[Text] : alternative Grad equations / A.N. Gorban, I.V. Karlin // Physical Review E. - 1996. - Vol. 54, № 4. - p. R3109-R3112
Перевод заглавия: Скорости рассеяния вместо моментов. Альтернативные уравнения Грэда
Аннотация: Scattering rates moments of collision integral! are treated as independent variables, and as an alternative to moments of the distribution function, to describe the rarefied gas near local equilibrium. A version of the entropy maximum principle is used to derive the Grad-like description in terms of a finite number of scattering rates. The equations are compared to the Grad moment system in the heat nonconductive case. Estimations for hard spheres demonstrate, in particular, some 10% excess of the viscosity coefficient resulting from the scattering rate description, as compared to the Grad moment estimation.
http://icm.krasn.ru/refextra.php?id=69,
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Горбань, Александр Николаевич
Труды сотрудников ИВМ СО РАН
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Найдено документов в текущей БД: 15
Numerical approximation of equations for heat-conducting compressible viscous medium
[Text] / E.D. Karepova, V.V. Shaidurov // RECENT ADVANCES IN FLUID MECHANICS. Ser. WSEAS Mechanical Engineering Series : WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC, 2009. - 6th WSEAS International Conference on Fluid Mechanics (JAN 10-12, 2009, Ningbo, PEOPLES R CHINA). - pp. 121-125. - Cited References: 0
. - ISBN 978-960-474-040-6
РУБ Engineering, Mechanical + Mathematics, Applied
Кл.слова (ненормированные):
Navier-Stokes equations -- compressible viscous medium -- finite element method -- Crank-Nicholson difference scheme
Аннотация: In this paper the Navier-Stokes equations are solved for heat-conductive medium. At first the system of equations are equivalently transformed and then discretized by bilinear finite elements in space and by Crank-Nicholson scheme in time. It produces stable scheme with low artificial viscosity.
Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaidurov, V.V.; Шайдуров, Владимир Викторович
Кл.слова (ненормированные):
Navier-Stokes equations -- compressible viscous medium -- finite element method -- Crank-Nicholson difference scheme
Аннотация: In this paper the Navier-Stokes equations are solved for heat-conductive medium. At first the system of equations are equivalently transformed and then discretized by bilinear finite elements in space and by Crank-Nicholson scheme in time. It produces stable scheme with low artificial viscosity.
Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaidurov, V.V.; Шайдуров, Владимир Викторович
The Numerical Spherically Symmetric Modeling of Deep-Seated Geodynamics
[Text] / A. V. Vyatkin, V. V. Shaidurov, G. I. Shchepanovskaya // NUMERICAL ANALYSIS AND ITS APPLICATIONS. Ser. Lecture Notes in Computer Science : SPRINGER-VERLAG BERLIN, 2009. - Vol. 5434: 4th International Conference on Numerical Analysis and Applications (JUN 16-20, 2008, Lozenetz, BULGARIA). - P128-138. - Cited References: 9
. - ISBN 978-3-642-00463-6
РУБ Computer Science, Theory & Methods + Mathematics, Applied + Statistics & Probability
Аннотация: In this paper a computer model is proposed which allows one to consider geodynamics processes of the Earth's expansion, contraction, heating and cooling. Geosphere dynamics is studied in the framework of a viscous heat-conducting compressible medium where medium density and viscosity vary with time and space. This model includes the Earth's crust, mantle, and the core as well.
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Вяткин, Александр Владимирович
Аннотация: In this paper a computer model is proposed which allows one to consider geodynamics processes of the Earth's expansion, contraction, heating and cooling. Geosphere dynamics is studied in the framework of a viscous heat-conducting compressible medium where medium density and viscosity vary with time and space. This model includes the Earth's crust, mantle, and the core as well.
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Вяткин, Александр Владимирович
Shear driven two-phase flows in vertical cylindrical duct
[Text] : статья / Y. Gaponenko, A. Mialdun, V. Shevtsova // International Journal of Multiphase Flow. - 2012. - Vol. 39. - p. 205-215, DOI 10.1007/s12217-008-9075-7
. - ISSN 0938-0108
Кл.слова (ненормированные):
Gas–liquid flow -- Entrainment -- Interface deformation -- Liquid bridge -- Free surface deformation -- Viscosity contrast
Аннотация: Experiments and numerical simulations were carried out for shear-driven two-phase flows in a confined volume of liquid under conditions of normal gravity. The geometry corresponds to a cylindrical liquid bridge surrounded by a concentric annular gas channel with external solid walls. The internal part consists of solid supports at the bottom and top, while the central part is a liquid zone filled with a viscous liquid and kept in its position by surface tension. Gas enters into the annular duct, flows between solid walls and upon reaching the liquid zone entrains initially quiescent liquid. The flow dynamics is governed by the Navier–Stokes equations in both fluids, which are numerically solved in the exact experimental geometry taking into account interface deformation by gravity. In the experiments 5 cSt silicone oil and air were used as test fluids and the flow was monitored by means of particle tracking velocimetry. The experiments were performed for unit aspect ratio (the ratio of liquid zone length to its radius), while the simulations of shear-driven flow were carried out for a wide range of parameters. A particular attention is focused on the effect of free surface shape and fluids viscosity contrast on the interfacial flow dynamics. The current study suggests a linear dependence between velocities of gas and liquid when the viscosity of the liquid is larger by two orders of magnitude than that of gas. Another relation is proposed when the fluids viscosity ratio, μl/μg, is less than 50.
