One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes. (English) Zbl 1504.35024
Luo, Albert C. J. (ed.) et al., Symmetries and applications of differential equations. In memory of Nail H. Ibragimov (1939–2018). Beijing: Higher Education Press; Singapore: Springer. Nonlinear Phys. Sci., 61-98 (2021).
Summary: The chapter considers one-dimensional flows of a polytropic gas in the Lagrangian coordinates in three cases: plain one-dimensional flows, radially symmetric flows, and spherically symmetric flows. The one-dimensional flow of a polytropic gas is described by one second-order partial differential equation in the Lagrangian variables. The Lie group classification of this PDE is performed. Its variational structure allows to construct conservation laws with the help of Noether’s theorem. These conservation laws are also recalculated for the gas dynamics variables in the Eulerian and mass Lagrangian coordinates. Additionally, invariant and conservative difference schemes are provided.
For the entire collection see [Zbl 1478.34001].
For the entire collection see [Zbl 1478.34001].
MSC:
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35B07 | Axially symmetric solutions to PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
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