Siberian Department, Russian Academy of Sciences, Akademgorodok, 660036 Krasnoyarsk, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shary, S.P.; Шарый С.П.
Construction of algorithms for analytical continuation
/ A. M. Fedotov // Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika. - 1995. - Is. 1. - P64-79
. - ISSN 0137-0782
Кл.слова (ненормированные):
Algorithms -- Error analysis -- Mathematical models -- Mathematical operators -- Matrix algebra -- Optimization -- Set theory -- Theorem proving -- Topology -- Uniqueness theorem -- Interpolation
Аннотация: The paper is devoted to the problem of analytical continuation of functions from sets, being within regularity sets, at the presence of errors in predetermination of initial data. The problem of constructing the optimal algorithms of continuation is considered. Estimations for the accuracy and stability of the optimal continuation algorithms are obtained. A new form is proposed of the uniqueness theorem of analytical functions - the theorem of asymptotic uniqueness and self-regularizating algorithms. Causes of computational instability of the analytical continuation problems are elucidated and a method for organization of a computational process with control of computational errors is proposed.
Scopus
Держатели документа:
Vychislitel'nyj Tsentr SO RAN, Krasnoyarsk, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Fedotov, A.M.; Федотов, Анатолий Михайлович
Кл.слова (ненормированные):
Algorithms -- Error analysis -- Mathematical models -- Mathematical operators -- Matrix algebra -- Optimization -- Set theory -- Theorem proving -- Topology -- Uniqueness theorem -- Interpolation
Аннотация: The paper is devoted to the problem of analytical continuation of functions from sets, being within regularity sets, at the presence of errors in predetermination of initial data. The problem of constructing the optimal algorithms of continuation is considered. Estimations for the accuracy and stability of the optimal continuation algorithms are obtained. A new form is proposed of the uniqueness theorem of analytical functions - the theorem of asymptotic uniqueness and self-regularizating algorithms. Causes of computational instability of the analytical continuation problems are elucidated and a method for organization of a computational process with control of computational errors is proposed.
Scopus
Держатели документа:
Vychislitel'nyj Tsentr SO RAN, Krasnoyarsk, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Fedotov, A.M.; Федотов, Анатолий Михайлович
Experimental and numerical analysis of mass transfer in a binary mixture with Soret effect in the presence of weak convection
[Text] / Y. . Gaponenko, A. . Mialdun, V. . Shevtsova // Eur. Phys. J. E. - 2014. - Vol. 37, Is. 10. - Ст. 90, DOI 10.1140/epje/i2014-14090-5. - Cited References: 18. - This work is supported by the PRODEX programme of the Belgian Federal Science Policy Office and ESA.
. - ISSN 1292-8941. - ISSN 1292-895X
РУБ Chemistry, Physical + Materials Science, Multidisciplinary + Physics, Applied + Polymer Science
Аннотация: One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.
WOS
Держатели документа:
[Gaponenko, Y.
Mialdun, A.
Shevtsova, V.] Univ Libre Bruxelles, MRC, EP CP 165 62, B-1050 Brussels, Belgium
[Gaponenko, Y.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН
Доп.точки доступа:
Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Shevtsova, V.; PRODEX programme of the Belgian Federal Science Policy Office; ESA
Аннотация: One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.
WOS
Держатели документа:
[Gaponenko, Y.
Mialdun, A.
Shevtsova, V.] Univ Libre Bruxelles, MRC, EP CP 165 62, B-1050 Brussels, Belgium
[Gaponenko, Y.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН
Доп.точки доступа:
Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Shevtsova, V.; PRODEX programme of the Belgian Federal Science Policy Office; ESA
Estimate of the vertical plankton biomass profile on the basis of measurements of fluorescent characteristics in pelagial of Lake Baikal
/ M. V. Panchenko [et al.] // Proceedings of SPIE - The International Society for Optical Engineering. - 2014. - Vol. 9292: 20th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics (23 June 2014 through 27 June 2014, ) Conference code: 110711. - Ст. 92922Y, DOI 10.1117/12.2075391
. -
Кл.слова (ненормированные):
biomass -- fluorescent analysis -- Lake Baikal. -- pelagial -- plankton -- vertical profile -- Air -- Atmospheric chemistry -- Biomass -- Calibration -- Carbon dioxide -- Fluorescence -- Geophysics -- Plankton -- Fluorescent analysis -- Fluorescent characteristic -- Lake Baikal -- pelagial -- Quantitative assessments -- Quantitative characteristics -- Spatial and temporal variability -- Vertical profile -- Lakes
Аннотация: We study the effect of physical, chemical and biological processes on gas exchange of CO2 in the air-water system in Lake Baikal. Photosynthesis of aquatic biota is known to play a crucial role in changing the concentration of carbon dioxide in the water. Fluorescent methods are considered to be of high performance in problems of determining quantitative characteristics of biomass, however they require preliminary calibration directly for a specific type of plankton. In the pelagic zone of Lake Baikal the species composition, quantitative and spatial distribution of phytoplankton are characterized by strong spatial and temporal variability. Therefore, the fluorescent devices calibration on a single reference does not provide acceptable accuracy of quantitative assessment of the biomass. The results discussed in the paper were obtained by shipboard measurements during the Baikal campaign of 2010-2011. Correlation between the biomass in 25-meter water layer and the integral value of the fluorescent signal in this layer was obtained for calibration. The report discusses the advantages and disadvantages of the chosen methods and the results of retrieval of the vertical profiles of the biomass for stations in the pelagic zone of Lake Baikal in spring for the 2010-2011 biennium.
