Regularization of the Solution to Degenerate Systems of Algebraic Equations Exemplified by Identification of the Virial Equation of State of a Real Gas

Thermodynamic calculation of a cycle in a two-phase region requires an equation of state of the working medium, which is used as a virial equation with unknown temperature functions. A degenerate system of algebraic equations has been constructed for unknown coefficients, which are the values of vir...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2024-07, Vol.64 (7), p.1381-1395
Main Author: Vikulov, A. G.
Format: Article
Language:English
Subjects:
Algebra
Computational Mathematics and Numerical Analysis
Equations of state
General Numerical Methods
Iterative algorithms
Mathematical analysis
Mathematics
Mathematics and Statistics
Real gases
Regularization
Temperature
Thermodynamics
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Summary:Thermodynamic calculation of a cycle in a two-phase region requires an equation of state of the working medium, which is used as a virial equation with unknown temperature functions. A degenerate system of algebraic equations has been constructed for unknown coefficients, which are the values of virial functions on a temperature mesh. Based on the regularization method, a variational-iterative algorithm for solving a degenerate system of equations has been developed. A computational experiment to confirm the effectiveness of the method was carried out.
ISSN:0965-5425
1555-6662
DOI:10.1134/S096554252470060X