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compressible fluid; Navier-Stokes equations; hydraulic systems
The aim of this paper is to proceed in the study of the system which will be specified below. The system concerns fluid flow in a simple hydraulic system consisting of a pipe with generator on one side and a valve or some more complicated hydraulic elements on the other end of the pipe. The purpose of the research is a rigorous mathematical analysis of the corresponding linearized system. Here, we analyze the linearized problem near the fixed steady state which already have been explicitly described. The theory of mixed linear partial differential systems and other tools are applied to derive as explicit form of the solution as possible.
[1] Čarnyj, I. A.: Unsteady Motion of Real Fluid in Pipes. Nedra, Moscow (1975).
[2] Evans, L. C.: Entropy and Partial Differential Equations. Department of Mathematics, UC Berkeley (2008).
[3] Glikson, A.: Some case of non-uniform and non-steady state of gas-mixture. Rend. Mat., VI. Ser. 3 451-479 (1970).
[4] Landau, L. D., Akhiezer, A. I., Lifshitz, E. M.: General Physics Mechanics and Molecular Physics. Nauka, Moscow (1969).
[5] Rajagopal, K. R., Tao, L.: Mechanics of Mixtures. Series on Advances in Mathematics for Applied Sciences 35 World Scientific, Singapore (1995). MR 1370661 | Zbl 0941.74500
[6] Ruzicka, M. C.: On bubbles rising in line. Int. J. Multiphase Flow 26 (2000), 1141-1181. DOI 10.1016/S0301-9322(99)00078-6 | Zbl 1137.76730
[7] Šklíba, J., Straškraba, I., Štengl, M.: Extended mathematical model of safety hydraulic circuit. Report SVÚSS Běchovice, Czech Republic registered as: SVÚSS 88-03022, December 1988.
[8] Soo, S. L.: Fluid Dynamics of Multiphase Systems. Blaisdell Publishing Company. A Division of Ginn and Company Waltham, Ma.-Toronto-London (1967). Zbl 0173.52901
[9] Straškraba, I.: Fully nonlinear two-phase flow. Acta Technica 3 (2014), 215-220. MR 3243606
[10] Straškraba, I., Vitásek, E.: The flow of a liquid with cavitation. J. Concr. Appl. Math. 8 (2010), 668-681. MR 2641512
[11] Wallis, G. B.: One-Dimensional Two Phase Flows. McGraw-Hill, New York (1969).
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