Computation of Stokes Flow due to the Motion or Presence of a Particle in a Tube

The computation of Stokes flow due to the motion or presence of a rigid particle in a fluid-filled tube with arbitrary geometry is discussed with emphasis on the induced upstream to downstream pressure change. It is proposed that expressing the pressure change as an integral over the particle surface involving (a) the a priori unknown traction, and (b) the velocity of the pure-fluid pressure-driven flow, simplifies the numerical implementation and ameliorates the effect of domain truncation. Numerical computations are performed based on the integral formulation in conjunction with a boundary-element method for a particle translating and rotating inside a cylindrical tube with a circular cross-section. The numerical results are consistent with previous asymptotic solutions for small particles, and complement available numerical solutions for particular types of motion     

Thermocapillary Convection and Buoyant-Thermocapillary Convection in the Annular Pools of Silicon Melt and Silicone Oil

The thermocapillary convection and buoyant-thermocapillary convection in the annular pool of silicon melt (Pr=0.011) and silicone oil (Pr=6.7) with depth d=10 mm differentially heated at the outer wall and cooled at the inner wall are investigated by 2-D numerical simulation. The numerical results exhibit that the thermocapillary flow is enhanced by buoyancy force for silicon melt while it is weakened for silicone oil. Linear stability analysis indicates that the buoyancy force destabilizes the thermocapillary convection, which is different from that for silicone oil. The detailed reason of different influence of buoyancy force on the thermocapillary flow with different Pr numbers is explained according to present numerical results.     

A numerical investigation of the failure of spherical shells in explosive loading

The results of numerical simulation of the deformation and failure of spherical shells in explosive loading are presented. The known criteria of failure of materials in dynamic loading are analyzed and the desirability of their use is shown. A comparison is made of the numerical results obtained and experimental data.Translated from Probblemy Prochnosti, No. 8, pp. 9–14, August, 1992.     

A statistical evaluation of micro‐crack initiation in thermally cut structural elements

The paper presents a numerical modelling of fatigue crack initiation in thermally cut structural elements by using improved Tanaka–Mura crack nucleation model. The main goal of the study is to analyse the influence of different grain orientations generated with Voronoi tessellation on the crack initiation period. The numerical modelling of the crack initiation period is performed on the test specimens made of high strength steel with martensitic microstructure. Because the specimens are assumed to be thermally cut without any additional treatment, surface roughness is taken into account in the numerical simulation. Several computational analyses with different grain orientations are performed on the each stress level. Therefore, the stress cycles interval [N₁, N₂] in which the crack is expected to be initiated with the probability P(N) is determined by using statistical analyses of obtained computational results. Experimental testing is also performed on the uniaxial test machine by stress ratio R = 0.1.     

Fracture mechanics analysis of a crack in a residual stress field

The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.     

Solution of the Ornstein–Zernike Equation in the Critical Region

A new numerical scheme for the solution of liquid state integral equations using the Baxter factorization of the Ornstein–Zernike equation is proposed. For short range potentials the method yields reliable results over the whole fluid region, including the vicinity of the critical point, and opens up new possibilities for numerical study of the critical behavior of integral equation approximations. To demonstrate the effectiveness of the method, numerical results are compared with the analytical solution of the mean spherical approximation for a hard-core plus Yukawa tail interaction potential. Accurate results for the critical exponents δ, γ, and η for this model are obtained.     

The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls

Summary A numerical investigation is made to establish whether multiple solutions exist for laminar, incompressible, steady flow in a parallel plate porous channel with uniform suction at both walls. For values of the wall suction Reynolds number,R, greater than 12.165 three numerical solutions are observed for eachR, while forR less than 12.165 only one solution for eachR can be found. A method involving the inclusion of exponentially small terms in a perturbation series is used to find two of the solutions analytically, while an appeal to the numerical results gives an indication of how the third solution can be obtained. The series involving the exponentially small terms, as well as predicting dual solutions, gives more accurate analytic results for the skin friction at the channel walls.     

