In this study, we introduce a way to control the viscosity of the numerical approximation in the Godunov-like smoothed particle hydrodynamics (SPH) methods. This group of SPH methods includes momentum and energy fluxes in the right-hand sides of the equations, which are calculated by the solution of the Riemann problem between each pair of neighboring particles within the support radius of the smoothing kernel, which is similar to the procedure for the calculation of fluxes across cell boundaries in Godunov schemes. Such SPH methods do not require the use of artificial viscosity since the significant numerical viscosity is already introduced by a Riemann problem solution. We demonstrate that such a numerical viscosity may be measured and obtain the explicit expression for it depending on smoothed particle properties. In particular, we have found that Godunov-like SPH method with interparticle contact algorithms produces numerical viscosity several orders of magnitude higher than physical viscosity in materials. Modern approaches, such as SPH with monotonic upstream-centered scheme for conservation laws or weighted essentially non-oscillatory reconstruction techniques, have not only lower numerical viscosity but also too large for modeling real-world viscous flows. By constructing a correcting viscous stress tensor based on the analytical solution for discontinuous viscous flow, it is possible to reduce the viscous stresses of numerical origin. The use of such a correction makes it possible to improve the agreement with experiments in the simulation of viscous flows without using schemes of higher order reconstruction.

The paper proposes a way to control the viscosity of numerical approximation in the contact SPH method. This variant of SPH contains momentum and energy fluxes in the right-hand sides of the equations, which are calculated using the solution of the Riemann problem between each pair of neighboring particles within the smoothing kernel support radius, which is similar to the procedure for calculating fluxes across cell boundaries in Godunov schemes. Such SPH method does not require the use of artificial viscosity, because the significant numerical viscosity is already introduced by a Riemann problem solution. The magnitude of numerical viscosity decreases linearly with particle size, however, it becomes comparable with the physical viscosity for most materials when the particle size is about $\thicksim 1\,$nm, which hampers the correct accounting for viscous effects in real-life problems. In this study we develop a method for reducing the viscous stresses of numerical origin, for which a correcting viscous stress tensor is constructed on the basis of the analytical solution for discontinuous viscous flow. The use of such correction makes it possible to improve the agreement with the experiment in the simulation of viscous flows.

The parameters of the shock adiabat of a porous material are calculated in the mesoscopic setting with the developed method of a moving window. The porous material is considered a framework of solid material that fills the space between pores, the mechanical properties and shock adiabat of which are often well known. The essence of the method is as follows: uncompressed material flows into the computational box with a constant velocity, while the outflow velocity from the box is chosen based on iterations so as to make the wave front immobile relative to the window, because the stationary mode of shock-wave propagation must be achieved to calculate the shock adiabats. The simulation of shock waves is performed both in the standard setting with an immobile piston (inverse-motion method) and in the system of a moving window. It is demonstrated that the wave profiles obtained with both methods are identical after the stationary mode is achieved. As an example, the shock adiabats of porous copper, which adequately reproduce experimental data for different porosities, are calculated. The proposed mesoscopic method of calculating the response of porous materials to shock compression in a moving window enables direct calculation of desired shock adiabats for porous materials that have not been studied experimentally.

Predictive simulation of the long-term response of multilayer targets with ceramics layers to shock compression demands appropriate material models. Because ceramics are complex brittle materials, which tend to lose their strength under heavy loads, such simulation requires the failure models well-proven for a wide range of strains and strain rates. Standard plate impact experiments provide the main data utilized for developing and validating the mechanical models of material response to shock compression. However, apart from the fact that such experimental data are inherently one-dimensional, they can be insufficient to verify the failure model at relatively low strain rates typical for long unloading waves. Here, we present the experimental results for explosive compression of a spherical multilayer shell initiated by a single detonator. The explosive-coated shell consists of the nested spherical layers: the outer made of boron carbide and the inner of lead. X-ray images showing the evolution of those layers after detonation are then compared with simulation results. Propagation of the compression wave through the layers resulting in ceramics damage is analyzed in detail. We demonstrate that the failure model of boron carbide should be adjusted for compressions below 10 GPa to achieve a good agreement with our experimental images. Such an improved failure model provides the predictive simulation of long-term dynamics of targets after unloading, and it has almost no effect on wave profiles after plate impact.