Полный текст на сайте правообладателя
Доп.точки доступа:
Mialdun, A.; Shevtsova, V.; Гапоненко, Юрий Анатольевич
Кл.слова (ненормированные):
Gas–liquid flow -- Entrainment -- Interface deformation -- Liquid bridge -- Free surface deformation -- Viscosity contrast
Аннотация: Experiments and numerical simulations were carried out for shear-driven two-phase flows in a confined volume of liquid under conditions of normal gravity. The geometry corresponds to a cylindrical liquid bridge surrounded by a concentric annular gas channel with external solid walls. The internal part consists of solid supports at the bottom and top, while the central part is a liquid zone filled with a viscous liquid and kept in its position by surface tension. Gas enters into the annular duct, flows between solid walls and upon reaching the liquid zone entrains initially quiescent liquid. The flow dynamics is governed by the Navier–Stokes equations in both fluids, which are numerically solved in the exact experimental geometry taking into account interface deformation by gravity. In the experiments 5 cSt silicone oil and air were used as test fluids and the flow was monitored by means of particle tracking velocimetry. The experiments were performed for unit aspect ratio (the ratio of liquid zone length to its radius), while the simulations of shear-driven flow were carried out for a wide range of parameters. A particular attention is focused on the effect of free surface shape and fluids viscosity contrast on the interfacial flow dynamics. The current study suggests a linear dependence between velocities of gas and liquid when the viscosity of the liquid is larger by two orders of magnitude than that of gas. Another relation is proposed when the fluids viscosity ratio, μl/μg, is less than 50.
Полный текст на сайте правообладателя
Доп.точки доступа:
Mialdun, A.; Shevtsova, V.; Гапоненко, Юрий Анатольевич
The effect of nanoparticle diffusion and thermophoresis on convective heat transfer of nanofluid in a circular tube
[Text] / I. I. Ryzhkov, A. V. Minakov // Int. J. Heat Mass Transf. - 2014. - Vol. 77. - P956-969, DOI 10.1016/j.ijheatmasstransfer.2014.05.045. - Cited References: 44. - This work is supported the Krasnoyarsk Regional Foundation of Scientific and Technical Activity (Grant No. 02/13) and the Russian President Grant No. MK-6296.2013.8.
. - ISSN 0017-9310. - ISSN 1879-2189
РУБ Thermodynamics + Engineering, Mechanical + Mechanics
Аннотация: Laminar convective heat transfer of water-alumina nanofluid in a circular tube with uniform heat flux is investigated numerically on the basis of two-component model, which takes into account nanoparticle transport by diffusion and thermophoresis. A new expression for thermophoretic mobility is suggested on the basis of existing experimental results and theoretical concepts. It is shown that thermophoresis leads to a significant reduction of nanoparticle volume fraction in the boundary layer near the wall. The corresponding viscosity reduction causes the velocity increase near the wall and flattening of velocity profile near the tube axis to keep the mass flow rate constant. The decrease of wall shear stress leads to the decrease of the required pressure drop. The calculations for two-component model provide higher values of the local and average heat transfer coefficients in comparison with the one-component model. The difference does not exceed 10% and decreases with increasing the thermal Peclet number. The calculations for one-component model show the independence of local and average Nusselt numbers on the nanoparticle volume fraction. The results for two-component model predict the increase of Nusselt number when the thermophoretic effect becomes stronger. The effectiveness of water-alumina nanofluid is analyzed by plotting the average heat transfer coefficient against the required pumping power. It is shown that the nanofluid shows better performance than the base fluid in the range of low pumping power and, correspondingly, low inlet velocity. (C) 2014 Elsevier Ltd. All rights reserved.
