On optimization of technical devices based on a hierarchy of mathematical models


  • A.S. Surovezhko Central Institute of Aviation Motors
  • S.I. Martynenko Central Institute of Aviation Motors




computational fluid dynamics, mathematical modeling, turbulent internal flows, fuel collector


A fuel collector problem is considered as an inverse problem of hydrodynamics: it is necessary to determine the distribution channel geometry of a collector for a uniform fuel distribution. However, the collector profiling based on the 3D stationary Navier-Stokes equations for turbulent flow of an incompressible viscous medium in rough channels requires impractical computational efforts. A hierarchy of mathematical models (1D Navier-Stokes equations for the collector profiling and 3D Navier-Stokes equations for 1D model validation) is used in this paper. It is shown that the hierarchy of models can significantly reduce amount of computational work needed for computing the optimal collector design. The developed approach is of interest for optimizing technical devices for various purposes.

Author Biographies

A.S. Surovezhko

S.I. Martynenko


  1. A. M. Elizarov, N. B. Il’insky, and A. B. Potashev, Inverse Boundary Value Problems of Aerohydrodynamics (Fizmatlit, Moscow, 1994) [in Russian].
  2. O. M. Alifanov, Inverse Heat Transfer Problems (Mashinostroenie, Moscow, 1988; Springer, Berlin, 1994).
  3. A. A. Samarskii and P. N. Vabishchevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics (Editorial, Moscow, 2004; Walter de Gryuter, Berlin, 2007).
  4. A. L. Bolsunovsky, N. P. Buzoverya, I. A. Gubanova, and M. A. Gubanova, “Solution of the Inverse Problem for an Airfoil within the Framework of the Reynolds Averaged Navier-Stokes Equations,” Uchen. Zap. TsAGI, No. 3, 50-59 (2013) [TsAGI Sci. J. 44 (3), 371-385 (2013)].
  5. T. S. Poveschenko, V. A. Gasilov, Yu. A. Poveschenko, and I. I. Galiguzova, The Method of Calculating the Flows in a Multi-Circuit Heat Exchange Network of a Nuclear Energetic Facility (NEF) , Preprint No. 67 (Keldysh Institute of Applied Mathematics, Moscow, 2015).
  6. A. A. Samarskii and Yu. P. Popov, Difference schemes of gas dynamics (Nauka, Moscow, 1975) [in Russian].
  7. L. M. Degtyarev and A. P. Favorskii, “A Flow Variant of the Sweep Method,” Zh. Vychisl. Mat. Mat. Fiz. 8 (3), 679-684 (1968) [USSR Comput. Math. Math. Phys. 8 (3), 252-261 (1968)].
  8. V. Volokhov, P. Toktaliev, S. Martynenko, et al., “Supercomputer Simulation of Physicochemical Processes in Solid Fuel Ramjet Design Components for Hypersonic Flying Vehicle,” in Communications in Computer and Information Science (Springer, Cham, 2016), Vol. 687, pp. 236-248.
  9. V. M. Akimov, V. I. Bakulev, R. I. Kurziner, et al., Theory and Calculation of Jet Engines (Mashinostroenie, Moscow, 1987) [in Russian].
  10. A. A. Inozemtsev, M. A. Nikhamkin, and V. L. Sandratskii, Basics of Designing Aircraft Engines and Power Plants (Mashinostroenie, Moscow, 2008) [in Russian].
  11. D. A. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (McGraw-Hill, New York, 1984; Mir, Moscow, 1990).
  12. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics , Vols. 1 and 2 (Springer, New York, 1988; Mir, Moscow, 1991).
  13. I. E. Idel’chik, Handbook of Hydraulic Resistance (Mashinostroenie, Moscow, 1992; Begell House, Danbury, 1996).



How to Cite

Суровежко А.С., Мартыненко С.И. On Optimization of Technical Devices Based on a Hierarchy of Mathematical Models // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2019. 20. 411-427. doi 10.26089/NumMet.v20r436



Section 1. Numerical methods and applications

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