Title:THE EXISTENCE AND STABILITY OF RELATIVISTIC SHOCK
WAVES: GENERAL CRITERIA
AND NUMERICAL SIMULATIONS FOR A NON-CONVEX EQUATION OF STATE
Authors:P.V.Tytarenko, V.I.Zhdanov (Astronomical Observatory of
Kyiv Schevchenko
University, 3 Observatorna St., Kyiv--53, UA-254053, Ukraine)
A small viscosity approach to discontinuous flows is discussed in relativistic hydrodynamics with a general (possibly, non-convex) equation of state that typically occurs in the domains of phase transitions. Different forms of criteria for the existence and stability of relativistic shock waves, such as evolutionarity conditions, entropy criterion and corrugation stability conditions are compared with the requirement of the existence of shock viscous profile. The latter is shown to be most restrictive in case of a single-valued shock adiabat expressed as a function of pressure. One-dimensional numerical simulations with artificial viscosity for a simple piecewise-linear equation of state are carried out to illustrate the criteria in the case of planar and spherical shock waves. The effect of a phase transition domain on the shock amplitude in the process of a hydrodynamical spherical collapse is demonstrated.
Key words: relativistic hydrodynamics, shock waves, anomalous equation
of state, instabilities, numerical methods
Comments: Figs. 5, Refs. 15, Tabs. 0.
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