Molecular dynamics simulations of shock waves using the absorbing boundary condition: A case study of methane

Alexey V. Bolesta, Lianqing Zheng, Donald L. Thompson, and Thomas D. Sewell

Phys. Rev. B 76, 224108 – Published 14 December 2007

Abstract

We report a method that enables long-time molecular dynamics (MD) simulations of shock wave loading. The goal is to mitigate the severe interference effects that arise at interfaces or free boundaries when using standard nonequilibrium MD shock wave approaches. The essence of the method is to capture between two fixed pistons the material state at the precise instant in time when the shock front, initiated by a piston with velocity $u_{p}$ at one end of the target sample, traverses the contiguous boundary between the target and a second, stationary piston located at the opposite end of the sample, at which point the second piston is also assigned velocity $u_{p}$ and the simulation is continued. Thus, the target material is captured in the energy-volume Hugoniot state resulting from the initial shock wave, and can be propagated forward in time to monitor any subsequent chemistry, plastic deformation, or other time-dependent phenomena compatible with the spatial scale of the simulation. For demonstration purposes, we apply the method to shock-induced chemistry in methane based on the adaptive intermolecular reactive empirical bond order force field [S. J. Stuart et al., J. Chem. Phys. 112, 6472 (2000)].

Received 5 April 2007

DOI:https://doi.org/10.1103/PhysRevB.76.224108

Authors & Affiliations

Alexey V. Bolesta^*, Lianqing Zheng^†, and Donald L. Thompson^‡

Department of Chemistry, University of Missouri-Columbia, Columbia, Missouri 65211, USA

Thomas D. Sewell^§

Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

^*Present address: Institute of Theoretical and Applied Mechanics, Institutskaja Strasse 4/1, Novosibirsk 630090, Russia.
^†Present address: School of Computational Science, Florida State University, Tallahassee, FL 32306.
^‡thompsondon@missouri.edu
^§sewell@lanl.gov

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Issue

Vol. 76, Iss. 22 — 1 December 2007

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Images

Figure 1
(Color online) Schematic illustration of how the shock absorbing boundary condition is applied. (a) A shock wave is generated in the sample by driving a rigid piston into it with constant velocity $u_{p}$ ; a second piston is contiguous to and equilibrated with the material on the opposite end of the simulation cell. (b) The shock wave reaches the second piston. (c) The second piston begins to move with the same fixed velocity as the first.Reuse & Permissions
Figure 2
Summary of details for determining when the second piston begins to move. (a) Internal energy profile along the shock direction; (b) time evolution of internal energy in the material subvolume (bin) closest to the second piston [zero displacement along the abscissa in (a) corresponds to internal energy $ε_{80}$ in (b)]. The time snapshot in (a) is for $t = 5.45 ps$ ; the line is the linear fit for the shocked material. The dashed horizontal line in (b) shows the extrapolated value for the internal energy, corresponding to the moment when the shock wave reaches piston-2. When the internal energy $ε_{80}$ reaches this value $(t = 5.57 ps)$ , the second piston is assigned a constant velocity $u_{p}$ .Reuse & Permissions
Figure 3
Shock strength dependence of (a) temperature, (b) shock speed, (c) compression ratio, and (d) shock pressure in liquid methane. The initial temperature and density are $111 K$ and $0.42 g ∕ {cm}^{3}$ , respectively. Solid symbols, simulation predictions, open symbols, experiment. Data for pressure, compression ratio, and shock velocity are from Nellis et al. (Ref. 23); temperature measurement is from Radousky et al. (Ref. 24).Reuse & Permissions
Figure 4
Spatial profiles of (a) density, (b) local velocity, (c) internal energy, and (d) temperature along the shock direction, for eight time snapshots before and after the absorbing boundary condition is applied to shocked solid methane. The piston velocity is $3 km ∕ s$ and the initial temperature is $50 K$ . The absorbing boundary condition is applied at $t = 5.57 ps$ (bold trace in the figures). Traces for successive snapshots are shifted vertically for clarity.Reuse & Permissions
Figure 5
(Color) Spatial profiles of (a) density, (b) local velocity, (c) internal energy, and (d) temperature along the shock direction at time $t = 10.0 ps$ for two simulations of shocked methane crystal differing only in the initial sample length. Red lines correspond to the simulation discussed in connection with Fig. 4, for which the absorbing boundary condition was applied at $t = 5.57 ps$ ; black lines correspond to a system twice as long in the shock direction, which has not reached maximum compression by the end of the simulation. The piston velocity is $3 km ∕ s$ and the initial temperature is $50 K$ .Reuse & Permissions
Figure 6
(Color online) Time dependence of molecular carbon cluster size in solid methane shocked with a piston velocity $u_{p} = 11 km ∕ s$ . The initial temperature and density were $50 K$ and $0.53 g ∕ {cm}^{3}$ , respectively. Curves $C_{2}$ , $C_{3}$ , $C_{4}$ , and $C_{5}$ correspond nominally to ethane, propane, isomers of butane, and isomers of pentane, respectively. The vertical dashed line at $t = 2.2 ps$ indicates the time at which the second piston began to move.Reuse & Permissions

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