Труды сотрудников ИВМ СО РАН

[Text] / V. Shaydurov [et al.] ; 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 090011. - (AIP Conference Proceedings), DOI 10.1063/1.4934336. - Cited References:16 . - РУБ Mathematics, Applied + Physics, Applied

Аннотация: In the paper, a semi-Lagrangian approximation is presented for the numerical solution of the two-dimensional time-dependent Navier-Stokes equations for viscous heat-conducting gas. In each equation, a combination of three first-order derivatives describing the transfer of a corresponding substance (density, velocity components, or internal energy) along trajectories is interpreted as the "transfer derivative" in the transfer direction. The other terms of the equations are written in the Euler form. On the sought-for time level, the standard conforming finite element method is realized for them with the linear elements on triangles and the bilinear ones on rectangles. The stencil adaptation along trajectories enables us to avoid the Courant-Friedrichs-Lewy upper limit which describes the dependence of the time step on the mesh-size of the space triangulation. At the end of the paper, a numerical example illustrates the implementation of the described algorithms.

WOS,
Scopus,
Смотреть статью

Держатели документа:
SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia.
Beihang Univ, Beijing 100191, Peoples R China.

Доп.точки доступа:
Shaydurov, V.V.; Шайдуров, Владимир Викторович; Liu, Tiegang; Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Yakubovich, M.V.; Якубович, Максим Викторович; Todorov, M.D. \ed.\

[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

/ V. V. Shaydurov, G. I. Shchepanovskaya, M. V. Yakubovich // Lobachevskii J. Math. - 2018. - Vol. 39, Is. 7. - P936-948, DOI 10.1134/S1995080218070193. - Cited References:20. - The work was partially supported by the Russian Foundation for Basic Research to projects nos. 17-01-000270 and No 16-41-243029 which is also supported by the Krasnoyarsk Regional Government and the Krasnoyarsk Regional Fund for the Support of Scientific and Technical Activities. . - ISSN 1995-0802. - ISSN 1818-9962РУБ Mathematics

Аннотация: In the paper, the numerical modeling of a supersonic flow around a wedge by viscous heat-conducting gas is considered. A numerical algorithm is proposed for the initial boundary-value problem for the Navier-Stokes equations. These equations are modified and amplified by new boundary conditions to provide the conservation law for the full energy: kinetic and inner. Then the combination of the Lagrangian approximation for the transfer operators and the conforming finite element method for other terms provides an efficient algorithm. Particular attention has been given to the approximation providing the conservation laws for mass and full energy at discrete level. Test calculations have been performed for a wide range of Mach and Reynolds numbers.

WOS,
Смотреть статью,
Scopus,
РИНЦ

Держатели документа:
Russian Acad Sci, Siberian Branch, Inst Computat Modeling, Akademgorodok 50-44, Krasnoyarsk 660036, Russia.
Tianjin Univ Finance & Econ, Zhujiang Rd 25, Tianjin 300222, Peoples R China.

Доп.точки доступа:
Shaydurov, V. V.; Shchepanovskaya, G. I.; Yakubovich, M. V.; Russian Foundation for Basic Research [17-01-000270, 16-41-243029]; Krasnoyarsk Regional Government; Krasnoyarsk Regional Fund for the Support of Scientific and Technical Activities