WOS
Держатели документа:
[Ryzhkov, Ilya I.] SB RAS, Inst Computat Modelling, Krasnoyarsk 660036, Russia
[Minakov, Andrey V.] Siberian Fed Univ, Inst Engn Phys & Radio Elect, Krasnoyarsk 660041, Russia
ИВМ СО РАН
Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Minakov, A.V.; Минаков, Андрей Викторович; Krasnoyarsk Regional Foundation of Scientific and Technical Activity [02/13]; Russian President Grant [MK-6296.2013.8]
Рубрики:
EXTENDED GRAETZ PROBLEM
PARTICLE MIGRATION
TRANSPORT
FLOW
SUSPENSIONS
DEPENDENCE
MECHANISM
WATER
FLUX
Кл.слова (ненормированные):
Nanofluid -- Forced convection -- Heat transfer -- Circular tube -- Thermophoresis -- Numerical simulation
EXTENDED GRAETZ PROBLEM
PARTICLE MIGRATION
TRANSPORT
FLOW
SUSPENSIONS
DEPENDENCE
MECHANISM
WATER
FLUX
Кл.слова (ненормированные):
Nanofluid -- Forced convection -- Heat transfer -- Circular tube -- Thermophoresis -- Numerical simulation
Аннотация: Laminar convective heat transfer of water-alumina nanofluid in a circular tube with uniform heat flux is investigated numerically on the basis of two-component model, which takes into account nanoparticle transport by diffusion and thermophoresis. A new expression for thermophoretic mobility is suggested on the basis of existing experimental results and theoretical concepts. It is shown that thermophoresis leads to a significant reduction of nanoparticle volume fraction in the boundary layer near the wall. The corresponding viscosity reduction causes the velocity increase near the wall and flattening of velocity profile near the tube axis to keep the mass flow rate constant. The decrease of wall shear stress leads to the decrease of the required pressure drop. The calculations for two-component model provide higher values of the local and average heat transfer coefficients in comparison with the one-component model. The difference does not exceed 10% and decreases with increasing the thermal Peclet number. The calculations for one-component model show the independence of local and average Nusselt numbers on the nanoparticle volume fraction. The results for two-component model predict the increase of Nusselt number when the thermophoretic effect becomes stronger. The effectiveness of water-alumina nanofluid is analyzed by plotting the average heat transfer coefficient against the required pumping power. It is shown that the nanofluid shows better performance than the base fluid in the range of low pumping power and, correspondingly, low inlet velocity. (C) 2014 Elsevier Ltd. All rights reserved.
WOS
Держатели документа:
[Ryzhkov, Ilya I.] SB RAS, Inst Computat Modelling, Krasnoyarsk 660036, Russia
[Minakov, Andrey V.] Siberian Fed Univ, Inst Engn Phys & Radio Elect, Krasnoyarsk 660041, Russia
ИВМ СО РАН
Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Minakov, A.V.; Минаков, Андрей Викторович; Krasnoyarsk Regional Foundation of Scientific and Technical Activity [02/13]; Russian President Grant [MK-6296.2013.8]
Invariance principle for extension of hydrodynamics: Nonlinear viscosity
[Text] / I. V. Karlin, G. . Dukek, T. F. Nonnenmacher // Phys. Rev. E. - 1997. - Vol. 55, Is. 2. - P1573-1576, DOI 10.1103/PhysRevE.55.1573. - Cited References: 6
. - ISSN 1063-651X
РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].
WOS
Держатели документа:
RUSSIAN ACAD SCI,CTR COMP,KRASNOYARSK 660036,RUSSIA
ИВМ СО РАН
Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Dukek, G.; Nonnenmacher, T.F.
Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].
WOS
Держатели документа:
RUSSIAN ACAD SCI,CTR COMP,KRASNOYARSK 660036,RUSSIA
ИВМ СО РАН
Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Dukek, G.; Nonnenmacher, T.F.
Invariance principle for extension of hydrodynamics: Nonlinear viscosity
/ I. V. Karlin, G. Dukek, T. F. Nonnenmacher // Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. - 1997. - Vol. 55, Is. 2. - P1573-1576
. - ISSN 1063-651X
Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].
Scopus
Держатели документа:
Department of Mathematical Physics, University of Ulm, Ulm, D-89069, Germany
Computing Center, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Dukek, G.; Nonnenmacher, T.F.
Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].
Scopus
Держатели документа:
Department of Mathematical Physics, University of Ulm, Ulm, D-89069, Germany
Computing Center, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Dukek, G.; Nonnenmacher, T.F.
