A general formulation of the thin-shell approximation for axisymmetric, hypersonic, hydromagnetic flows

Statistics – Computation

Scientific paper

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Axisymmetric Flow, Hypersonic Flow, Magnetohydrodynamic Flow, Shock Waves, Stellar Models, Thin Walled Shells, Approximation, Astrophysics, Boundary Value Problems, Computational Fluid Dynamics, Conservation Laws, Gas Dynamics, Thickness, Time Dependence

Scientific paper

Many gas dynamic problems in astrophysics involve the hypersonic expansion of a material shell supported by pressure forces. The thin-shell approximation basically consists of treating the shell as a two-dimensional surface. Various restricted versions of this approximation are often employed in axisymmetric configurations to determine either the motion of the shell under the condition that it contains a negligible mass, or the steady state geometrical form of the shell whenever the inertial terms are included. In this paper, a general system of time-dependent equations for the axisymmetric, hypersonic, hydromagnetic flow of a swept-up massive shell is formulated based upon the thin-shell approximation. The method of analysis incorporates previously considered physical aspects, such as the centrifugal correction, with the following new features: thermal pressure within the shell, finite thickness of the shell, and magnetic fields.

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