phone +7 (3412) 91 60 92
mail imi@udsu.ru
ru-RU Russian
Home » Issues » Archive of Issues » 2017 - 3 issue » pp. 460-469

Archive of Issues

Russia Izhevsk
Year
2017
Volume
27
Issue
3
Pages
460-469
<<
>>
Section Mechanics
Title Application of WENO scheme for simulation of turbulent flow in a channel with backward-facing step
Author(-s) Shumikhin A.A.a, Koroleva M.R.a, Dadikina S.Yu.a, Karpov A.I.ab
Affiliations Institute of Mechanics, Ural Branch of the Russian Academy of Sciencesa, Udmurt State Universityb
Abstract The technique of viscous gas turbulent flow simulation based on high-order approximation WENO scheme (Weighted Essentially Non-oscillatory scheme) is described. This scheme is characterized by significant stability when calculations are performed, because WENO allows to eliminate nonphysical oscillations of a numerical solution which can occur during calculations. The system of governing equations describing the flow of viscous gas based on the Navier-Stokes equations is presented. The algorithms of 3-rd and 5-th accuracy orders are developed and implemented. The numerical methods used in the calculations of gas flow are described. Turbulence modeling is carried out using the method of large vortices. The proposed algorithms have been used to study the flow of viscous gas in a channel with backward-facing step. Reynolds number of the flow in the channel was Re=15000. Comparison of simulation results with experimental data has been made.
Keywords WENO scheme, method of large vortices, turbulence, Computational Fluid Dynamics
UDC 532.517.4, 519.632.4
MSC 76F65, 65N08
DOI 10.20537/vm170313
Received 1 August 2017
Language Russian
Citation Shumikhin A.A., Koroleva M.R., Dadikina S.Yu., Karpov A.I. Application of WENO scheme for simulation of turbulent flow in a channel with backward-facing step, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 460-469.
References
  1. Liu X-D., Osher S., Chan T. Weighted essentially non-oscillatory schemes, J. Comput. Phys., 1994, vol. 115, issue 1, pp. 200-212. DOI: 10.1006/jcph.1994.1187
  2. Jiang G.-S., Shu C.-W. Efficient implementation of weighted ENO schemes, J. Comput. Phys., 1996, vol. 126, issue 1, pp. 202-228. DOI: 10.1006/jcph.1996.0130
  3. Shu C.-W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE Report No. 97-65., NASA-CR/97-206253, 1997, 83 p. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980007543.pdf
  4. Balsara D., Shu C.-W. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys., 2000, vol. 160, issue 2, pp. 405-452. DOI: 10.1006/jcph.2000.6443
  5. Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment, Monthly Weather Review, 1963, vol. 91, no. 3, pp. 99-164. DOI: 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
  6. Ducros F., Nicoud F., Poinsot T. Wall-adapting local eddy-viscosity models for simulations in complex geometries, Proceeding of the 6th ICFD Conference on Numerical Methods for Fluid Dynamic. Oxford, United Kingdom, 1998, pp. 293-299.
  7. Volkov K.N., Emel'yanov V.N. Modelirovanie krupnykh vikhrei v raschetakh turbulentnykh techenii (Large Eddy Simulation in predicting of turbulent flows), Мoscow: Fizmatlit, 2008, 368 p.
  8. Karpov A.I., Shumikhin A.A. A parametric study of internal turbulent flows by the Large Eddy Simulation, Vestn. Udmurt. Univ. Mat. Mech. Komp'yut. Nauki, 2009, no. 4, pp. 62-70 (in Russian). DOI: 10.20537/vm090406
  9. Shumikhin A.A., Karpov A.I. Large-Eddy Simulation of the turbulent diffusion flame, Vychislitel'naya mekhanika sploshnykh sred, 2012, vol. 5, no. 2, pp. 199-207 (in Russian). DOI: 10.7242/1999-6691/2012.5.2.24
  10. Steger J.L., Warming R.F. Flux vector splitting of the inviscid gasdynamic equations with application to finite difference methods, J. Comput. Phys., 1981, vol. 40, issue 2, pp. 263-293. DOI: 10.1016/0021-9991(81)90210-2
  11. van Leer B. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys., 1979, vol. 32, issue 1, pp. 101-136. DOI: 10.1016/0021-9991(79)90145-1
  12. Osher S., Chakravarthy S. Upwind schemes and boundary conditions with applications to Euler equations in general geometries, J. Comput. Phys., 1983, vol. 50, issue 3, pp. 447-481. DOI: 10.1016/0021-9991(83)90106-7
  13. Anderson W.K., Thomas J.L., van Leer B. Comparison of finite volume flux vector splittings for the Euler equations, AIAA Journal, 1986, vol. 24, no. 9, pp. 1453-1460. DOI: 10.2514/3.9465
  14. Terekhov V.I., Smul'skii Ya.I., Sharov K.A. Interference of separated flows behind backward-facing step in the presence of passive control, Technical Physics Letters, 2012, vol. 38, issue 2, pp. 125-128. DOI: 10.1134/S1063785012020149
Full text
/doc/issues-2017/17-03-13.pdf
<< Previous article
Next article >>