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arXiv · 2205.10950

New conserved integrals and invariants of radial compressible flow in $n>1$ dimensions

Stephen C. Anco·Sara Seifi·Amanullah Dar
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Abstract

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.

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Stephen C. Anco, Sara Seifi, Amanullah Dar. 2023-02-21. New conserved integrals and invariants of radial compressible flow in $n>1$ dimensions. https://doi.org/10.1098/rspa.2022.0743

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