Numerical simulation of aerodynamics of simple geometries using approximate calculation of flow through the facet of the computational cell using the AUSM±up2 method


View article
PDF, 976.0 KB


A three-dimensional distribution of a high-velocity gas flow around simple geometric models on an unstructured grid was calculated. The obtained results were verified.
It was realized by using HySol computer code and UST3D family of computer codes, which implement the donor cell method and schemes of the AUSM family of algorithms for calculating flows through the facet of the computational cell. These codes were developed in IPMech RAS. They are based on the model of a viscous compressible heat-conducting gas, which is described by a spatial non-stationary system of Navier-Stokes equations, solved on three-dimensional unstructured tetrahedral meshes.

AUSM+-up2 scheme, Navier-Stokes equations, perfect gas, unstructured mesh, cross-verification.

DOI: http://doi.org/10.33257/PhChGD.23.1.983


Volume 23, issue 1, 2022 year


Численное моделирование аэродинамики простых геометрий с использованием приближенного вычисления потоков через грань расчетной ячейки методом AUSM±up2

Проведено трехмерное численное моделирование обтекания высокоскоростным потоком газа простых геометрических моделей на неструктурированной сетке. Была произведена верификация полученных результатов.
Для численного моделирования использовались компьютерный код HySol и семейство компьютерных кодов UST3D, реализующих метод донорных ячеек и схемы семейства AUSM алгоритмов для вычисления потоков через грань расчетной ячейки. Данные коды были разработаны в ИПМех РАН. В основе кодов лежит модель вязкого сжимаемого теплопроводного газа, которая описывается пространственной нестационарной системой уравнений Навье-Стокса, решаемой на трехмерных неструктурированных тетраэдральных сетках.

схема AUSM+-up2, уравнения Навье-Cтокса, совершенный газ, неструктурированная сетка, перекрестная верификация

DOI: http://doi.org/10.33257/PhChGD.23.1.983


Volume 23, issue 1, 2022 year



1. Schmisseur J.D. A Hypersonics Into the 21st Century: A Perspective on AFOSR-Sponsored Research in Aerothermodynamics // 43rd AIAA Fluid Dynamics Conference, June 2013.
2. Bertin J. Hypersonic Aerothermodynamics // AIAA Education Series, 1994. P. 627.
3. Lunev V.V. Hypersonic aerodynamics. M.: Mechanicalengineering, 1975, P. 328.
4. Anderson J. Hypersonic and High-Temperature Gas Dynamics Second Edition // AIAA Education Series, 2006.
5. Zheleznyakova A.L., Surzhikov S.T. Application of the method of splitting by physical processes for the computation of a hypersonic flow over an aircraft model of complex configuration. High Temperature, 2013, Vol. 51, no 6, pp. 816–829.
6. Zheleznyakova A.L., Surzhikov S.T. Calculation of a hypersonic flow over bodies of complex configuration on unstructured tetrahedral meshes using the AUSM scheme High Temperature,2014, Vol. 52, no 2, pp. 271–281.
7. Surzhikov S.T. Validation of computational code UST3D by the example of experimental aerodynamic data // Journal of Physics: Conference Series. 2017. Vol. 815 012023.
8. Yatsukhno D.S., Surzhikov S.T. Method for Splitting into Physical Processes in Task of the Flow Over a Perspective High-Speed Vehicle Modelling. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2018, no. 1, pp. 20–33.
9. Surzhikov S.T. Computer aerophysics of descent spacecraft. Two-dimensional models. M.: Fizmatlit, 2018, P. 544.
10. Surzhikov S.T. Аerophysics of the hypersonic air flow above surface of space vehicle at altitudes of less than 60 km Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki. [Herald of the Bauman Moscow State Tech. Univ., Natural Sciences. Eng.], 2016, no. 5 (68), pp. 33‒45.
11. Zabarko D.A., Kotenev V.P. Numerical study of laminar flows of a viscous chemically reacting gas near blunt bodies Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki. [Herald of the Bauman Moscow State Tech. Univ., Natural Sciences. Eng.], 2006, no. 1 (20), pp. 77‒95.
12. Surzhikov S.T. Numerical interpretation of experimental data on aerodynamics of the HB-2 model using computer codes USTFEN and PERAT-3D // Physical-Chemical Kinetics in Gas Dynamics, Vol. 21, no 1, 2020.
13. Kryukov I.A., Ivanov I.E., Larina E.V. Software package hySol for the numerical simulation of high-speed flows. // Physical and chemical kinetics in gas dynamics. - 2021. - Vol. 22, no. 1.
14. Ermakov M.K., Kryukov I.A. Verification and validation of aerodynamic codes using the example of the flow around sharp and blunt cones // Physical-Chemical Kinetics in Gas Dynamics, Vol. 22, no. 4, 2021.
15. Aerodynamics. – 2nd ed. / ed. Kalugin V.T. - M.: Publishing house of Bauman University, 2017. – P. 607.
16. Marchuk G.I. Splitting methods. M.: Nauka, 1988. P. 263.
17. Liou M.S., Steffen Jr. C.J. A new flux splitting scheme // J. Comp. Phys. 1993. Vol. 107., no. 1. pp. 23-39.
18. Roache P.J. Computational Fluid Dynamics. Hermosa Publishers, 1972. P. 434.
19. Kim K.H., Kim C., and Rho O.H. Methods for the Accurate Computations of Hypersonic Flows I. AUSMPW+ Scheme. // Journal of Computational Physics, Vol. 174, no. 1, November 2001. pp. 38-80.
20. Liou M.S. A Sequel to AUSM, Part II: AUSM+-up // J. Comput. Phys, Vol. 214, 2006. pp. 137 170.
21. Chang C.H., Liou M.S. A New approach to the simulation of compressible multifluid flows with AUSM+ scheme // 16th AIAA CFD Conference. Orlando, FL. June 23-26, 2003. AIAA Paper 2003-4107.
22. Silvestrov P. V., Surzhikov S.T. Calculation of aerothermodynamics for high-speed X-43 using computer code UST3D and UST3D-AUSMPW // Physical-Chemical Kinetics in Gas Dynamics, Vol. 20, no 4, 2019.
23. Kitamura K., Liou M.S., and Chang C.H. Extension and Comparative Study of AUSM-Family Schemes for Compressible Multiphase Flow September 2014. Vol. 16., no. 3. pp. 632 674.
24. Liou M.S. A Sequel to AUSM: AUSM+ // J. Comput. Phys, 1996. pp. 364-382.
25. Van Leer B. Flux-vector splitting for the Euler equations // 8th Int. Conf. on Num. Meth. in Fluid Dyn. Lecture Notes in Physics. Berlin: Springer. 1982. pp. 507-512.
26. SolidWorks. Practical guide. M.: Binom, 2004.
27. Krasilshchikov A.P., Guriyashkin L.P. Experimental studies of bodies of revolution in hypersonic flows. - M.: FIZMATLIT, 2007. - P. 208.
28. GOST 4401-81. The standard atmosphere.
29. Geuzaine C., Remacle J.F. Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. // International Journal fo Numerical Methods in Engineering, No. 79 (11), 2009. pp. 1309-1331.