Advertisement

A Technology for Grid Generation in Volumes Bounded by the Surfaces of Revolutions

  • Alla I. Anuchina
  • Natalya A. ArtyomovaEmail author
  • Vyacheslav A. Gordeychuck
  • Olga V. Ushakova
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 131)

Abstract

A technology for structured grid generation in the volumes bounded by surfaces of revolutions is suggested. The technology is designed for modeling the processes of multi-component hydrodynamics. The technology is developed within variational approach for generation of optimal grids. It includes several types of algorithms for different types of constructions. The basic construction is the volume of revolution obtained by the rotation through 180° about the axis of a generatrix consisting of straight line segments, arcs of circles and ellipses. The generalization of the volumes of revolution (volumes formed by the surfaces of revolution with parallel axes) and constructions obtained by the deformation of the volume of revolution by the another volume of revolution or its generalization are also considered. Algorithms perform the description of the geometry of constructions, generation of initial grids, correction of grids to the boundary of constructions, deformation of grids and constructions, optimization and testing of grids.

References

  1. 1.
    Anuchina, N.N., Volkov, V.I., Gordeychuk, V.A., Es’kov, N.S., Ilyutina, O.S., Kozyrev, O.M.: Numerical simulation of 3D multi-component vortex flows by MAH-3 code. In: Ushakova, O.V. (ed.), Advances in Grid Generation, pp. 337–380. Nova Science, New York (2007)Google Scholar
  2. 2.
    Bronina, T.N.: Algorithm for constructing initial three-dimensional structured grids for the domains of revolution. Proc. Steklov Inst. Math. Suppl. 1, S36–S43 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Khairullina, O.B., Sidorov, A.F., Ushakova, O.V.: Variational methods of construction of optimal grids. In: Thompson, J.F., Soni, B.K., Weatherill, N.P. (eds.), Handbook of Grid Generation, pp. 36-1–36-25. CRC Press, Boca Raton (1999)Google Scholar
  4. 4.
    Killeen, J.: Controlled Fusion. Academic Press, New York (1976)Google Scholar
  5. 5.
    Prokhorova, M.F.: Problems of homeomorphism arising in the theory of grid generation. Proc. Steklov Inst. Math. Suppl. 1, S165–S182 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Staten, M.L., Owen, S.J., Shontz, S.M., Salinger, A.G., Coffey, T.S.: A comparison of mesh morphing methods for 3D shape optimization. In: Quadros, W.R. (eds.) Proceedings of the 20th International Meshing Roundtable, pp. 293–311. Springer, Berlin (2011)CrossRefGoogle Scholar
  7. 7.
    Ushakova, O.V.: Optimization algorithms for three-dimensional grids in domains of rotations. Proc. Steklov Inst. Math. Suppl. 1, S228–S259 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ushakova, O.V.: Nondegeneracy tests for hexahedral cells. Comput. Methods Appl. Mech. Eng. 200, 1649–1658 (2011)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ushakova, O.V.: An algorithm of correcting a grid with respect to the surface of revolution. Vopr. At. Nauki Tekh. Mat. Model. Fiz. Protsessov. 1, 16–27 (2016)Google Scholar
  10. 10.
    Ushakova, O.V.: An algorithm of correcting a grid with respect to a deformed domain of revolution. Vopr. At. Nauki Tekh. Mat. Model. Fiz. Protsessov. 2, 53–65 (2017)Google Scholar
  11. 11.
    Ushakova, O.V.: An algorithm of correcting a grid for a region formed by surfaces of revolution with parallel axes of revolution. Vopr. At. Nauki Tekh. Mat. Model. Fiz. Protsessov. 1, 30–41 (2018)Google Scholar
  12. 12.
    Ushakova, O.V.: Criteria for hexahedral cell classification. Appl. Numer. Math. 127, 18–39 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Zegeling, P.A.: Moving grid techniques. In: Thompson, J.F., Soni, B.K., Weatherill, N.P. (eds.), Handbook of Grid Generation, pp. 37-1–37-22. CRC Press, Boca Raton (1999)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alla I. Anuchina
    • 1
  • Natalya A. Artyomova
    • 2
    Email author
  • Vyacheslav A. Gordeychuck
    • 1
  • Olga V. Ushakova
    • 2
    • 3
  1. 1.Federal State Unitary Enterprise “Russian Federal Nuclear Center–Academician E. I. Zababakhin All-Russian Research Institute of Technical Physics” (FSUE “RFNC-VNIITF”)SnezhinskRussia
  2. 2.Institute of Mathematics and Mechanics named after academician N.N. KrasovskiiEkaterinburgRussia
  3. 3.Ural Federal University named after the first President of Russia B. N. YeltsinEkaterinburgRussia

Personalised recommendations