# A Theorem on Multiple Frequencies for Three-Dimensional Unsteady Gas Flows

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

Release:

2017, Vol. 3. №1

Title:
A Theorem on Multiple Frequencies for Three-Dimensional Unsteady Gas Flows

For citation: Bautin S. P. 2017. “A Theorem on Multiple Frequencies for Three-Dimensional Unsteady Gas Flows”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 3, no 1, pp. 111-123. DOI: 10.21684/2411-7978-2017-3-1-111-123

Sergei P. Bautin, Dr. Sci. (Phys.-Math), Professor, Department of Higher and Applied Mathematics, Snezhinsk Physical-Technical Institute, National Research Nuclear University MEPhI (Snezhinsk); eLibrary AuthorID, sbautin@usurt.ru

Abstract:

The analytical construction of the exact and approximate flows of the compressible viscous heat conducting gas causes great difficulties. We propose a technique for simulating one-dimensional flows of a compressible viscous heat-conducting gas in which gas-dynamic parameters are presented as infinite sums of harmonics from a spatial variable with unknown coefficients depending on time. For the unknown coefficients, infinite systems of ordinary differential equations are obtained. When the finite number of terms in the trigonometric series is taken into account, the corresponding finite systems are numerically integrate. In this paper, this method investigates the special cases of three-dimensional non-stationary periodic flows. For the unknown coefficients of infinite trigonometric series, an infinite system of ordinary differential equations is obtained. A concrete property of the solutions of this system is established: the multiplicity theorem describing the set of frequencies arising in the solution.

Keywords:

References:

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