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Khabakhpasheva T.I.,Lavrentyev Institute of Hydrodynamics | Korobkin A.A.,University of East Anglia
Journal of Fluids and Structures | Year: 2013

The problem of elastic wedge impact onto the free surface of an ideal incompressible liquid of infinite depth is considered. The liquid flow is two-dimensional, symmetric and potential. The side walls of the wedge are modelled as Euler beams, which are either simply supported or connected to the main structure by linear springs. The liquid flow, the deflection of wedge walls and the size of wetted region are determined simultaneously within the Wagner theory of water impact. We are concerned with the impact conditions of strong coupling between the hydrodynamic loads and the structural response. The coupling is well pronounced for elastic wedges with small deadrise angles. This is the case when the fully nonlinear models fail and approximate models based on the Wagner approach are used. In contrast to the existing approximate models, we do not use any further simplifications within the Wagner theory. Calculations of the velocity potential are reduced to analytical evaluation of the added-mass matrix. Hydrodynamic pressures are not evaluated in the present analysis. In order to estimate the maximum bending stresses, both stages when the wedge surface is partially and totally wetted are considered.Three approximate models of water impact, which are frequently used in practical computations, are examined and their predictions are tested against the present numerical solution obtained by the normal mode method within the Wagner theory. It is shown that the decoupled model of elastic wedge impact, which does not account for the beam inertia, provides a useful formula for estimating the maximum bending stress in thick wedge platings. © 2012 Elsevier Ltd.

Khludnev A.,Lavrentyev Institute of Hydrodynamics
European Journal of Mechanics, A/Solids | Year: 2012

In the paper, we propose an elastic plate model with delaminated thin rigid inclusions and provide mathematical analysis of the model. Both vertical and horizontal displacements of the plate are taken into account. It is assumed that the inclusion is delaminated which leads to an appearance of a crack. To provide a mutual non-penetration between crack faces we impose non-linear boundary conditions at the crack faces with unknown set of a contact. A correct problem formulation is proposed, and an existence of solutions is proved for different locations of the rigid inclusion inside of the elastic body. © 2011 Elsevier Masson SAS. All rights reserved.

Karabut E.,Lavrentyev Institute of Hydrodynamics
Comptes Rendus - Mecanique | Year: 2013

Some approach to the solution of boundary value problems for finding functions that are analytical in a wedge is proposed. If the ratio of the angle at the wedge vertex to the number π is rational, then the boundary value problem is reduced to the finite system of ordinary differential equations. Such approach, applied to the problem of inertial motion of a liquid wedge, made it possible to sum the series with small denominators arising in the problem and find four exact examples of self-similar flows with a free boundary. © 2013 Académie des sciences.

Khludnev A.,Lavrentyev Institute of Hydrodynamics
European Journal of Mechanics, A/Solids | Year: 2010

In the paper, an optimal control problem of crack growth is considered, allowing to choose the most safe inclusions in elastic bodies from the standpoint of their influence on a crack propagation. © 2009 Elsevier Masson SAS. All rights reserved.

Kupershtokh A.L.,Lavrentyev Institute of Hydrodynamics
Computers and Mathematics with Applications | Year: 2011

We propose several simple interpolations of the isotherms for real fluids in the region below the binodal curve, where data concerning the equation of state is absent, especially in the thermodynamically prohibited region. All interpolations satisfy the boundary conditions at the points on the binodal curve. The Maxwell rule is also fulfilled. As an example, we construct several isotherms for real water. The data for the isotherms of water, in the liquid and vapor states, is given in tabular form. All smooth interpolations of the isotherms show similar hydrodynamic behavior of two-phase systems in LBE simulations. The reduced specific volumes of the liquid and vapor phases and the reduced pressure on the binodal curve obtained in the LBE simulations for the different interpolations agree well with the experimental data for real EOS of water. The surface tension depends on the form of the interpolation of the isotherm under the binodal curve. Hence, the value of surface tension can be varied in some range by changing the interpolation curve. Actually, our variant of the LBE method allows one to obtain the values of the liquid and vapor densities at the interface corresponding to the saturation curve of real fluids with high accuracy. At low temperatures, the large values of the liquid-to-vapor density ratio can be obtained, in accordance with the EOS of real fluids. © 2011 Elsevier Ltd. All rights reserved.

Kupershtokh A.L.,Lavrentyev Institute of Hydrodynamics
Computers and Mathematics with Applications | Year: 2014

The three-dimensional simulations of an anisotropic decay of binary mixtures of a dielectric liquid with solute gas in a strong electric field are carried out. The Lattice Boltzmann Equation method (LBE) is exploited for computer simulations of the evolution of such systems with the newly arising interfaces between vapor and liquid phases. The parallel implementation of the LBE algorithm is realized on a large number of cores in the GPU. For the GPU programming, the CUDA technology is used. It is important that new regions of the low-density phase appear as thin quasi-cylindrical gas-vapor channels oriented along the electric field. The gas-vapor channels expand because of the diffusion of the solute gas from the mixture, evaporation of liquid into the channels and also due to the coalescence of channels with each other. The critical values of electric field necessary for such decay of a binary mixture are considerably lower than the critical electric field for pure dielectric liquids. Hence, if we take into account a solute gas, the electric fields for which the anisotropic mechanism of streamer channels generation and growth is operated, become considerably lower. Thus, at a breakdown of dielectric liquids in a strong electric field, the anisotropic instability is possibly the key mechanism of the generation of a gas phase, inception of conducting streamer structures, their fast growth in the form of thin filamentary channels, as well as branching of streamer structures during propagation. © 2013 Elsevier Ltd. All rights reserved.

Kupershtokh A.L.,Lavrentyev Institute of Hydrodynamics
Computers and Mathematics with Applications | Year: 2010

The numerical stability of the lattice Boltzmann equation (LBE) method in simulations of a fluid described by an equation of state with possible vapor-liquid phase transitions is considered. The Courant-Friedrichs-Lewy number defined by the advection term in the Boltzmann equation is exactly equal to unity in classical LBE models. However, this condition does not ensure the numerical stability of LBE simulations with the equation of state. In our numerical LBE simulations, we find out that instability arises initially in the liquid phase, even if the vapor phase and, consequently, the vapor-liquid interface are absent. We demonstrate both in numerical tests and theoretically that the numerical stability of LBE simulations requires the criterion over(c, ̃) ≤ over(c, ̃)cr to be fulfilled for the liquid phase, where over(c, ̃) = cs Δ t / h is the hydrodynamic Courant number. The hydrodynamic Courant number is proportional to the speed of sound cs, obtained from an equation of state of a fluid. This criterion is very similar to the well-known criteria of numerical stability of explicit finite difference schemes for a compressible fluid. The critical value of the Courant number over(c, ̃)cr depends neither on the temperature T, nor on the fluid velocity, nor on the form of the equation of state. This critical value is equal to over(c, ̃)cr = 1.1547 for the kinetic temperature of LBE pseudo-particles over(θ, ̃) = 1 / 3. © 2009 Elsevier Ltd. All rights reserved.

Rudoy E.M.,Lavrentyev Institute of Hydrodynamics
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2015

The equilibrium problem of the elastic body with a delaminated thin rigid inclusion is considered. In this case, there is a crack between the rigid inclusion and the elastic body. We suppose that the nonpenetration conditions are prescribed on the crack faces. We study the dependence of the energy of the body on domain variations. The formula for the shape derivative of the energy functional is obtained. Moreover, it is shown that for the special cases of the domain perturbations such derivative can be represented as invariant integrals. © 2014, Springer Basel.

Ovcharova A.S.,Lavrentyev Institute of Hydrodynamics
Physics of Fluids | Year: 2011

We consider a deformation and a rupture of a thin liquid film which is hanging between two solid flat walls under the action of concentrated thermal load action. A two-dimensional model is applied to describe the motion of thin layers of viscous non-isothermal liquid under micro-gravity conditions. For flow simulation, two-dimensional Navier-Stokes equations are used. A computational analysis of the influence of thermal loads on the deformation and the rupture behavior of the thin freely hanging film is carried out. It is shown that the rupture of the thin film with generation of a droplet can occur under the thermal beam of specific width acting on the free surface of the film. The results of the model problem solutions are presented. © 2011 American Institute of Physics.

Khludnev A.,Lavrentyev Institute of Hydrodynamics | Negri M.,University of Pavia
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2013

The paper concerns the control of rigid inclusion shapes in elastic bodies with cracks. Cracks are located on the boundary of rigid inclusions and in the bulk. Inequality type boundary conditions are imposed at the crack faces to guarantee mutual non-penetration. Inclusion shapes are considered as control functions. First we provide the problem formulation and analyze the shape sensitivity with respect to geometrical perturbations of the inclusion. Then, based on Griffith criterion, we introduce the cost functional, which measures the shape sensitivity of the problem with respect to the geometry of the inclusion, provided by the energy release rate. We prove existence of optimal shapes for the problem considered. © 2012 Springer Basel AG.

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