Bulletin of the American Physical Society
16th APS Topical Conference on Shock Compression of Condensed Matter
Volume 54, Number 8
Sunday–Friday, June 28–July 3 2009; Nashville, Tennessee
Session B4: CM1: Continuum Modeling 
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Chair: Yasuyuki Horie, Eglin Air Force Base Room: Hermitage D 

B4.00001: ABSTRACT WITHDRAWN 
Monday, June 29, 2009 9:15AM  9:30AM 
B4.00002: Development of a Thermal Model for Hypervelocity Impact into Aerogel William Anderson, Frank Cherne The STARDUST mission was the first to return cometary material from a known source. The spacecraft passed through the comet's coma at a relative velocity of 6.5 km/s, collecting the dust particles by impact into very lowdensity silica aerogel. The low impedance of the aerogel allowed shock stress to remain low, but at the expense of producing very high shock temperatures, which thermally compromised the samples. To support the sample analysis community, we are developing a new model to invert impact track geometries to get detailed thermal histories of some samples during capture. This project requires development of a specialized hydrocode that can deal with large lengthscale disparities and extreme volumetric compressions, while remaining capable of being run efficiently. Also required are material models for the shocked aerogel with accurate thermodynamic, mechanical, and transport properties at a wide range of conditions. We present results for this project and discuss problems that remain. [Preview Abstract] 
Monday, June 29, 2009 9:30AM  9:45AM 
B4.00003: Analytical Solution for Isentropic Flows in Solids Olivier Heuze In 1860, Riemann gave the equations system and the exact solution for the isentropic flows in ideal gases. This solution is based on the hypergeometric function. For monatomic, diatomic or polyatomic gases, the polytropic exponent is $(2n+1)/(2n1)$ and the solution is obtained through polynoms of degree $n$. We have to notice that, if Riemann uses the polytropic exponent to show the interest in these practical cases, it is more rigorous to use the fundamental derivative, defined by Thompson in 1971, which is an adimensionnal number associated to the convexity of isentropes. Different authors have given further details for this solution: Hadamard (1903), Courant and Friedrichs (1948), Landau and Lifschitz (1959) and Stanyukovitch (1960). But to our knowledge, nothing has been done to apply it for solids. Properties of shock waves in solid materials can often be described by the equation D=c+s u, where D and u are the shock and particle velocities, and c and s properties of the material. We can notice that s is strongly linked to the fundamental derivative. This means that the assumption of constant fundamental derivative is useful for these solids and that we can apply the exact Riemann solution for them. The hypergeometric function remains very complicated in that case, but can be developed in power series which converges very efficiently. Then, if we just change the coefficients of Riemann polynom for polyatomic gases, we obtain a very good approximation for solids. [Preview Abstract] 
Monday, June 29, 2009 9:45AM  10:00AM 
B4.00004: Simulations of pressureinduced phase transitions at the continuum scale Daniel Orlikowski, Roger Minich, Jeff H. Nguyen, Neil C. Holmes To describe pressureinduced phase transitions, we have a developed continuum model and have performed hydrodynamic simulations that are compared to recent rampedcompression experiments in water. The model incorporates modern nucleation theory through scaled quantities for nucleation and growth. The form of the phase fraction order parameter requires a selfconsistent iteration per hydrodynamic time step. We focus our simulations on recent rampcompression experiments of liquid water, where the system undergoes a pressureinduced phase transition into ice VII, however, other systems will be shown. Also, a comparison with other common continuum models will be presented. [Preview Abstract] 
Monday, June 29, 2009 10:00AM  10:15AM 
B4.00005: Numerical study of mixing induced by shock compression Lili Wang The mixing in a stratified cylindrical shell driven by cylindrical shock compression is numerically studied using the 7th order weighted essentially nonoscillatory shockcapturing method, combined with the 3th RungeKutta method. In order to investigate the effect of initial perturbations on the mixing growth, several different spectral shapes were introduced at the outer interface of the shell. In each case, random phases were assigned to each mode and randomized amplitudes were selected from the given spectrum. Three regimes were observed during the evolution history: (1) The shell implodes compressing the inner material. Two mixing zones grow at the shell surfaces due to the interfacial instability. (2) After the shock wave reaches the center and reflects outwards, the shell bounces off and moves back out. (3) At latetime the shell moves less and the two mixing zones grow quite steadily. If the shell is thin enough or the mixing has undergone enough time, the shell is broken up and the two mixing zones join to one. To characterize the mixing evolution, statistical quantities together with the mixing zone width were defined based on the simulation data, such as the actual product, maximum possible product, and mixing fraction. The flow features were analyzed using these measures. It was found that growth of the mixing zone is quite sensitive to the initial perturbation scale. The mixing zone grows more slowly with smaller scale perturbations. The imprint of initial perturbation spectra is obvious in earlytime, but vanishes in latetime, except that the initial perturbation scale varies a lot. [Preview Abstract] 
Monday, June 29, 2009 10:15AM  10:30AM 
B4.00006: Stability and ambiguous representation of shock wave discontinuity in media with arbitrary thermodynamic properties Alexander Likhachev, Andrey Konyukhov, Vladimir Fortov, Alexey Oparin, Sergey Anisimov The nonlinear analysis of the plane shock wave stability in media with arbitrary equation of state has been carried out numerically in a systematic way. The simulation has been conducted in the viscous one and multidimensional formulations. The real and properly constructed model equations of state have been used in calculations. The behavior of neutrally stable shock waves as well as shocks in the region of their ambiguous representation overlapped Hugoniot segments meeting the linear criteria of the shock wave instability [D'yakov, Zh. Eksp. Teor. Fiz. \textbf{27}, 288 (1954)] has been studied. It is shown that unlike linear theory predictions the neutrally stable shock wave perturbations are damped but this process is rather slower than in the case of the absolutely stable shock wave. Within regions of ambiguous representation shocks split with irreversible transition to one of admissible wave configurations. The formation of a cellular detonationlike front structure has been revealed in multidimensional simulation (the region of ambiguous shock representation due to instability condition L$>$1+2M). [Preview Abstract] 
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