Numerical and experimental simulation of wave formation during explosion welding

The results of numerical and experimental simulation of wave formation under an oblique impact of metal plates during explosion welding are presented. The numerical simulation was carried out on the basis of the Maxwell relaxation model and by a molecular dynamics method. In the experiments, the impact of metal plates was investigated with X-ray radiography of phenomena in front of and behind the point of contact, and the preserved samples were studied metallographically. It is shown that the numerical simulation correctly reproduces the formation and evolution of waves on the contact boundary. Simultaneously, constraints are pointed out that prohibit the use of the elastoplastic model in the impact zone of the plates starting from the moment when the material of the plate in this zone is decomposed into thin jets. In this zone, the dependence of the specific deformation energy E on the tensor C _j ⁱ is no longer described by a convex function. It is this fact that motivated the transition to the molecular dynamics model.     

Numerical simulation of the process of nonequilibrium counterflow capillary imbibition

The convergence of the Galerkin method of solving the Cauchy–Dirichlet problem for the Barenbratt–Gilman equation is studied. On the basis of theoretical results, a numerical algorithm for this problem is developed. Results of a numerical experiment are presented.     

Numerical simulation of the process of formation of shock waves in electron gas in a field-effect transistor

The formation of shock waves in the electron gas of a field-effect transistor is simulated taking into account the coupled hydrodynamic and electromagnetic processes approximated, respectively, by the shallow water equations and electrostatic potential equations.     

Numerical simulation of the fractional-order control system

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractionalorder dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.     

Numerical simulation two phase flows of casting filling process using SOLA particle level set method

Mould filling process is a typical gas–liquid metal two phase flow phenomenon. Numerical simulation of the two phase flows of mould filling process can be used to properly predicate the back pressure effect, the gas entrapment defects, and better understand the complex motions of the gas phase and the liquid phase. In this paper, a novel sharp interface incompressible two phase numerical model for mould filling process is presented. A simple ghost fluid method like discretization method and a density evaluation method at face centers of finite difference staggered grid are proposed to overcome the difficulties when solving two phase Navier–Stokes equations with large-density ratio and large-viscosity ratio. A new mass conservation particle level set method is developed to capture the gas–liquid metal phase interface. The classical pressure-correction based SOLA algorithm is modified to solve the two phase Navier–Stokes equations. Two numerical tests including the Zalesak disk problem and the broken dam problem are used to demonstrate the accuracy of the present method. The numerical method is then adopted to simulate three mould filling examples including two high speed CCD camera imaging water filling experiments and an in situ X-ray imaging experiment of pure aluminum filling. The simulation results are in good agreement with the experiments.     

Numerical simulation of Richtmyer-Meshkov instability

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock     

Numerical simulation of dynamic sand dunes

The physics of granular materials is interesting from many points of view because they exhibit a wealth of phenomena that have both fluid and solid aspects [C.S. Campbell, Annu. Rev. Fluid. Mech. 22 (1990) 57, H.M. Jaeger, S.R. Nagel, R.P. Behringer, Phys. Today 494 (1996) 32]. Recently a difficult pattern was observed if sand falls in the space between two plates and passes an obstacle [Y. Amarouchene, J.F. Boudet, H. Kellay, Phys. Rev. Lett. 86 (2001) 4286]. The interesting behaviour occurs on top of the obstacle where a dynamic dune with a parabolic tip is formed. Inside this parabola, a triangular region of non- or very slow flowing sand is observed. Using factor analysis it is possible to extract latent parameters from a dynamic process. Applying a three factor model we can clearly identify the inner triangle (1st factor) and the outer parabolic pattern (3rd factor). The second factor we interpret as shock wave. Most interactions between particles take place in a relatively small region. We show that the pattern formation process depends on the restitution coefficients (particle–particle and particle–obstacle) and also on the particle size. These findings cannot be observed if standard velocity profiles are used to analyse the data. Our findings show, that most interactions take place in a relatively small area correlating with the particle size. If the interactions between different particles and particle–obstacle are elastic the formation of a non-flowing triangular region is more difficult as if inelastic collisions are used. The factor curves also clearly show that a pattern formation process has to be finished, before the next pattern can be formed.     

Numerical spherically-symmetric simulation of deep-seated geodynamics

A computer model is proposed that enables us to consider the geodynamic processes of expansion, contraction, warming, and cooling of the Earth. The dynamics of geospheres is studied within the framework of a model of a viscous heat-conducting compressible medium with density and viscosity varying in time and space. The proposed model allows us to consider not only the crust and the upper mantle of the Earth, but also the deeper structure including the core.     

Numerical simulation of the spatial dynamics of isothermic glaciers

Translated fromIssledovaniya po Prikladnoi Matematike, No. 19, 1992, pp. 56–67.     

Numerical simulation for the three-dimension fractional sub-diffusion equation

Fractional sub-diffusion equations have been widely used to model sub-diffusive systems. Most algorithms are designed for one-dimensional problems due to the memory effect in fractional derivative. In this paper, the numerical simulation of the 3D fractional sub-diffusion equation with a time fractional derivative of order $\alpha$ $(0<\alpha <1)$ is considered. A fractional alternating direction implicit scheme (FADIS) is proposed. We prove that FADIS is uniquely solvable, unconditionally stable and convergent in $H^1$ norm by the energy method. A numerical example is given to demonstrate the efficiency of FADIS.     