Numerical simulation of the dynamics of a liquid crystal in the case of plane strain using GPUs
/ O. V. Sadovskaya // AIP Conference Proceedings. - 2014. - Vol. 1629: 6th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2014 (26 June 2014 through 1 July 2014, ) Conference code: 109043. - P303-310, DOI 10.1063/1.4902286
. -
Кл.слова (ненормированные):
CUDA technology -- dynamics -- elasticity -- finite-difference scheme -- Liquid crystal -- parallel computational algorithm -- resonance frequency -- rotational waves -- thermal conductivity -- viscosity
Аннотация: Parallel computational algorithm is worked out for numerical implementation of two-dimensional dynamic model of a liquid crystal, which takes into account the mutual influence of three physical effects - transfer of acoustic energy due to translational motion, viscoelastic rotation of the particles under the action of tangential stresses, anisotropic thermal expansion and compression. The algorithm is based on the Godunov gap decay method, the Ivanov scheme with controlled dissipation of energy and the splitting method with respect to spatial variables. The CUDA technology for computer systems with graphic accelerators is used. Results of computations demonstrating the efficiency of proposed method and algorithm are represented.
Scopus,
Полный текст (доступен только в локальной сети),
WOS
Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovskaya, O.V.; Садовская, Оксана Викторовна
Кл.слова (ненормированные):
CUDA technology -- dynamics -- elasticity -- finite-difference scheme -- Liquid crystal -- parallel computational algorithm -- resonance frequency -- rotational waves -- thermal conductivity -- viscosity
Аннотация: Parallel computational algorithm is worked out for numerical implementation of two-dimensional dynamic model of a liquid crystal, which takes into account the mutual influence of three physical effects - transfer of acoustic energy due to translational motion, viscoelastic rotation of the particles under the action of tangential stresses, anisotropic thermal expansion and compression. The algorithm is based on the Godunov gap decay method, the Ivanov scheme with controlled dissipation of energy and the splitting method with respect to spatial variables. The CUDA technology for computer systems with graphic accelerators is used. Results of computations demonstrating the efficiency of proposed method and algorithm are represented.
Scopus,
Полный текст (доступен только в локальной сети),
WOS
Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovskaya, O.V.; Садовская, Оксана Викторовна
Stability analysis of shear flows in a Hele-Shaw cell
[Text] / A. A. Chesnokov, I. V. Stepanova // Appl. Math. Comput. - 2015. - Vol. 265. - P320-328, DOI 10.1016/j.amc.2015.05.019. - Cited References:19. - The work is supported by Russian Foundation of Basic Research (project 14-31-50572), the Program of Leading Scientific Schools Supporting (project 2133.2014.1) and Integrating project of SB RAS (44).
. - ISSN 0096-3003. - ISSN 1873-5649
РУБ Mathematics, Applied
Аннотация: A mathematical model describing motion of an inhomogeneous incompressible fluid in a Hele-Shaw cell is considered. Linear stability analysis of shear flow class is provided. The role of inertia, linear friction and impermeable boundaries in Kelvin Helmholtz instability is studied. Hierarchy of simplified one-dimensional models of viscosity- and density stratified flows is obtained in long wave approximation. Interpretation of Saffman-Taylor instability is given in the framework of these models. (C) 2015 Elsevier Inc. All rights reserved.
WOS,
Scopus
Держатели документа:
Novosibirsk State Univ, Novosibirsk 630090, Russia.
RAS, SB, Lavrentyev Inst Hydrodynam, Novosibirsk, Russia.
RAS, SB, Inst Computat Modeling, Krasnoyarsk, Russia.
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Russian Foundation of Basic Research [14-31-50572]; Program of Leading Scientific Schools Supporting [2133.2014.1]Integrating project of SB RAS
Рубрики:
POROUS-MEDIA
INSTABILITIES
FLUID
Кл.слова (ненормированные):
Hele-Shaw flows -- Wave solutions -- Stability -- Layered flows
POROUS-MEDIA
INSTABILITIES
FLUID
Кл.слова (ненормированные):
Hele-Shaw flows -- Wave solutions -- Stability -- Layered flows
Аннотация: A mathematical model describing motion of an inhomogeneous incompressible fluid in a Hele-Shaw cell is considered. Linear stability analysis of shear flow class is provided. The role of inertia, linear friction and impermeable boundaries in Kelvin Helmholtz instability is studied. Hierarchy of simplified one-dimensional models of viscosity- and density stratified flows is obtained in long wave approximation. Interpretation of Saffman-Taylor instability is given in the framework of these models. (C) 2015 Elsevier Inc. All rights reserved.
WOS,
Scopus
Держатели документа:
Novosibirsk State Univ, Novosibirsk 630090, Russia.
RAS, SB, Lavrentyev Inst Hydrodynam, Novosibirsk, Russia.
RAS, SB, Inst Computat Modeling, Krasnoyarsk, Russia.
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Russian Foundation of Basic Research [14-31-50572]; Program of Leading Scientific Schools Supporting [2133.2014.1]Integrating project of SB RAS
Reynolds-averaged modeling of turbulent flows of power-law fluids
[Text] / A. A. Gavrilov, V. Y. Rudyak // J. Non-Newton. Fluid Mech. - 2016. - Vol. 227. - P45-55, DOI 10.1016/j.jnnfm.2015.11.006. - Cited References:24. - This work was supported by the Russian Scientific Foundation (Contract no. 14-19-00312).
