Lagrangian Hydrodynamic Simulations Research Articles

Resolution criteria to avoid artificial clumping in Lagrangian hydrodynamic simulations with a multiphase interstellar medium

ABSTRACT Large-scale cosmological galaxy formation simulations typically prevent gas in the interstellar medium (ISM) from cooling below $\approx 10^4\, \mathrm{K}$. This has been motivated by the inability to resolve the Jeans mass in molecular gas ($\ll 10^5\, \mathrm{M}_{\odot }$) which would result in undesired artificial clumping. We show that the classical Jeans criteria derived for Newtonian gravity are not applicable in the simulated ISM if the spacing of resolution elements representing the dense ISM is below the gravitational force softening length and gravity is therefore softened and not Newtonian. We re-derive the Jeans criteria for softened gravity in Lagrangian codes and use them to analyse gravitational instabilities at and below the hydrodynamical resolution limit for simulations with adaptive and constant gravitational softening lengths. In addition, we define criteria for which a numerical runaway collapse of dense gas clumps can occur caused by oversmoothing of the hydrodynamical properties relative to the gravitational force resolution. This effect is illustrated using simulations of isolated disc galaxies with the smoothed particle hydrodynamics code swift. We also demonstrate how to avoid the formation of artificial clumps in gas and stars by adjusting the gravitational and hydrodynamical force resolutions.

Solutions of the converging and diverging shock problem in a medium with varying density

We consider the solutions of the Guderley problem, consisting of a converging and diverging hydrodynamic shock wave in an ideal gas with a power law initial density profile. The self-similar solutions and specifically the reflected shock coefficient, which determines the path of the reflected shock, are studied in detail for cylindrical and spherical symmetries and for a wide range of values of the adiabatic index and the spatial density exponent. Finally, we perform a comprehensive comparison between the analytic solutions and Lagrangian hydrodynamic simulations by setting proper initial and boundary conditions. A very good agreement between the analytical solutions and the numerical simulations is obtained. This demonstrates the usefulness of the analytic solutions as a code verification test problem.

Piston driven shock waves in non-homogeneous planar media

In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure piston, propagating in a non-homogeneous planar medium consisting of an ideal gas. Power law temporal and spatial dependency is assumed for the piston pressure and initial medium density, respectively. The similarity solutions are written in both Lagrangian and Eulerian coordinates. It is shown that the solutions take various qualitatively different forms according to the value of the pressure and density exponents. We show that there exist different families of solutions, for which the shock propagates at a constant speed, accelerates, or slows down. Similarly, we show that there exist different types of solutions, for which the density near the piston is either finite, vanishes, or diverges. Finally, we perform a comprehensive comparison between the planar shock solutions and Lagrangian hydrodynamic simulations, by setting proper initial and boundary conditions. A very good agreement is reached, which demonstrates the usefulness of the analytic solutions as a code verification test problem.

Investigation of dynamic fragmentation of laser shock-loaded tin at different phases with the integrated diagnostic techniques

We investigated the dynamic fragmentation of laser shock-loaded tin to gain insights on the underlying mechanism of this process. In the experiments, tin samples were shock-loaded by nanosecond laser over sequential pressures ranging from 7 GPa to 43 GPa. Integrated diagnostic techniques, including four-frame optical transverse shadowgraph imaging system, soft recovery, and photonic Doppler velocimetry (PDV), were employed. They provide the shape of the ejecta in the dynamic fragmentation process, the recovered ejecta, as well as the loading parameters. These experimental results were compared with those obtained using one-dimensional Lagrangian hydrodynamics simulation. The crossed results over sequential pressures allowed us to gain better insights on the different dynamic fragmentation processes of spall fracture and micro-spalling, which can help develop reliable models for dynamic fragmentation of triangular-wave shocking metals.

Microsecond ramp compression of a metallic liner driven by a 5 MA current on the SPHINX machine using a dynamic load current multiplier pulse shaping

SPHINX is a 6 MA, 1-μs Linear Transformer Driver (LTD) operated by the CEA Gramat (France) and primarily used for imploding Z-pinch loads for radiation effects studies. Among the options that are currently being evaluated to improve the generator performances are an upgrade to a 20 MA, 1-μs LTD machine and various power amplification schemes, including a compact Dynamic Load Current Multiplier (DLCM). A method for performing magnetic ramp compression experiments, without modifying the generator operation scheme, was developed using the DLCM to shape the initial current pulse in order to obtain the desired load current profile. In this paper, we discuss the overall configuration that was selected for these experiments, including the choice of a coaxial cylindrical geometry for the load and its return current electrode. We present both 3-D Magneto-hydrodynamic and 1D Lagrangian hydrodynamic simulations which helped guide the design of the experimental configuration. Initial results obtained over a set of experiments on an aluminium cylindrical liner, ramp-compressed to a peak pressure of 23 GPa, are presented and analyzed. Details of the electrical and laser Doppler interferometer setups used to monitor and diagnose the ramp compression experiments are provided. In particular, the configuration used to field both homodyne and heterodyne velocimetry diagnostics in the reduced access available within the liner's interior is described. Current profiles measured at various critical locations across the system, particularly the load current, enabled a comprehensive tracking of the current circulation and demonstrate adequate pulse shaping by the DLCM. The liner inner free surface velocity measurements obtained from the heterodyne velocimeter agree with the hydrocode results obtained using the measured load current as the input. An extensive hydrodynamic analysis is carried out to examine information such as pressure and particle velocity history profiles or magnetic diffusion across the liner. The potential of the technique in terms of applications and achievable ramp pressure levels lies in the prospects for improving the DLCM efficiency through the use of a closing switch (currently under development), reducing the load dimensions and optimizing the diagnostics.

A role for electron viscosity in plasma shock heating

The contribution of electron viscosity to shock heating of high-Z plasmas is investigated. A classical shock profile calculation is employed to show that the electron viscosity substantially affects the structure of strong shock waves in a fully ionized plasma by reducing the overheating of the ions in the viscous subshock. This effect is present for an average ion charge Z above 10. Computer simulations of Z-pinch implosions are then employed to demonstrate that this effect of electron viscosity can also be accounted for in Lagrangian hydrodynamic simulations that use artificial viscosity. This is accomplished by dividing the corresponding viscous heat release between the ion and electron components of the plasma according to the ratio of their physical viscosities. When this is done in the time-varying, ionizing plasma environment of Z-pinch implosions that are theoretically designed to generate K-shell emission in titanium and krypton, it is found that electron viscous heating can be substantial, leading to sizable reductions in ion temperatures and 10%–20% increases in K-shell emission under certain implosion conditions.

Two-dimensional model of thermal smoothing of laser imprint in a double-pulse plasma

The laser prepulse effect on the thermal smoothing of nonuniformities of target illumination is studied by means of a two-dimensional Lagrangian hydrodynamics simulation, based on the parameters of a real experiment. A substantial smoothing effect is demonstrated for the case of an optimum delay between the prepulse and the main heating laser pulse. The enhancement of the thermal smoothing effect by the laser prepulse is caused by the formation of a long hot layer between the region of laser absorption and the ablation surface. A comparison with experimental results is presented.

2D Modeling of thermal smoothing of laser imprint in a double-pulse plasma

Laser prepulse effect on thermal smoothing of non-uniformities of target illumination is studied by means of 2D Lagrangian hydrodynamics simulation, based on parameters of real experiment. A substantial smoothing effect is demonstrated in case of an optimum delay between the prepulse and main heating laser pulse. The cause of enhancement of thermal smoothing effect by laser prepulse is the formation of long hot layer between the region of laser absorption and ablation surface. Comparison with experimental results is presented.