Invariant functional forms for k(p,p) type equations of state for hydrodynamically driven flow.

Hrbek, G.

Technical Information Center Oak Ridge Tennessee

关键词: Computer codes;    Hydrodynamics;    Shock waves;    Equations of state;    Mach number;   

RP-ID  :  DE2001783303

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

A complete Lie group analysis of the general ID hydrodynamic flow problem for a general K(p,P) type equation of state is presented. Since many equations of state (e.g., Vinet, Birch-Murnaghan, Shaker, ant Tait) are of this form, one can use the techniques presented here to study their behavior. Making use of the full transformation group, the hyperbolic conservation laws for mass, momentum, and energy reduce to non-linear, ordinary differential equations. These equations describe the density, particle velocity, and pressure behind the shock as functions of the shock from Mach number. Note that unlike the classical result that defines the flow only at the strong shock limit, in this analysis the Mach number is allowed to be one or greater. This allows the behavior of a shocked material to be described down to the acoustic limit. This technique is illustrated using the Tait EOS for a shock moving through NaC1. Finally, the ratios of the group parameters are shown to have definite physical meanings defined in terms of the equation of state and the physical conditions occurring during the event that has produced the shock wave.