. - ISSN 0377-0257. - ISSN 1873-2631
РУБ Mechanics
Аннотация: The paper presents a novel Reynolds-averaged turbulence model for flows of power-law fluid. The model uses the elliptic relaxation approach to capture the near-wall turbulence anisotropy. The turbulence model for Newtonians fluids is modified by introducing closed approximations of correlations between velocity and viscosity fluctuations. The approximation for non-Newtonian extra stress is derived with the assumption of smallness of molecular viscosity fluctuations. A closed model for the averaged molecular viscosity is derived which takes into account its nonlinear dependence on the shear rate. Validation of the model against the direct numerical simulation (DNS) data for power-law fluids flows in the pipe demonstrates that new model is able to predict the main features of the non-Newtonian turbulence. Mean velocity, turbulent energy and averaged molecular viscosity distributions agree well with DNS data. (c) 2015 Published by Elsevier B.V.
WOS
Держатели документа:
ICM SB RAS, Inst Thermophys SB RAS, Krasnoyarsk Branch, 50-44 Akad Gorodok, Krasnoyarsk 660036, Russia.
Novosibirsk State Univ Architecture & Civil Engn, 113 Leningradskaya Str, Novosibirsk 630008, Russia.
Доп.точки доступа:
Gavrilov, Andrey A.; Rudyak, Valeriy Ya; Russian Scientific Foundation [14-19-00312]
Рубрики:
DRAG-REDUCING FLUIDS
PIPE-FLOW
NEWTONIAN FLUIDS
NEAR-WALL
EPSILON
Кл.слова (ненормированные):
Shear-thinning fluids -- Power-Law fluid -- Turbulence model -- RANS modeling
DRAG-REDUCING FLUIDS
PIPE-FLOW
NEWTONIAN FLUIDS
NEAR-WALL
EPSILON
Кл.слова (ненормированные):
Shear-thinning fluids -- Power-Law fluid -- Turbulence model -- RANS modeling
Аннотация: The paper presents a novel Reynolds-averaged turbulence model for flows of power-law fluid. The model uses the elliptic relaxation approach to capture the near-wall turbulence anisotropy. The turbulence model for Newtonians fluids is modified by introducing closed approximations of correlations between velocity and viscosity fluctuations. The approximation for non-Newtonian extra stress is derived with the assumption of smallness of molecular viscosity fluctuations. A closed model for the averaged molecular viscosity is derived which takes into account its nonlinear dependence on the shear rate. Validation of the model against the direct numerical simulation (DNS) data for power-law fluids flows in the pipe demonstrates that new model is able to predict the main features of the non-Newtonian turbulence. Mean velocity, turbulent energy and averaged molecular viscosity distributions agree well with DNS data. (c) 2015 Published by Elsevier B.V.
WOS
Держатели документа:
ICM SB RAS, Inst Thermophys SB RAS, Krasnoyarsk Branch, 50-44 Akad Gorodok, Krasnoyarsk 660036, Russia.
Novosibirsk State Univ Architecture & Civil Engn, 113 Leningradskaya Str, Novosibirsk 630008, Russia.
Доп.точки доступа:
Gavrilov, Andrey A.; Rudyak, Valeriy Ya; Russian Scientific Foundation [14-19-00312]
A Mathematical Model of the Passage of an Asteroid-Comet Body through the Earth's Atmosphere
[Text] / V. Shaydurov, G. Shchepanovskaya, M. Yakubovich ; ed. M. D. Todorov // APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES : AMER INST PHYSICS, 2015. - Vol. 1684: 7th International Conference on Application of Mathematics in Technical (JUN 28-JUL 03, 2015, Albena, BULGARIA). - Ст. UNSP 020003. - (AIP Conference Proceedings), DOI 10.1063/1.4934284. - Cited References:23
. -
РУБ Mathematics, Applied + Physics, Applied
Аннотация: In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth's atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) and the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.
WOS,
Scopus,
Смотреть статью
Держатели документа:
SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Krasnoyarsk 660041, Russia.
Доп.точки доступа:
Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Yakubovich, M.V.; Якубович, Максим Викторович; Todorov, M.D. \ed.\; Шайдуров, Владимир Викторович
Рубрики:
BOUNDARY-CONDITIONS
SIMULATION
Кл.слова (ненормированные):
Time-dependent Navier-Stokes equations -- viscous heat-conducting gas -- friable asteroid-comet body -- ionization and decomposition of molecules -- semi-Lagrangian approximation -- conforming finite element method
BOUNDARY-CONDITIONS
SIMULATION
Кл.слова (ненормированные):
Time-dependent Navier-Stokes equations -- viscous heat-conducting gas -- friable asteroid-comet body -- ionization and decomposition of molecules -- semi-Lagrangian approximation -- conforming finite element method
Аннотация: In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth's atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) and the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.
