The relevance of study of the liquid stratified density, in particular sea water, is very important for science and technology. The results of such research can be used in the study of the sea water flow around underwater vessels and parts of ships submerged in water, in the study of sea currents behind the islands and, consequently, the safety of navigation. In this paper NaCl salt water solution is considered as a stratified liquid. This is the most common liquid in nature (water in the seas and oceans). The flow of a stratified fluid has characteristics other than flow of a homogeneous fluid. When studying the two-dimensional structure of the flow around the obstacle, such phenomena as outstripping disturbance – fluid blocking in front of obstacle and connected internal waves were discovered. Examining the thin structure of the flow with more details, it is possible to identify other features. This paper investigates numerically a three-dimensional flow of stratified liquid around a circular cylinder in a wide range of Reynolds and Froude numbers. It is found that the region occupied by the internal waves extends to a considerable distance up from the front critical point of the cylinder. The finite difference method of Belotserkovsky-Gushchin-Konshin having the second order of accuracy in spatial coordinates is used as a numerical method of research. The method was repeatedly tested and showed good results. It is implemented in stages: at first the approximate velocity values are computed then the pressure is computed based on these values, after that velocities are revised and finally the salinity is calculated. The software package implementing this method is adapted for machines with parallel architecture using MPI technology. Computations were carried out on the supercomputer MVS-1000.
Turner J.S. Buoyancy Effct In Fluids. Cambridge. Cambridge University Press Publ., 1973, 368 p.[ In Russ: Effekty plavuchesti v zhidkostyakh., Moscow, Mir Publ., 1977, 431 p.]
Gushchin V.A. Zhurnal vychislitelnoy matematiki i matematicheskoi fiziki RAN — Journal of Computational Mathematics and Mathematical Physics, 1981, vol.21, no.4, pp.1003–1017.
Mitkin.V., Chashechkin. Yu. Journal of Visualization, 2006 no.9, pp.301–308.
Samarsky A.A., Nikolaev E.S. Metody resheniya setochnych uravneniy [Methods for solving finite-difference equation]. Moscow, Nauka Publ., 1978, 592 p.
Easton C.R. Journal of Computational Physics, 1972, vol.9, mo.2, pp.375–379.
Gushchin V.A., Mitkin V.V., Rozhdestvenskaya T.I., Chashechkin Yu.D. Prikladnaya mekhanika i tekhnicheskaya fizika – Journal of Applied Mechanics and Technical Physics, 2007, vol.48, no.1, pp.43–54.
Gushchin V.A., Mitkin V.V., Rozhdestvenskaya T.I., Chashechkin Yu.D. Prikladnaya mekhanika i tekhnicheskaya fizika — Journal of Applied Mechanics and Technical Physics, 2007, vol.48, no.1, pp.34–43.
Gushchin V.A., and Rozhdestvenskaya T.I. Prikladnaya mekhanika i tekhnicheskaya fizika – Journal of Applied Mechanics and Technical Physics, 2011, vol.52, no.6, pp.69–76.
Gushchin V.A., and Rozhdestvenskaya T.I. Prikladnaya mekhanika i tekhnicheskaya fizika – Journal of Applied Mechanics and Technical Physics, 2011, vol.52, no.6, pp.905–911.
Antonov A.S. Parallelnoe programmirovanie s ispolsovaniem technologii MPI [Parallel programming using MPI technology]. Moscow, MSU Publ., 2004, 71 p.
Zhang H.-Q, Fey U., Noack B.R, Koenig, M., Eckelman, H. Physics of Fluids, 1995, vol.7, no.4, pp.779–794.
Rozhdestvenskaya T.I. Chislennoe issledovanie svoistv neodnorodnykh zhidkostey pri obtekanii imi krugovogo tsilindra [Numerical study of the properties of inhomogeneous liquids flowing around a circular cylinder]. Sbornik nauchnykh trudov XI Vserossiyskogo syezda po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki [Proceedings of the ХI all-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics], Kazan 2015, pp.3232–3233.
Rozdestvenskaya T.I. Chislennnye isledovaniya svoystv neodnorodnykh zhidkostey pri obtekanii imi krugovogo tsilindra [Numerical study of the properties of inhomogeneous liquids flowing around a circular cylinder]. Tezisy dokladov Mezdunarodnoy konferentsii «Sovremennuye problemy mekhaniki sploshnoy sredy», posvjashchennoy pamyati akademika L.I. Sedova v svjazi so 110-letiem so dnya ego rozhdeniya [International conference "Current problems of continuum mechanics" dedicated to the memory of academician L.I. Sedov in connection with the 110th anniversary of his birth. Abstracts]. Moscow, 2017.
Рождественская Т.П. Численное исследование трехмерных течений неоднородной жидкости около кругового цилиндра. Математическое моделирование и численные методы, 2019, № 1, с. 86–99.
Количество скачиваний: 57