Numerical simulation of seismic activity by the grid-characteristic method

Seismic activity in homogeneous and layered enclosing rock masses is studied. A numerical mechanical-mathematical model of a hypocenter is proposed that describes the whole range of elastic perturbations propagating from the hypocenter. Synthetic beachball plots computed for various fault plane orientations are compared with the analytical solution in the case of homogeneous rock. A detailed analysis of wave patterns and synthetic seismograms is performed to compare seismic activities in homogeneous and layered enclosing rock masses. The influence exerted by individual components of a seismic perturbation on the stability of quarry walls is analyzed. The grid-characteristic method is used on three-dimensional parallelepipedal and curvilinear structured grids with boundary conditions set on the boundaries of the integration domain and with well-defined contact conditions specified in explicit form.     

Multi response simulation and optimization of gas tungsten arc welding

In the fabrication of a pressure vessel, the successful bending operation (after welding) demands higher tensile strength of weld bead. Therefore, to achieve typical tensile strength and hardness is the primary objective of this paper. Stainless steel 304 is widely used material in almost all the industrial applications, hence it is selected as a candidate material for study of tungsten inert gas (TIG) welding process. In order to produce, a high quality and reliable welding, the welding process needs to be robust in performance. A recently developed popular experimental approach known as definitive screening design (DSD) is used for process improvement. These optimum variable settings necessary for consistent welding are obtained through the application of simulation by using central composite design. The typical values of tensile strength and hardness are obtained at a low value of purging gas flow rate, filler rod dia.; intermediate values of root gap, plate thickness; and at high values of electrode dia., current, and gas flow rate.     

Flow simulation in process control

Production plants containing compartments whose material in-process inventory cannot be measured directly, require an input/ouput analysis to detect possible malfunctions. Flow simulation models quantifying the space-time behaviour of the material spectrum are shown to be an adequate tool for identifying the type and site of the control instruments necessary to guarantee timely detection of any significant material diversion.     

Numerical methods for simulation of large systems

The numerical solution of large initial value problems, including those that are derived as approximations to systems of partial differential equations, may encounter difficulties using conventional numerical methods because of stiffness (large range of eigenvalues of the associated linear system). In a nonlinear system, the eigenvalues may change greatly during the solution and a system that is initially well behaved may become stiff, yielding increased computer cost or inaccuracies. This paper contains a discussion of various definitions of stiffness, and several methods for overcoming it, including a new method for identifying and partitioning a two-time-scale system into fast and slow sub-systems. Also included are some experiences using the DARE continuous system simulation language for systems as large as 200 coupled nonlinear ordinary differential equations.     

Numerical simulation of the two-phase fluid filtration in heterogeneous media

Under study is numerical solution of the problems of two-phase filtration. The formulation of the problem is given in terms of velocity, pressure and saturation. To approximate the velocity and pressure, the mixed finite elementmethod is used. The flux schemes are applied for discretization of the convection term in the saturation equation. We present the results of numerical solution of a model problem for heterogeneous media.     

Numerical simulation of the resonant forbidden bragg reflection in germanium

??Forbidden?? reflections are observed in synchrotron radiation diffraction when the energy of incident radiation is close to the absorption edges in crystals. In the present paper, a new method for calculating the intensity of thermal-motion-induced forbidden reflections is proposed. It includes two steps: simulation of the temporary atomic displacements with the help of the ab initio molecular dynamics followed by quantum-mechanical calculations of the resonant scattering amplitude for various configurations. This technique is applied to the calculation of the 600 reflection thermal behavior in Ge and gives an adequate quantitative fitting of experimental data. The proposed simulation method of the thermal-motion-induced forbidden reflections is suitable for any crystal structure and promises to explain many results obtained up to now in synchrotrons.     

Numerical simulation of the velocity distribution for a hard-sphere gas

The kinetic features of energy exchange between hard-sphere molecules are numerically simulated. The results deviate from the usual the Maxwell distribution. The high-speed tail of the molecule distribution is cut off due to the dominant deceleration of fast particles. For mixtures of gases with various molecular masses, the energy redistribution between the degrees of freedom leads to different stationary temperatures of the components.     

Numerical simulation for the initial-boundary value problem of the Klein-Gordon-Zakharov equations

In this paper,a new conservative finite difference scheme with a parameter θ is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov (KGZ) equations.Convergence of the numerical solutions are proved with order O(h 2 + τ 2) in the energy norm.Numerical results show that the scheme is accurate and efficient.     

Numerical simulation of biofilm growth in porous media

Biofilms are very important in controlling pollution in aquifers. The bacteria may either consume the contaminant or form biobarriers to limit its spread. In this paper we review the mathematical modeling of biofilm growth at the microscopic and macroscopic scales, together with a scale-up technique. At the pore-scale, we solve the Navier-Stokes equations for the flow, the advection-diffusion equation for the transport, together with equations for the biofilm growth. These results are scaled up using network model techniques, in order to have relations between the amount and distribution of the biomass, and macroscopic properties such as permeability and porosity. A macroscopic model is also presented. We give some results.