WOS,
Scopus,
Смотреть статью
Держатели документа:
SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Krasnoyarsk 660041, Russia.
Доп.точки доступа:
Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Yakubovich, M.V.; Якубович, Максим Викторович; Todorov, M.D. \ed.\; Шайдуров, Владимир Викторович
Моделирование нестационарного контакта в подшипнике качения
[Текст] : статья / В. А. Иванов, Н. В. Еркаев // Вестник Сибирского государственного аэрокосмического университета им. академика М.Ф. Решетнева. - 2015. - Т. 16, № 3. - С. 580-586
. - ISSN 1816-9724
Перевод заглавия: Simulation of non-steady contact in rolling bearings
Кл.слова (ненормированные):
Transient mode -- contact interaction -- lubricant layer -- нестационарный режим -- контактное взаимодействие -- смазочный слой
Аннотация: Рассмотрена задача нестационарного гидродинамического контакта ролика с упругим слоем с учетом прогиба поверхности, а также влияния давления на коэффициент вязкости. Зависимость вязкости от давления задана экспоненциальной функцией. В работе использовался итерационный метод численного решения уравнения Рейнольдса совместно с интегральным уравнением связи прогиба поверхности с давлением в смазочном слое. Показано, что вертикальное перемещение ролика вызывает дополнительное существенное возрастание давления в смазочном слое, пропорциональное вертикальной скорости. Коэффициент линейной зависимости несущей способности от вертикальной скорости назван коэффициентом демпфирования. В результате расчетов получены зависимости несущей способности и коэффициента демпфирования смазочного слоя от величины минимального зазора между роликом и пластиной. С использованием найденных функций изучен переходный процесс установления стационарного режима при резком изменении внешней нагрузки. Найдено характерное время установления и определены временные вариации пиковых значений давления. Исследовано влияние пьезокоэффициента вязкости на максимальные значения давления, достигаемые в процессе установления. Найдено критическое значение пьезокоэффициента, при котором эффект возрастания давления, обусловленный увеличением вязкости, компенсируется влиянием деформации упругой поверхности.
This article deals with the problem of non-steady hydrodynamic contact of a roller with finite size elastic plate. The lubricant viscosity coefficient is assumed to be exponential function of the pressure. For this problem, an iterative numerical method was elaborated to solve the 2-D Reynolds’ equation consistently with the integral equation of relationship between the surface deflection and pressure distribution in the lubrication layer. A normal motion of the roller causes additional pressure enhancement in the lubrication layer, which is proportional to the normal velocity. Coefficient of proportionality is called as damping coefficient. Carrying capacity and damping coefficient are determined from numerical solution as functions of minimal distance between the roller and plate. The obtained functions were used for modeling of the roller oscillations due to sudden variations of the external loading. Characteristic relaxation time and temporal variations of the pressure maximum are determined. Dependence of the pressure maximum on a special piezo-coefficient was investigated, which is a parameter of the exponential function approximating relationship between viscosity and pressure. Higher values of the piezo-coefficient yield larger values of the pressure maximum in the lubrication layer during the relaxation period. However, deflection of the body surfaces makes an opposite effect on the pressure. Therefore behavior of the pressure maximum is determined by two opposite factors related to the viscosity piezo-effect and surface deformations. From numerical simulations, a critical value of the piezo-coefficient is found when the influence of the piezo-coefficient is compensated by that of deformation of the elastic plate.
РИНЦ,
Полный текст сборника
Держатели документа:
Институт вычислительного моделирования CО РАН
Сибирский федеральный университет, Политехнический институт
Доп.точки доступа:
Еркаев, Николай Васильевич; Erkaev N.V.; Ivanov V.A.
Перевод заглавия: Simulation of non-steady contact in rolling bearings
| УДК |
Кл.слова (ненормированные):
Transient mode -- contact interaction -- lubricant layer -- нестационарный режим -- контактное взаимодействие -- смазочный слой
Аннотация: Рассмотрена задача нестационарного гидродинамического контакта ролика с упругим слоем с учетом прогиба поверхности, а также влияния давления на коэффициент вязкости. Зависимость вязкости от давления задана экспоненциальной функцией. В работе использовался итерационный метод численного решения уравнения Рейнольдса совместно с интегральным уравнением связи прогиба поверхности с давлением в смазочном слое. Показано, что вертикальное перемещение ролика вызывает дополнительное существенное возрастание давления в смазочном слое, пропорциональное вертикальной скорости. Коэффициент линейной зависимости несущей способности от вертикальной скорости назван коэффициентом демпфирования. В результате расчетов получены зависимости несущей способности и коэффициента демпфирования смазочного слоя от величины минимального зазора между роликом и пластиной. С использованием найденных функций изучен переходный процесс установления стационарного режима при резком изменении внешней нагрузки. Найдено характерное время установления и определены временные вариации пиковых значений давления. Исследовано влияние пьезокоэффициента вязкости на максимальные значения давления, достигаемые в процессе установления. Найдено критическое значение пьезокоэффициента, при котором эффект возрастания давления, обусловленный увеличением вязкости, компенсируется влиянием деформации упругой поверхности.