Ceramic materials have a long-term industrial demand due to their high mechanical hardness and chemical and temperature resistance. They are brittle and tend to lose strength under heavy loads which complicates the development of a comprehensive material model for simulation of engineering prototypes containing ceramic parts. We developed an improved failure model of ceramics based on the well-known Johnson–Holmquist approach. This model redefines the damage rate equation using a consistent definition of the total plastic strain in the failed material. It reduces the number of free model parameters and enables the plastic strain to be explicitly accumulated during the failure process. The corresponding non-iterative algorithm utilizing this explicit failure model is developed. It is successfully validated by simulation of the wave profiles obtained in plate-impact experiments with boron carbide using the contact smoothed particle hydrodynamic method.

Thermonuclear fusion flare, fireball expansion, and evaporation of the liquid-film chamber wall are simulated by combining two one-dimensional (1D) codes DEIRA and RAMPHY. The considered process is divided into two phases: the DEIRA code is used to simulate the fast ignition and burn of a cylindrical target with DT fuel and a lead tamper, while the RAMPHY code is applied to describe the subsequent quasi-spherical expansion of the fireball. By the end of the first phase, the neutron and X-ray output from the target as well as the debris motion are determined. The fast ions are practically fully absorbed by the lead tamper of the fusion target. At the second stage, which starts with the arrival of the main shock at the target surface, the fireball expansion and the behavior of the wall liquid film are considered. The fireball front propagates with a velocity close to the self-similar value. The liquid film is first evaporated by the X-ray pulse, and then by the heat flux generated when the fireball collides with the primary vapor layer. Mechanical loading on the liquid film remains within the 100-MPa range. (C) 2016 Elsevier B.V. All rights reserved.

A mesomechanical simulation of shock loading of porous aluminum has been carried out for thermo-elastic-plastic medium using a modified 2D SPH method. The periodic structure of porous aluminum is set explicitly and possesses the properties of a solid aluminum. The shock compression is modeled by the impingement of a porous plate with a rigid wall. The calculated flow fields of the material show the main moments of loading dynamics: a multiwave shock structure at a low shock intensity, collapse of the pores in a strong shock wave, and the formation of material compaction in two stages at the front, the formation of pressure oscillations behind the shock front, and the influence of thermal conductivity on oscillation damping. The calculated Hugoniot adiabat is in good agreement with the experimental data.

For a plane brittle failure wave in a material loaded by an elastic compression wave, an analytic solution is obtained on the basis of a model with a Drucker-Prager type condition and a given value of the failure wave propagation velocity. The wave failure model supplemented with threshold criteria is generalized to two-dimensional flows in breaking plates. Collision of glass plates with a rigid wall is modelled and three- and two-wave failure structures in the plate are obtained. Some data on the leading elastic wave decay and the arrest of the failure wave under the action of the overtaking unloading that propagates from the region of spread of the fractured material near the wall are obtained.

Radiation hydrodynamics 1D simulations were performed with two concurrent codes, DEIRA and RAMPHY. The DEIRA code was used for DT capsule implosion and burn, and the RAMPHY code was used for computation of X-ray and fast ions deposition in the first wall liquid film of the reactor chamber. The simulations were run for 740 MJ direct drive DT capsule and Pb thin liquid wall reactor chamber of 10 m diameter. Temporal profiles for DT capsule leaking power of X-rays, neutrons and fast He-4 ions were obtained and spatial profiles of the liquid film flow parameter were computed and analyzed.

