New conserved integrals and invariants of radial compressible flow in n > 1 dimensions
| Autor: | Stephen C. Anco, Sara Seifi, Amanullah Dar |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 479 |
| ISSN: | 1471-2946 1364-5021 |
| DOI: | 10.1098/rspa.2022.0743 |
| Popis: | Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in $n>1$ dimensions. Apart from entropy, which is a well-know invariant, three additional invariants are found from an explicit determination of invariants up to first-order. One holds for a general equation of state, and the two others hold only for entropic equations of state. A recursion operator on invariants is presented, which produces two hierarchies of higher-order invariants. Each invariant yields a corresponding integral invariant, describing an advected conserved integral on transported radial domains. In addition, a direct determination of kinematic conserved densities uncovers two "hidden" non-advected conserved integrals: one describes enthalpy-flux, holding for barotropic equations of state; the other describes entropy-weighted energy, holding for entropic equations of state. A further explicit determination of a class of first-order conserved densities shows that the corresponding non-kinematic conserved integrals on transported radial domains are equivalent to integral invariants, modulo trivial densities. Comment: 20 pages. Discussion of scaling properties and analysis applications of the new conserved integrals has been added |
| Databáze: | OpenAIRE |
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