On some classes of solutions of aerohydromechanic equations


The article gives a review of the method of constructing parametric solutions of polynomial form for systems of partial differential equations and its application to some aerohydromechanic equations. For example the parametric solutions are constructed and their classification is carried out for the system of equations, describing the plane flows of the ideal gas with the constant entropy. Particularly, the solutions of simple wave type are demonstrated. Also the solutions of transonic equations, describing flows of gas with local supersonic zones in Laval nozzles are obtained.

About the authors

Yulia A Kazakova

Ulyanovsk State Technical University

Email: kazakovaua@mail.ru
аспирант, каф. высшей математики; Ульяновский государственный технический университет; Ulyanovsk State Technical University


  1. Velmisov P. A., Todorov M. D., Kazakova Yu. A. Some classes of the solutions of aerohydromechanic equations, Proc. of the 34th Conference on Applications of Mathematics in Engineering and Economics (AMEE 08) // AIP Conf. Proc., 2009. Vol. 1067, no. 1. Pp. 427-441.
  2. Вельмисов П. А., Казакова Ю. А., Васильева А. А. Некоторые классы решений уравнений газовой динамики / В сб.: Математические методы и модели: теория, приложения и роль в образовании. Ульяновск: УлГТУ, 2009. С. 232-242.
  3. Вельмисов П. А., Казакова Ю. А., Сагдеева Ю. К. О некоторых классах решений уравнений аэрогидромеханики / В сб.: Прикладная математика и механика. Ульяновск: УлГТУ, 2009. С. 285-291.
  4. Рыжов О. С. Исследование трансзвуковых течений в соплах Лаваля. М.: ВЦ АН СССР, 1965. 238 с.
  5. Рыжов О. С. О работе сопел Лаваля в нерасчетных режимах // Ж. вычисл. мат. и мат. физ., 1967. Т. 7, № 4. С. 859-866.
  6. Velmisov P. A., Krupennikov A. V., Kazakova Yu. A. On some classes of solutions of differential equations with partial derivatives; applications in gas dynamics (in Russian) / In: Education, science and economics at universities. Integration to international educational area: International conference (Plock, Poland, 20-25 September 2010). Plock: University in Plock, 2010. Pp. 384-394.
  7. Adamson T. C. Unsteady transonic flows in two-dimensional channels // J. Fluid Mech., 1972. Vol. 52, no. 3. Pp. 437-449.



Abstract - 24

PDF (Russian) - 8


Article Metrics

Metrics Loading ...


  • There are currently no refbacks.

Copyright (c) 2011 Samara State Technical University

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies