This paper analyzes weighted essentially non-oscillatory (WENO)-schemes for the solution of one-dimensional Euler equations with a Mie−Grüneisen type of equation of state. The least dissipative and oscillatory modifications of WENO-schemes in characteristic variables with a monotonicity-preserving (MP) limiter are presented. A modified scheme, MP-WENO-SM, is developed, demonstrating the smallest amplitude of oscillations in the solution of the test problems with discontinuous initial data.

Работа посвящена анализу WENO-схем для решения одномерных уравнений Эйлера с уравнением состояния типа Ми-Грюнайзена. Представлены модификации WENO-схем в характеристических переменных с сохраняющим монотонность (monotonicity-preserving, MP) лимитером, являющиеся наименее диссипативными и осциллирующими. Разработана модифицированная схема MP-WENO-SM, демонстрирующая наименьшую амплитуду осцилляций решения на тестовых задачах с разрывными начальными данными.

A mathematical model based on the multiphase Baer–Nunziato model is presented. The effectiveness of this model is demonstrated by numerically solving shock wave problems in condensed matter in the presence of an explicit contact boundary with vacuum. The results of numerical simulation of problems of the interaction of femtosecond laser radiation with an aluminum target are considered. The advantage of using the Baer-Nunziato model compared to a single-phase hydrodynamic model when calculating the dynamics of the contact boundary is demonstrated. The ease of implementation and the ability to easily introduce additional submodels, such as combustion, make this approach attractive for modeling high-energy processes in multiphase media.

Using two-dimensional cylindrically symmetric physical and mathematical model and an algorithm, a numerical investigation of the problem of irradiating a volumetric aluminum target with a single femtosecond laser pulse is carried out. The problem has a number of fundamental and practical applications related to the hardening effect of residual plastic deformations after the passage of a laser-induced shock wave, in particular, laser shock hardening technology, also known in the literature as laser forging, laser riveting, or laser peening. The axial symmetry of laser beam permits one to reduce the dimension of the problem from three to two and save considerable computational resources. Semiempirical equation of state of aluminum in the Mie–Grüneisen form is used with the adjustment of parameters according to the cold curve of the metal and the data of shock-wave experiments. The law of shock wave propagation and attenuation is investigated, and the stages of (1) single, (2) transient, and (3) hemispherical shock wave propagation are identified. The size and shape of the area on which the strengthening effect can be carried out by a single femtosecond laser pulse are described.

Evolution of wavefront geometry during propagation and attenuation of initially planar shock waves generated by femtosecond laser pulses in aluminum is studied. We demonstrate that three stages of shock front inflection take place in consistent hydrodynamics and molecular dynamics simulations. During the first stage, the distance traveled by a near-planar wave D-SW(sic)R-L is smaller than the radius of heated laser spot RL. Wave attenuation is associated with one-dimensional plane (1D) rarefaction wave coming from the free surface. Such rarefaction wave shapes the shock wave to a 1D triangular pressure profile along direction normal to target surface with a shock front followed by an unloading tail. The second transitional stage starts after propagation of D-SW ~ R-L, at which the unloading lateral waves begin to arrive to a symmetry axis of flow and initiate inflection of the initially planar shock front. Next at the third stage, the wavefront geometry is finally rounded and rapid attenuation of shock pressure begins at D-SW?R-L. It is shown that such divergent shock wave cannot generate plastic deformations in aluminum shortly after propagation of D-SW ~ R-L. Thus, we may estimate the maximal peening depth as a radius of focal spot, which sets an upper limit for the laser shock peening. The cessation of plastic deformation is caused by the fall of the shockwave amplitude below the elastic limit. In this case, the elastic-plastic wave transitions to a purely elastic mode of propagation. For large-sized light spots, this transition ends in the 1D mode of propagation.

Laser shock peening with ultrashort laser pulses has been studied by hydrodynamic and atomistic simulations, as well as experimentally. It has been shown that, in contrast to traditional nanosecond pulses, ultrashort laser pulses allow one to increase the produced pressures by two or three orders of magnitude from 1–10 GPa to 1000 GPa (1 TPa). The physics of phenomena changes fundamentally because shock waves generating pressures exceeding the bulk modulus of a metal melt it. It has been shown for the first time that the shock melting depth at pressures about 1 TPa is an order of magnitude larger than the thickness of the melt layer caused by heat conduction. The appearance, propagation, and damping of a melting shock wave in titanium have been studied. The damping of the shock wave makes it possible to modify the surface layer, where the melting regime changes from a fast one in the shock jump to a slow propagation of the melting front in the unloading tail behind the shock wave. It has been shown experimentally that the ultrafast crystallization of the melt forms a solid layer with a structure strongly different from that before the action. The measured depth of this layer is in good agreement with the calculation.

Intense laser radiation leads to irreversible changes in the crystal structure of a target, which are used in laser shock peening technologies. Processes determining the thickness of the residual deformation layer and related residual stresses are studied in this work. It is known that the end of peening is caused by the decaying of the laser shock wave. New information on the transformation of the wave from the elastoplastic to elastic propagation mode under a picosecond impact is obtained. The elastic shock wave is inefficient for peening. The classical configuration with a plastic jump and an elastic precursor ahead of it turns out to disappear during transformation. In this case, the leading edge of the expanding plastic layer gradually decreases its velocity below the bulk velocity of sound, is smeared inside the rarefaction wave, and stops.

The problem of irradiation of a thin gold film deposited on a glass substrate by a narrowly focused single femtosecond laser pulse is considered. Different surface structures can emerge depending on amount of radiation energy absorbed by an irradiated surface.The most important thermal driver for the formation of surface structures is the lateral electron heat flow in the film. This effect consists from three stages: (1) the distribution of the absorbed in the skin layer of laser energy from the frontal boundary of the film to the rear boundary to equalize the temperature; (2) lateral transfer of energy along the film from the center to the edges; (3) cooling and recrystallization of the heated region of the light spot. A model for the study of the effect is presented based on the two-temperature equations of S. I. Anisimov and coauthors and the semi-empirical wide-range equation of state of metal. The model takes into account Gaussian pulse absorption, electron thermal conductivity and electron-ion relaxation in the metal. If the invested energy is large enough, the shock-wave effect on the formation of holes in the film becomes possible. It includes following stages: (1) generation of a shock wave in the glass due to the transfer of energy from the metal; (2) spherization of the formed shock wave, i.e. transition from one-dimensional to two-dimensional propagation mode; (3) transverse propagation of the shock wave in the substrate along the boundary with the film; (4) accumulation of momentum of a film in direction of vacuum. Pressure behind the shock pushes material of a film away from the substrate. When material of a film accumulates enough momentum (and thus velocity in direction to vacuum) it loses connection with substrate. This leads to formation of a hole. Layers of backing material at the same time acting on film as the pistons. A hydrodynamic model for the study of holes formation based on the equations of hydrodynamics of the ideal Euler medium is presented.

The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finite-difference formulation with the help of the simplest linearized version of the classical Godunov scheme. It is experimentally shown that this version guarantees an entropy nondecrease. As a result, the growth of entropy on shock waves can be simulated without using any correction terms or additional conditions.

Описан процесс построения новой модели (бифуркационной модели турбулентности), описывающей течение сплошной среды как в ламинарном, так и турбулентном режимах. Главной ее особенностью является ламинарно-турбулентный переход, возникающий как новое решение уравнения для напряжений Рейнольдса, замыкающего систему RANS (Reynolds-averaged Navier-Stokes). Статья состоит из трех основных разделов. В первом рассказывается о схемах замыкания второго порядка уравнений Навье-Стокса, осредненных по Рейнольдсу. Во втором разделе изложен вывод уравнений модели турбулентного течения в сдвиговом слое. Третий раздел содержит описание модели турбулентного пограничного слоя на плоской пластине. Приводятся расчеты рассматриваемых течений, результаты сравниваются с экспериментальными.

Thin films on substrate are important class of targets for surface nanomodification for plasmonic or sensoric applications. There are many papers devoted to this problem. But all of them are concentrated on dynamics of a film, paying small attention to substrate. In these papers the substrate is just an object absorbing the first shock. Here we present another point of view directed onto dynamics of a substrate. We consider (i) generation of a shock wave (SW) in a support by impact of a contact; (ii) transition from one-dimensional to twodimensional (2D) propagation of SW; (iii) we analyze lateral propagation of the SW along a film-support contact; and (iv) we calculate pressure in the compressed layer behind the decaying SW. This positive pressure acting from substrate to the film accelerates the film in direction to vacuum. Above some threshold, velocity of accelerated film is enough to separate the film from support. In these cases the circle of separation is significantly wider than the circle of the focal laser spot on film surface. Absorbed laser heat exponentially decays around an irradiated spot F = F-c exp(-r(2)/R-L(2)), where R-L is radius of a Gaussian beam, F and F-c are local and central fluences, r is a radius from the axis. While the law of decay for the 2D SW in substrate is the power law. Therefore in our case of powerful laser action the edge of a separation circle is defined by propagation of the SW in the support.

The paper is devoted to the mathematical modeling of the problem of two metal plates impact using two approaches. In the first approach, the problem is solved using three-dimensional Euler equations and the stiffened gas equation of state for the media. The parameters of the equation of state are calibrated using wide-range equations of state computations of the parameters of shock waves which form after the impact. The second approach is based on one-dimensional two-fluid seven-equation model. In simulations of metal plates impact, we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7

In this article, we describe a new mathematical model (bifurcational turbulence model) and justify its suitability for the prediction of laminar and turbulent boundary layer characteristics. The main specific feature of the model is the laminar-turbulent transition, arising as a new solution of the equation for Reynolds stresses, closing the system of Reynolds-averaged Navier-Stokes (RANS) equations. The article is divided into three main parts. The first part describes the RANS and second-order closure conditions together with the premises that we use to obtain the model equations in the closed form. In the second part, we derive the equations of the turbulent-flow model in the shear layer. In the third part, we consider the boundary-layer turbulence transition over a flat plate and present the results of numerical simulations compared with the experimental data.

We investigate behavior of the ruthenium targets under x-ray. In this paper, the two-temperature equation of state for Ru is developed. Electronic spectrum of ruthenium is calculated using density functional theory. We have defined an electron-ion coupling parameter of ruthenium and its two-temperature thermal conductivity. With this input we run our two-temperature hydrodynamic code.

A linearized version of the classical Godunov scheme as applied to nonlinear discontinuity decays is described. It is experimentally shown that this version guarantees an entropy nondecrease, which makes it possible to simulate entropy growth on shock waves. The structure of shock waves after the discontinuity decays is studied. It is shown that the width of the shock waves and the time required for their formation depend on the choice of the Courant number. The accuracy of the discontinuous solutions is tested numerically.

Numerous papers are devoted to the problem of irradiating thin films on the substrate for surface nano-modification. But all of them concern the dynamics of the dynamics, paying almost no attention to substrate just as object of the first shockwave absorption. A different point of view with an emphasis on the dynamics of a substrate is presented. Under powerful laser action upon a thin metal film a hole arises. Its radius depends on the absorbed laser energy. Experimental results, quantitative theoretical model and numerical research are presented and show that the hole formation is influenced by propagation of the shock wave in the substrate, but not in the film itself. Four stages are considered. (i) Shockwave generation in a support because of an impact of a contact. (ii) Transition from one-dimensional to two-dimensional propagation of the shockwave. (iii) Lateral propagation of the shockwave along a film-support contact. And (iv) calculating pressure in the compressed layer behind the decaying shockwave. This positive pressure acting from substrate on the film accelerates the film in direction to vacuum. Above some threshold, velocity of accelerated film is enough to separate the film from support. In these cases the circle of separation is significantly wider than the focal laser spot on film surface.