Method SMIF for Incompressible Fluid Flows Modeling

  • Valentin Gushchin
  • Pavel Matyushin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


For solving of the Navier-Stokes equations describing 3D incompressible viscous fluid flows the Splitting on physical factors Method for Incompressible Fluid flows (SMIF) with hybrid explicit finite difference scheme (second-order accuracy in space, minimum scheme viscosity and dispersion, capable for work in the wide range of Reynolds (Re) and internal Froude (Fr) numbers and monotonous) based on the Modified Central Difference Scheme and the Modified Upwind Difference Scheme with a special switch condition depending on the velocity sign and the signs of the first and second differences of the transferred functions has been developed and successfully applied. At the present paper the description of the numerical method SMIF and it’s application for simulation of the 3D separated homogeneous and density stratified fluid flows around a sphere are demonstrated.


direct numerical simulation viscous fluid visualization of vortex structures flow regime formation mechanisms of vortices sphere 


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  1. 1.
    Lin, Q., Lindberg, W.R., Boyer, D.L., Fernando, H.J.S.: Stratified flow past a sphere. J. Fluid Mech. 240, 315–354 (1992)CrossRefGoogle Scholar
  2. 2.
    Chomaz, J.M., Bonneton, P., Hopfinger, E.J.: The structure of the near wake of a sphere moving horizontally in a stratified fluid. J. Fluid Mechanics 254, 1–21 (1993)CrossRefGoogle Scholar
  3. 3.
    Belotserkovskii, O.M., Gushchin, V.A., Konshin, V.N.: Splitting method for studying stratified fluid flows with free surfaces. Zh. Vychisl. Mat. i Mat. Fiz (Computational Mathematics and Mathematical Physics) 27, 594–609 (1987)MathSciNetGoogle Scholar
  4. 4.
    Gushchin, V.A., Konshin, V.N.: Computational aspects of the splitting method for incompressible flow with a free surface. J. Computers and Fluids 21(3), 345–353 (1992)CrossRefzbMATHGoogle Scholar
  5. 5.
    Gushchin, V.A., Kostomarov, A.V., Matyushin, P.V., Pavlyukova, E.R.: Direct Numerical Simulation of the Transitional Separated Fluid Flows Around a Sphere and a Circular Cylinder. J. of Wind Engineering and Industrial Aerodynamics 90(4-5), 341–358 (2002)CrossRefGoogle Scholar
  6. 6.
    Gushchin, V.A., Kostomarov, A.V., Matyushin, P.V.: 3D visualization of the separated fluid flows. Journal of Visualization 7(2), 143–150 (2004)CrossRefGoogle Scholar
  7. 7.
    Gushchin, V.A., Matyushin, P.V.: Vortex formation mechanisms in the wake behind a sphere for 200 < Re < 380. Fluid Dynamics 41(5), 795–809 (2006)CrossRefzbMATHGoogle Scholar
  8. 8.
    Baydulov, V.G., Matyushin, P.V., Chashechkin, Y.D.: Structure of a diffusion-induced flow near a sphere in a continuously stratified fluid. Doklady Physics 50(4), 195–199 (2005)CrossRefGoogle Scholar
  9. 9.
    Baydulov, V.G., Matyushin, P.V., Chashechkin, Y.D.: Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid. Fluid Dynamics 42(2), 255–267 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gushchin, V.A., Mitkin, V.V., Rozhdestvenskaya, T.I., Chashechkin, Y.D.: Numerical and experimental study of the fine structure of a stratified fluid flow over a circular cylinder. Journal of Applied Mechanics and Technical Physics 48(1), 34–43 (2007)CrossRefGoogle Scholar
  11. 11.
    Gushchin, V.A., Matyushin, P.V.: Numerical Simulation and Visualization of Vortical Structure Transformation in the Flow past a Sphere at an Increasing Degree of Stratification. Comput. Math. and Math. Physics 51(2), 251–263 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Gushchin, V.A., Rozhdestvenskaya, T.I.: Numerical study of the effects occurring near a circular cylinder in stratified fluid flows with short buoyancy periods. Journal of Applied Mechanics and Technical Physics 52(6), 905–911 (2011)CrossRefGoogle Scholar
  13. 13.
    Matyushin, P.V., Gushchin, V.A.: Transformation of Vortex Structures in the wake of a sphere moving in the stratified fluid with decreasing of internal Froude Number. J. Phys.: Conf. Ser. 318, 62017 (2011)CrossRefGoogle Scholar
  14. 14.
    Gushchin, V.A., Narayanan, P.S., Chafle, G.: Parallel computing of industrial aerodynamics problems: clean rooms. In: Schiano, P., Ecer, A., Periaux, J., Satofuka, N. (eds.) Parallel CFD 1997. Elsevier Science B.V. (1997)Google Scholar
  15. 15.
    Chong, M.S., Perry, A.E., Cantwell, B.J.: A general classification of three-dimensional flow field. Phys. Fluids A2(5), 765–777 (1990)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Valentin Gushchin
    • 1
  • Pavel Matyushin
    • 1
  1. 1.Institute for Computer Aided DesignRussian Academy of SciencesMoscowRussia

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