Analytical methods for the hydrodynamical evolution of supernova remnants. II - Arbitrary form of boundary conditions

Details Analytical methods for the hydrodynamical evolution of supernova remnants. II - Arbitrary form of boundary conditions Analytical methods for the hydrodynamical evolution of supernova remnants. II - Arbitrary form of boundary conditions

Oct 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...249..761g&link_type=abstract

Astrophysical Journal, Part 1, vol. 249, Oct. 15, 1981, p. 761-786.

Astronomy and Astrophysics

Astrophysics

6

Boundary Conditions, Boundary Value Problems, Cosmology, Hydrodynamic Equations, Iterative Solution, Pressure Distribution, Supernova Remnants, Adiabatic Flow, Astronomical Models, Density Distribution, Entropy, Nebulae, Shock Wave Propagation

Scientific paper

A generalized formalism is introduced to obtain formulas which are valid for the most general boundary conditions at the outer edge when computing the hydrodynamical evolution of supernova remnants. The higher orders of the approximation are based on an iteration method, and the second-order solution gives the pressure distribution with a relative accuracy of 0.0001 in self-similar cases. The assumption of a linear pressure distribution is shown to imply self-similarity of the flow whenever the entropy distribution is a power law. The problem of adiabatic, spherical self-similar flow is also considered, and the original system of equations is reduced to a single, nonlinear, first-order differential equation in dimensionless coordinates with an explicit parametric family of solutions. A completely integrable family of solutions is obtained, and is found to represent strong shock propagation through a homologously contracting outer medium, where the density distribution is a power law.

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