Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Koroleva M. R., Tenenev V. A. Tabulation of the Riemann problem solution in Godunov method for Soave – Redlich – Kwong equation of state. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 2, pp. 189-202. DOI: 10.18500/1816-9791-2025-25-2-189-202, EDN: FPIOWJ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.05.2025
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
[533+536]:51-73
DOI: 
10.18500/1816-9791-2025-25-2-189-202
EDN: 
FPIOWJ

Tabulation of the Riemann problem solution in Godunov method for Soave – Redlich – Kwong equation of state

Autors: 
Koroleva Maria Ravilevna, Udmurt Federal Research Center of the Ural Branch of the RAS
Tenenev Valentin A., Udmurt Federal Research Center of the Ural Branch of the RAS
Abstract: 
The work is devoted to the using of the exact solutions of the Riemann problem on the decay of an arbitrary discontinuity to describe the real gases flows with the Soave – Redlich – Kwong equation of state. The governing mathematical expressions are formulated for constructing an exact solution to the Riemann problem. The features of the functions included in the solution are investigated. It is demonstrated that the form of the Soave – Redlich – Kwong equation of state does not allow to define explicitly the relationship between pressure and internal energy of the gas. The connection between these is determined through gas temperature that leads to significant complication of the task solution technique on the discontinuities. The arising difficulties are determined, firstly, by the features of the mathematical formulation of the problem. It includes a number of nonlinear equations and definite integrals that require the using of the iterative methods to find an exact Riemann solution. This leads to a significant increase in numerical algorithm complexity. Secondly, the specific behavior of some functions in the mathematical model does not guarantee the correct construction of an exact solution to the Riemann problem in using the iterative methods. All these reasons make the classical approach inappropriate for solving complex problems of nonstationary gas dynamics for a real Soave – Redlich – Kwong gas. The approach proposed in this work uses interpolation of solutions constructed on the preliminary accurate calculations of the Riemann problem, performed without additional assumptions over the entire range of changes in gas-dynamic parameters. The use of tabulated values provides the accuracy of constructing an approximate solution and reduces the complexity of the computational algorithm. In the present work this approach is used for numerical simulation of the hydrogen flow in shock tube in a wide range of gas parameters in the fields of classical and non-classical gas dynamics and for numerical simulation of the gas dynamics of a hydrogen safety valve. The obtained results confirm that the use of tabulated parameters is justified in a wide range of gas parameters variations, and the proposed approach can be used to solve complex problems of non-stationary gas dynamics, including those with areas of mixed nonlinearity.
Key words: 
Riemann problem
Godunov method
real gas
discontinuity decay
Soave – Redlich – Kwong equation of state
solution tabulation
interpolation
Acknowledgments: 
The work was carried out within the framework of the state assignment of the Ural Branch of the Russian Academy of Sciences “Design and development of new research methods in natural sciences, technology and social-humanitarian directions based on deep neural network technologies, machine learning and mathematical modeling” (project No. 22040700011-4).
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Received: 
15.04.2024
Accepted: 
10.09.2024
Published: 
30.05.2025
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