One-Dimensional Flows of a Polytropic Gas: Lie Group Classification, Conservation Laws, Invariant and Conservative Difference Schemes

DOI10.1007/978-981-16-4683-6_2zbMath1504.35024arXiv2011.14397OpenAlexW3107712397MaRDI QIDQ5050875

Vladimir Dorodnitsyn, R. V. Kozlov, Sergey V. Meleshko

Publication date: 18 November 2022

Published in: Nonlinear Physical Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.14397

zbMATH Keywords

spherically symmetric flowsradially symmetric flowsplain one-dimensional flows

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Symmetries, invariants, etc. in context of PDEs (35B06) Axially symmetric solutions to PDEs (35B07)

Cites Work

• Transformation groups in network spaces
• A new conservation theorem
• Applications of symmetry methods to partial differential equations
• Nonlocal symmetries. Heuristic approach
• The ``PODMODELI program. Gas dynamics
• Non-local symmetries and conservation laws for one-dimensional gas dynamics equations.
• Magnetohydrodynamics and fluid dynamics: action principles and conservation laws
• Conservative difference schemes for one-dimensional flows of polytropic gas
• One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: symmetry classification, conservation laws, difference schemes
• Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models
• Lie group classification of second-order ordinary difference equations
• Continuous symmetries of difference equations
• Scaling symmetries, conservation laws and action principles in one-dimensional gas dynamics
• Thermodynamically matched difference schemes
• Applications of Lie Groups to Difference Equations
• Invariant variation problems
• Symmetry-preserving difference schemes for some heat transfer equations
• A Heat Transfer with a Source: the Complete Set of Invariant Difference Schemes
• Continuous symmetries of Lagrangians and exact solutions of discrete equations
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Symmetries, Conservation Laws, Invariant Solutions and Difference Schemes of the One-dimensional Green-Naghdi Equations
• Invariant conservation law-preserving discretizations of linear and nonlinear wave equations
• Variational principles in continuum mechanics
• Symmetries and differential equations
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