Verification of the Calculation of Stationary Subsonic Flows and Presentation of Results

  • Victor V. VyshinskyEmail author
  • Grigory B. Sizykh
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 133)


In some regions located far from the streamlined body’s boundary, the flow can be vortex and non-barotropic but the Euler equations model the flow of a viscous gas to high precision. It was assumed that in such regions the consequences of the Euler equations must also be satisfied to high precision. One of these consequences is maximum principle for pressure for subsonic stationary three-dimensional vortex flows of an ideal gas. This maximum principle for pressure includes the Q parameter, the image of the level surfaces of which is currently widely used to visualize the flow pattern. The maximum principle reveals the meaning of the surface Q = 0. It separates the flow regions Q > 0, in which there can be no local pressure maximum points, from the regions Q < 0, where there can be no local pressure minimum points. A similar meaning of the Q parameter was known earlier only for an incompressible fluid. The expression for the Q parameter contains only the first derivatives of the velocity components, which allows determining the sign of the Q parameter even for numerical solutions obtained by low-order approximation methods. The chapter gives examples of the use of this principle for verification of Computational Fluid Dynamic (CFD) simulation results.


Euler equations Navier-Stokes equations Subsonic vortex flows Subsonic maximum principle for pressure Forms of calculated results presentation Verification of calculation results 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (MIPT)DolgoprudnyRussian Federation
  2. 2.Central Aerohydrodynamic Institute named after prof. N.E. ZhukovskyZhukovskyRussian Federation

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