A characteristics-based method for shock-ramp data analysis

Abstract

For the data analysis problem of shock-ramp compression, i.e., ramp compression after a relatively strong initial shock, a characteristics-based method that strictly deals with the initial hydrodynamic shock is described in detail. Validation of this analysis method using simulated shock-ramp data generated by molecular dynamics and one-dimensional radiation hydrodynamic code is also presented.

Figures (5)

• Figure 1: (a) An illustration of the typical setup of laser driven ramp/shock-ramp experiments relevant to this manuscript. (b) An illustration of the characteristics. The intersect of the i-th right-going (compression) wave and the j-th left-going (rarefaction) wave is labeled as (i,j).
• Figure 2: Typical flow field of planar shock-ramp compression. (a) A sketch of the Lagrangian flow field. The flow field is believed to be isentropic if the initial shock is excluded, i.e., in the shaded area hear. (b) The heatmap of longitudinal stress in an MD simulation of shock-ramped silocon. (c) Near the free surface, the sample undergoes release and recompression after the initial shock, during which the stress and density values follow a different "release curve".
• Figure 3: The actual flow field (a) and its isentropic substitution (b) near the shock breakout event. By setting the pre-shock free surface velocity to $U_H-a_H$, the backward characteristics method would give the correct release fan in the part of flow field of interest here (shaded area). In practice since the jump in $u_{fs}$ is not infinitely sharp, a linear stretch is applied to the $u_{fs}<U_H$ part.
• Figure 4: The remaining error after the $c_L(a)$ iteration converges for the case of shock-ramped silicon shown in Fig. \ref{['fig1']} (b). (a) The basic shock-free algorithm. (b) Our algorithm with explicit treatment of the initial shock. The absolute differences in particle velocity are shown as colors. The two panels shares the same color range.
• Figure 5: Validation of the proposed back-calculation algorithm in simulation data. Six shock-ramp simulation cases generated by non-equilibrium molecular dynamics or the radiation hydrodynamics code MULTIRAMIS1988 are presented. For each case, the free surface velocity profiles, the converged $c_L(a)$ relation, and the reconstructed pressure-density curve are shown. Three different analysis modes are compared against each other: mode 1 is the basic iterative characteristics-based algorithm introduced in Section \ref{['section2']}; mode 2 is a minimum modification of mode 1 that the final integration step follows eqns. \ref{['eq:PrhoH1']} and \ref{['eq:PrhoH2']} rather than eqns. \ref{['eq:Prho01']} and \ref{['eq:Prho02']}; mode 3 is the method proposed by this work. Mode 3 works well for panels (a)-(e) where the initial shock is a simple hydrodynamic shock, but not for panel (f) where the initial shock shows distinctive elastic-plastic two-wave structure.