This article deals with the problem of non-steady hydrodynamic contact of a roller with finite size elastic plate. The lubricant viscosity coefficient is assumed to be exponential function of the pressure. For this problem, an iterative numerical method was elaborated to solve the 2-D Reynolds’ equation consistently with the integral equation of relationship between the surface deflection and pressure distribution in the lubrication layer. A normal motion of the roller causes additional pressure enhancement in the lubrication layer, which is proportional to the normal velocity. Coefficient of proportionality is called as damping coefficient. Carrying capacity and damping coefficient are determined from numerical solution as functions of minimal distance between the roller and plate. The obtained functions were used for modeling of the roller oscillations due to sudden variations of the external loading. Characteristic relaxation time and temporal variations of the pressure maximum are determined. Dependence of the pressure maximum on a special piezo-coefficient was investigated, which is a parameter of the exponential function approximating relationship between viscosity and pressure. Higher values of the piezo-coefficient yield larger values of the pressure maximum in the lubrication layer during the relaxation period. However, deflection of the body surfaces makes an opposite effect on the pressure. Therefore behavior of the pressure maximum is determined by two opposite factors related to the viscosity piezo-effect and surface deformations. From numerical simulations, a critical value of the piezo-coefficient is found when the influence of the piezo-coefficient is compensated by that of deformation of the elastic plate.
РИНЦ,
Полный текст сборника
Держатели документа:
Институт вычислительного моделирования CО РАН
Сибирский федеральный университет, Политехнический институт
Доп.точки доступа:
Еркаев, Николай Васильевич; Erkaev N.V.; Ivanov V.A.
Semi-Lagrangian method for advection problem with adaptive grid
/ A. Efremov [et al.] // AIP Conference Proceedings. - 2016. - Vol. 1773: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 (22 June 2016 through 27 June 2016, ) Conference code: 124420, DOI 10.1063/1.4964997
. -
Аннотация: In the paper, the semi-Lagrangian method is considered for the numerical solution of the advection problem. A numerical solution is constructed as a piecewise constant function on a rectangular grid. The proposed method is stable and gives an approximate solution with the first order of accuracy. To reduce the effect of smoothing an approximate solution because of numerical viscosity, a mesh refinement is applied in the vicinity of large gradients of the approximate solution. The localization of the smoothing effect is illustrated by a numerical example. In contrast to the traditional Eulerian schemes, semi-Lagrangian algorithms do not involve a time step restriction. © 2016 Author(s).
Scopus,
Смотреть статью,
WOS,
Полный текст (доступен только в ЛВС)
Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Efremov, A.; Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaydurov, V.V.; Шайдуров, Владимир Викторович; Vyatkin, A.
Аннотация: In the paper, the semi-Lagrangian method is considered for the numerical solution of the advection problem. A numerical solution is constructed as a piecewise constant function on a rectangular grid. The proposed method is stable and gives an approximate solution with the first order of accuracy. To reduce the effect of smoothing an approximate solution because of numerical viscosity, a mesh refinement is applied in the vicinity of large gradients of the approximate solution. The localization of the smoothing effect is illustrated by a numerical example. In contrast to the traditional Eulerian schemes, semi-Lagrangian algorithms do not involve a time step restriction. © 2016 Author(s).
Scopus,
Смотреть статью,
WOS,
Полный текст (доступен только в ЛВС)
Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Efremov, A.; Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaydurov, V.V.; Шайдуров, Владимир Викторович; Vyatkin, A.
519.63
П 53
П 53
Полулагранжевый метод для решения уравнения адвекции на адаптивной сетке
[Текст] : научное издание / А. В. Вяткин [и др.] // Решетневские чтения. - 2016. - Т. 2, № 20. - С. 124-126
. - ISSN 1990-7702
Перевод заглавия: SEMI-LAGRANGIAN METHOD ON ADAPTIVE GRID FOR ADVECTION EQUATION
Кл.слова (ненормированные):
уравнение адвекции -- полуЛагранжевый метод -- адаптация сетки -- Advection equation -- Semi-Lagrangian method -- adaptive grid
Аннотация: В математическом моделировании сложных физических процессов и задач, в том числе в космической отрасли, широко применяется полулагранжевый подход. Представлен численный метод решения краевой задачи для уравнения адвекции, использующий апостериорную адаптацию сетки в областях с большим градиентом решения.
