Analysis of simulation technique for steady shock waves in materials with analytical equations of state

Evan J. Reed, Laurence E. Fried, William D. Henshaw, and Craig M. Tarver

Phys. Rev. E 74, 056706 – Published 20 November 2006

Abstract

We calculate and analyze a thermodynamic limit of a multiscale molecular dynamics based scheme that we have developed previously for simulating shock waves. We validate and characterize the performance of the former scheme for several simple cases. Using model equations of state for chemical reactions and kinetics in a gas and a condensed phase explosive, we show that detonation wave profiles computed using the computational scheme are in good agreement with the steady state wave profiles of hydrodynamic direct numerical simulations. We also characterize the stability of the technique when applied to detonation waves and describe a technique for determining the detonation shock speed.

Received 1 February 2006

DOI:https://doi.org/10.1103/PhysRevE.74.056706

Authors & Affiliations

Evan J. Reed^1,*, Laurence E. Fried¹, William D. Henshaw², and Craig M. Tarver¹

¹Chemistry and Materials Science Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
²Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California 94550, USA

^*Electronic address: reed23@llnl.gov

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Vol. 74, Iss. 5 — November 2006

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Images

Figure 1
Rayleigh lines on a Hugoniot for a chemically reactive system with reaction parameter $λ$ . The $λ = 0$ Hugoniot represents the unreacted material and the $λ = 1$ Hugoniot is fully reacted. The straight Rayleigh lines describe the $p − V$ space thermodynamic pathway of a steady shock.Reuse & Permissions
Figure 2
Comparison of ideal gas detonation wave profiles calculated using the TMSST technique and the steady state of hydrodynamic direct numerical simulations. Excellent agreement is achieved behind the shock front.Reuse & Permissions
Figure 3
Comparison of model condensed phase explosive detonation wave profiles calculated using the TMSST technique and the steady state of hydrodynamic direct simulations. Excellent agreement is achieved behind the shock front.Reuse & Permissions
Figure 4
Comparison of the thermodynamic pressure-volume space trajectory of the steady-state wave of direct hydrodynamic simulations to the TMSST technique. The Rayleigh line is shown by the dotted line. The simulation begins at $\frac{V}{V_{0}} = 1$ and proceeds up in pressure as compression occurs. Once initial compression has occurred, the chemical reaction occurs and the trajectory proceeds down the Rayleigh line. Since the chemical reaction results in volume changes slow enough for viscous effects to be negligible, the thermodynamic pressure is equal to the Rayleigh pressure during the chemical reaction portion of the shock.Reuse & Permissions
Figure 5
Simulations at three different shock speeds using the TMSST in a model condensed phase explosive. Shocks at speeds 11.1 and $11.0 km ∕ s$ represent overdriven detonation conditions as in the ACD path in Fig. 1. Shock speed $10.9 km ∕ s$ is represented by path AB in Fig. 1 and is not a valid steady solution. In this case, the TMSST volume diverges when the shock wave mechanical stability conditions are no longer met, indicating there are no steady solutions for that shock speed. In this fashion the shock speed that takes the material to the sonic state (Rayleigh line AEF in Fig. 1) can be determined by bracketing with no prior knowledge of the equations of state or chemical reactions present.Reuse & Permissions
Figure 6
Comparison of the time dependence of the thermodynamic trajectory of a material element flowing through a steady state wave in hydrodynamic simulations to various types of shock thermostatting techniques. The TMSST of this work is unique in that the intermediate states between the shock front and final state of the shock are correctly captured leading to a wave profile in agreement with hydrodynamic direct simulations. The model condensed phase explosive equation of state of Fig. 3 is utilized in these simulations.Reuse & Permissions

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