Background Image
Previous Page  20 / 21 Next Page
Information
Show Menu
Previous Page 20 / 21 Next Page
Page Background

in the shock tube at the initial stage. The comparison of experimental and

computational physical dependences (see Fig 8) allows noting satisfactory

coincidence between them.

Conclusion.

The numerical methods and the computation code for

non-stationary one-dimensional radiation magnetogasdynamic models are

developed, which are intended to describe the thermophysical processes in

various types of shock tubes. The numerical solution of the non-stationary

radiation magnetogasdynamic model described in this article is based

on the splitting method according to the physical processes and spatial

directions. The solution of the splitted equations is to be found using

the developed non-linear quasimonotonous compact difference scheme of

the higher order of accuracy, which allows achieving the seventh order of

accuracy in the spatial smooth part of the numerical solution. The proposed

mathematical apparatus can be used for solving more complicated Reynolds

equations. The solution to the formulated problem will enhance the further

experimental and theoretical research into the shock tubes.

The work has been fulfilled in the Laboratory for Radiation Gas

Dynamics at Ishlinskii Institute for Problems in Mechanics of the Russian

Academy of Science (RAS) within the programme of RAS Fundamental

Research.

REFERENCES

[1] Riddell F.R. Study of hypersonic flows. New York-London, Acad. press, 1962. 513 p.

(Russ. ed.: Issledovanie giperzvukovykh techenii. Sb. statei pod red. F.R. Riddella.

Moscow, Mir Publ., 1964. 544 p.).

[2] Kovenia V.M., Yanenko N.N. Metod raschepleniia v zadachakh gazovoi dinamiki

[Splitting method in gas dynamics problems]. Moscow, Nauka Publ., 1981. 304 p.

[3] Volkov K.N., Emelianov V.N. Modelirovanie krupnykh vikhrei v raschetakh

turbulentnykh techenii [Large eddy simulation (LES) for the turbulent flow

calculations]. Moscow, Fizmatlit Publ., 2008. 364 p.

[4] Marchuk G.I., Shaidurov V.V. Povyshenie tochnosti resheniia raznostnykh skhem

[The improvment of difference scheme solution accuracy]. Moscow, Nauka Publ.,

1979. 320 p.

[5] Dovgilovich L.E., Sofronov I.L. O primenenii kompaktnykh skhem dlia

resheniia volnovogo uravneniia [On application of compact schemes for

solving wave equations]. Moscow, Preprint No. 84 of Keldysh Institute

of Applied Mathematics, IPM im. M.V. Keldysha Publ., 2008. 27 p. URL:

http://library.keldysh.ru/preprint.asp?id=2008-84

(accessed 30.08.2013).

[6] Barth T.J. On unstructured grids and solvers in Computational Fluid Dynamics.

Belgium, The von Karman Institute for Fluid Dynamics, 1990, Lecture Notes Series

1990-04.

[7] Saveliev A.D. Sostavnyie kompaktnyie skhemy vysokogo poriadka dlia

modelirovaniia techeniia viazkogo gaza [High-order composite compact schemes for

simulation of viscous gas flows.

Zhurnal vychislitel’noi matematiki i matematicheskoi

fiziki

[J. of Computational Mathematics and Mathematical Physics], 2007, vol. 47,

No. 8, pp. 1387–1401 (in Russ.).

22 ISSN 0236-3941. HERALD of the BMSTU. Series “Mechanical Engineering”. 2014. No. 1