The semi-Lagrangian approach is widely used for numerical modeling in complex natural phenomena; it includes a space sciences and technologies. In the paper, the semi-Lagrangian method is considered for the numerical solution of the advection problem. A numerical solution is constructed as a piecewise constant function on a rectangular grid. To reduce the effect of smoothing an approximate solution due to numerical viscosity, a mesh refinement is applied in the vicinity of large gradients of the approximate solution. The localization of the smoothing effect is illustrated by a numerical example.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Вяткин, А.В.; Vyatkin A.V.; Ефремов, А.А.; Efremov A.A.; Карепова, Е.Д.; Karepova E.D.; Шайдуров, В.В.; Shaidurov V.V.
Перевод заглавия: SEMI-LAGRANGIAN METHOD ON ADAPTIVE GRID FOR ADVECTION EQUATION
| УДК |
Кл.слова (ненормированные):
уравнение адвекции -- полуЛагранжевый метод -- адаптация сетки -- Advection equation -- Semi-Lagrangian method -- adaptive grid
Аннотация: В математическом моделировании сложных физических процессов и задач, в том числе в космической отрасли, широко применяется полулагранжевый подход. Представлен численный метод решения краевой задачи для уравнения адвекции, использующий апостериорную адаптацию сетки в областях с большим градиентом решения.
The semi-Lagrangian approach is widely used for numerical modeling in complex natural phenomena; it includes a space sciences and technologies. In the paper, the semi-Lagrangian method is considered for the numerical solution of the advection problem. A numerical solution is constructed as a piecewise constant function on a rectangular grid. To reduce the effect of smoothing an approximate solution due to numerical viscosity, a mesh refinement is applied in the vicinity of large gradients of the approximate solution. The localization of the smoothing effect is illustrated by a numerical example.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Вяткин, А.В.; Vyatkin A.V.; Ефремов, А.А.; Efremov A.A.; Карепова, Е.Д.; Karepova E.D.; Шайдуров, В.В.; Shaidurov V.V.
539.37
О-13
О-13
ОБ ОПРЕДЕЛЯЮЩИХ УРАВНЕНИЯХ ВОЛОКНИСТЫХ КОМПОЗИТОВ, ПО-РАЗНОМУ СОПРОТИВЛЯЮЩИХСЯ РАСТЯЖЕНИЮ И СЖАТИЮ
[Текст] : статья / В. М. Садовский, О. В. Садовская, И. Е. Петраков // Решетневские чтения. - 2018. - Т. 1, № 22. - С. 578-580
. - ISSN 1990-7702
Перевод заглавия: ON CONSTITUTIVE EQUATIONS OF FIBROUS COMPOSITES, DIFFERENTLY RESISTANT TO TENSION AND COMPRESSION
Кл.слова (ненормированные):
волокнистый композит -- упругость -- пластичность -- вязкость -- реологическая схема -- вариационное неравенство -- fibrous composite -- elasticity -- plasticity -- viscosity -- Rheological scheme -- variational inequality
Аннотация: Предложен метод построения определяющих соотношений общего вида, учитывающих упругие, пластические и вязкие свойства волокнистых композитных материалов, по-разному сопротивляющихся растяжению и сжатию.
We developed the method of constructing constitutive equations of a general form, taking into account elastic, plastic and viscous properties of fibrous composite materials, which differ in their resistance to tension and compression.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Садовский, В.М.; Sadovskii V.M.; Садовская, О.В.; Sadovskaya O.V.; Петраков, И.Е.; Petrakov I.E.
Перевод заглавия: ON CONSTITUTIVE EQUATIONS OF FIBROUS COMPOSITES, DIFFERENTLY RESISTANT TO TENSION AND COMPRESSION
| УДК |
Кл.слова (ненормированные):
волокнистый композит -- упругость -- пластичность -- вязкость -- реологическая схема -- вариационное неравенство -- fibrous composite -- elasticity -- plasticity -- viscosity -- Rheological scheme -- variational inequality
Аннотация: Предложен метод построения определяющих соотношений общего вида, учитывающих упругие, пластические и вязкие свойства волокнистых композитных материалов, по-разному сопротивляющихся растяжению и сжатию.
We developed the method of constructing constitutive equations of a general form, taking into account elastic, plastic and viscous properties of fibrous composite materials, which differ in their resistance to tension and compression.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Садовский, В.М.; Sadovskii V.M.; Садовская, О.В.; Sadovskaya O.V.; Петраков, И.Е.; Petrakov I.E.