Some New Approaches to Solving Navier-Stokes Equations for Viscous Heat-Conducting Gas

  • Vladimir V. Shaydurov
  • Galina I. Shchepanovskaya
  • Maxim V. Yakubovich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)


The algorithm for numerical solving the Navier-Stokes equations for two-dimensional motion for viscous heat-conducting gas is proposed. The discretization of equations is performed by a combination of a special version of the trajectory method for a substantial derivative and the finite element method with piecewise bilinear basis functions for other terms. The results of numerical studies of the structure of a supersonic flow in a plane channel with an obstacle for a wide range of Mach numbers and Reynolds numbers are presented. Velocity and pressure fields are investigated, and the vortex structure of flow is studied in the circulation area of the obstacle.


Navier-Stokes equations viscous heat-conducting gas numerical modeling trajectories finite element method 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vladimir V. Shaydurov
    • 1
    • 2
  • Galina I. Shchepanovskaya
    • 1
  • Maxim V. Yakubovich
    • 1
  1. 1.Institute of Computational Modeling of Siberian BranchRussian Academy of ScienceKrasnoyarskRussia
  2. 2.Beihang UniversityBeijingChina

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