The thermomechanical processes occurring in the blanket of a heavy-ion inertial thermonuclear fusion reactor are analyzed. The heat-release density in the structural materials and the blanket coolant is calculated on the basis of prescribed characteristics of the neutron pulse from a ~1 GJ microexplosion of a target. Calculations of the nonstationary thermoelastic stress and pressure fields as well the temperature of the wall and blanket coolant are performed using simple one-dimensional models. The amplitude and frequency characteristics of the stress and pressure waves generated by the energy released in the microexplosion are obtained. The thermal relaxation processes occurring in the elements of the blanket between successive microexplosions are analyzed.

An analytical solution for a plane brittle fracture wave in a material loaded by an elastic impact wave is obtained using the failure model with a failure condition of the Drucker Prager type and the given velocity of propagation of the fracture wave. The two-dimensional fracture wave model supplemented by the threshold criteria is used for computing impact failure of glass plates. For the plates with free lateral boundaries threeand two-wave failure structures were revealed. Data on the attenuation of the heading elastic wave and the stoppage of the failure wave under an overtaking release wave are presented.

An improved smoothed particle hydrodynamics (SPH) method is described; in this method, the solution to the Riemann problem in strength media is described. Generalization of this approach to solving heat conduction problems is performed. The improved SPH method is used to solve a wide range of problems. Problems of heat conduction and volume energy release accompanied by spallation effects, simulation of high speed perforation, and propagation of failure waves in brittle materials are considered. Shock wave compression of porous materials and diffraction of detonation waves in heterogeneous explosives are simulated on the mesostructure scale.

The simultaneous development of the MHD instabilities of Raylegh-Taylor and Kelvin-Helmholtz types at the interface between high-conducting plasmoid and surrounding non- or low-conducting gas is considered. The linear stage of the RTI development is studied analytically for incompressible and compressible fluids. The nonlinear stage of the individual development of the RTI and the coupled development of both instabilities has been investigated numerically. The time-dependent two-dimensional numerical model based on the solution of the Euler gasdynamic equations with body momentum and energy sources of MHD origin has been developed and used in calculations. A disturbance introducing in the background flow has been periodic with varied assignment type and wave length. Fundamental difference between the results of linear and nonlinear analysis has been revealed. In particular, the increment of the RTI development at nonlinear stage is one-two order of magnitude less than that predicted by linear theory and rather weakly depends on initial disturbance mode. In linear analysis the coupled development of the RTI and the KHI is determined by simple summing of the two effects in the expression of wave increment, whereas in nonlinear case the mutual influence of the instabilities leads to essential alterations in their development, main of which is the intensive "layer-by-layer" destruction of the plasmoid surface.

Results of hypervelocity impact tests at an electromagnetic launcher with plasma armature are described. The tests were performed with a thick duralumin disk of 80–100mm diameter and of 40mm height impacted by a lexan cylinder of 1.5–3g mass. The projectile velocity amounted to 4–5.5km/s. The launcher operational characteristics are described. In the tests, various configurations of the target fracture were obtained including cratering and spall cracks, disks and cones. The computer simulations were accomplished by means of a 2D axisymmetrical SPH code using interparticle contact algorithms. In these algorithms, stresses and velocity at the contact points of Lagrangian particles are computed by the linear Riemann solver. For description of material failure, a model based on a threshold stress criterion was used. The main features of material distribution and target fracture are reproduced in simulations.

The special features of the concept of a hybrid power-generating plant, which combines the fusion and fission processes in a cylindrical target initiated by a high-power heavy-ion accelerator, are analyzed. The main advantages of the proposed setup are: burning of unenriched 238 U in the reactor cavity, continuous removal of fission products from the core, and impossibility of an uncontrollable nuclear reaction. The characteristics of matched heavy ion accelerator, target, reactor chamber, and blanket with circulating coolant in the blanket are presented, and the power parameters of the electric power plant are estimated.