Geodesic
Incorporation of Fluid Compressibility
Russian journal of nonlinear dynamics, Tome 17 (2021) no. 2, pp. 195-209

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This paper is concerned with assessing the correctness of applying various mathematical models for the calculation of the hydroshock phenomena in technical devices for modes close to critical parameters of the fluid. We study the applicability limits of the equation of state for an incompressible fluid (the assumption of constancy of the medium density) to the simulation of processes of the safety valve operation for high values of pressures in the valve. We present a scheme for adapting the numerical method of S. K. Godunov for calculation of flows of incompressible fluids. A generalization of the method for the Mie – Grüneisen equation of state is made using an algorithm of local approximation. A detailed validation and verification of the developed numerical method is provided, and relevant schemes and algorithms are given. Modeling of the hydroshock phenomenon under the valve actuation within the incompressible fluid model is carried out by the openFoam software. The comparison of the results for the weakly compressible and incompressible fluid models allows an estimation of the applicability ranges for the proposed schemes and algorithms. It is shown that the problem of the hydroshock phenomenon is correctly solved using the model of an incompressible fluid for the modes characterized by pressure ratios of no more than 1000 at the boundary of media discontinuity. For all pressure ratios exceeding 1000, it is necessary to apply the proposed weakly compressible fluid approach along with the Mie – Grüneisen equation of state.
Keywords: hydraulic device, mathematical model, numerical simulation, water, weakly compressible fluid approach
Mots-clés : Godunov’s method, Mie – Grüneisen equation of state, incompressible fluid. 
@article{ND_2021_17_2_a4,
     author = {T. Raeder and V. A. Tenenev and A. A. Chernova},
     title = {Incorporation of {Fluid} {Compressibility}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {195--209},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2021_17_2_a4/}
}
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T. Raeder; V. A. Tenenev; A. A. Chernova. Incorporation of Fluid Compressibility. Russian journal of nonlinear dynamics, Tome 17 (2021) no. 2, pp. 195-209. http://geodesic.mathdoc.fr/item/ND_2021_17_2_a4/