Scopus
Держатели документа:
Institute of Atmospheric Optics, Siberian Branch, Russian Academy of SciencesTomsk, Russian Federation
Limnological Institute, Siberian Branch, Russian Academy of SciencesIrkutsk, Russian Federation
Institute of Computational Modeling, Siberian Branch, Russian Academy of SciencesKrasnoyarsk, Russian Federation
Доп.точки доступа:
Panchenko, M.V.; Sakirko, M.V.; Usoltseva, M.V.; Popovskaya, G.I.; Domysheva, V.M.; Shimaraev, M.N.; Zavoruev, V.V.; Pestunov, D.A.
Кл.слова (ненормированные):
biomass -- fluorescent analysis -- Lake Baikal. -- pelagial -- plankton -- vertical profile -- Air -- Atmospheric chemistry -- Biomass -- Calibration -- Carbon dioxide -- Fluorescence -- Geophysics -- Plankton -- Fluorescent analysis -- Fluorescent characteristic -- Lake Baikal -- pelagial -- Quantitative assessments -- Quantitative characteristics -- Spatial and temporal variability -- Vertical profile -- Lakes
Аннотация: We study the effect of physical, chemical and biological processes on gas exchange of CO2 in the air-water system in Lake Baikal. Photosynthesis of aquatic biota is known to play a crucial role in changing the concentration of carbon dioxide in the water. Fluorescent methods are considered to be of high performance in problems of determining quantitative characteristics of biomass, however they require preliminary calibration directly for a specific type of plankton. In the pelagic zone of Lake Baikal the species composition, quantitative and spatial distribution of phytoplankton are characterized by strong spatial and temporal variability. Therefore, the fluorescent devices calibration on a single reference does not provide acceptable accuracy of quantitative assessment of the biomass. The results discussed in the paper were obtained by shipboard measurements during the Baikal campaign of 2010-2011. Correlation between the biomass in 25-meter water layer and the integral value of the fluorescent signal in this layer was obtained for calibration. The report discusses the advantages and disadvantages of the chosen methods and the results of retrieval of the vertical profiles of the biomass for stations in the pelagic zone of Lake Baikal in spring for the 2010-2011 biennium.
Scopus
Держатели документа:
Institute of Atmospheric Optics, Siberian Branch, Russian Academy of SciencesTomsk, Russian Federation
Limnological Institute, Siberian Branch, Russian Academy of SciencesIrkutsk, Russian Federation
Institute of Computational Modeling, Siberian Branch, Russian Academy of SciencesKrasnoyarsk, Russian Federation
Доп.точки доступа:
Panchenko, M.V.; Sakirko, M.V.; Usoltseva, M.V.; Popovskaya, G.I.; Domysheva, V.M.; Shimaraev, M.N.; Zavoruev, V.V.; Pestunov, D.A.
A second-order method for additive stiff problems
[Текст] : статья / E.A. Novikov // Научно-технические ведомости СПбГПУ. Физико-математические науки. - 2013. - Т. 2, № 182. - С. 164-170
Аннотация: A second-order accuracy method for additive stiff systems of ordinary differential equations is developed. Inequalities for accuracy control are obtained. Numerical results are presented.
Полный текст на сайте журнала
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Новиков, Евгений Александрович
Аннотация: A second-order accuracy method for additive stiff systems of ordinary differential equations is developed. Inequalities for accuracy control are obtained. Numerical results are presented.
Полный текст на сайте журнала
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Новиков, Евгений Александрович