Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2014)

Two-dimensional model of solid media to describe fluid waves

About the authors:

Sergey L. Deryabin, Dr. Sci. (Phys.-Math.), Professor, Department of Higher and Applied Mathematics, Ural State University of Railway Transport (Ekaterinburg)
Alexey V. Mezentsev, Senior Lecturer, Department of Higher and Applied Mathematics, Ural State University of Railway Transport (Ekaterinburg)


To describe the propagation of long waves many models of equations of shallow water are used. It should be mentioned, that the models of shallow water cannot provide us with depth distributions of velocity and density of the fluid. This research describes the parameters of the wave model of two-dimensional gas dynamics for the polytropic gas with gas politropy rate equal to 7. Solutions for the two of the initial-boundary value problems describing the current of the fluid from the surface of the bottom to the surface of water are provided. The current has a weak discontinuity within itself and it is, therefore, a piecewise component. Boundary conditions are found: on the bottom surface, on the water surface and on the weak discontinuity. The boundary conditions can be used for numerical calculations.


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