Calculations of the temperature and flow field in a room ventilated by a radial air distributor

In ventilated or air-conditioned rooms optimal conditions of temperature, humidity and air velocity are required. In the present study the behaviour of a jet emerging from a radial plate distributor and the resulting air flow in the room were investigated. To predict the behaviour of the air flow a numerical scheme was used to solve the conservation equations for mass, momentum and energy with the k/ε-turbulence model. The numerical results are compared with available experimental data.     

Volume integral equations in non-linear 3-D magnetostatics

In this paper a discussion of volume integral formulations in three-dimensional non-linear magnetostatics is presented. Integral formulations are examined in connection with Whitney's elements in order to find new approaches. A numerical algorithm based on a formulation implying properly the continuity conditions of magnetic field strength H, i.e. an h-type formulation, is introduced. Results of demanding application problems are shown demonstrating the characteristics of this kind of volume integral approach. In addition, a discussion of the parallelized version of the numerical code based on the h-type approach is presented appended with numerical results illustrating the advantages of combining integral formulations with concurrent computing.     

Correlated lattice models in the local approximation — Aspects of a numerical renormalization group treatment

The numerical renormalization group method is applied to an Anderson impurity with an energy dependent coupling to the conduction band. We describe how the discrete spectra resulting from the numerical calculation can be reliably smoothed using a continued fraction expansion. The investigations are connected with the study of models in infinite spatial dimensions.     

Influence of residual stresses in the performance of cold-drawn pearlitic wires

The mechanical properties of cold-drawn pearlitic wires are controlled largely by the microstructure developed during processing and, to some extent, by the residual stresses during drawing. The advent of powerful computers and the availability of equipment to perform diffraction experiments, have made possible numerical predictions and accurate measurements of residual stresses. This paper—a review of work done by the author and collaborators—shows how stress-relaxation losses, environmental assisted cracking and fatigue life of cold-drawn pearlitic wires are influenced by residual stresses. The role of pre-stretching loads, or of stress relieving treatments, on stress-relaxation can be understood when the profile of residual stresses is known. Some awkward results in times to fracture during hydrogen embrittlement tests can be explained if accurate values of residual stresses near the surface are known, and the same is true of fatigue life. In this context numerical simulations and measurements performed on cold-drawn pearlitic wires, with different profiles of residual stresses, have shown very good quantitative agreement.     

Method of investigating the nonaxisymmetric dynamic form changing of collapsible shells. Report 2. Calculations and experiment

The theory and numerical method of calculating the significant nonstationary form change of nonaxisymmetric elastoplastic shells with allowance for material failure are confirmed. The confirmation is based on numerical experimentation, and comparison of numerical results with test calculations and experimental data. Satisfactory accuracy is noted for this numerical method and the computational results obtained. Some characteristic features of the dynamic failure of the shells are disclosed.Translated from Problemy Prochnosti, No. 4, pp. 41–48, April, 1996.     

Thermal stress evaluation in the steel continuous casting process

Two numerical models for the thermal stress and plastic strain analysis in the solid shell at the initial stage of a steel continuous casting process, are presented and their performances evaluated. First, a numerical procedure based on a natural extension of the semi‐analytical study proposed by Weiner and Boley (J. Mech. Phys. Solids 1963; 11 :145–154) is introduced and validated by comparison with their semi‐analytical 1‐D solution. The basic hypotheses of this model, and particularly the extended plane strain condition with uniform axial strain, are afterwards tested in more complex and realistic situations by comparing results with those obtained by an alternative numerical scheme presented by Fachinotti (Doctoral Thesis, Universidad Nac. Litoral, Argentina, 2001) and Fachinotti and Cardona (Internal Report, CIMEC, sent to IJNME, 2002). Finally, results of a typical and representative 3D simulation, corresponding to a slab continuous casting process, are shown. Copyright © 2005 John Wiley & Sons, Ltd.     

Accuracy in finite element computation for eigenfrequencies

In this paper we propose an original numerical method to get upper and lower bounds for the eigenfrequencies of an elastic structure. This method is based on a ‘static’ formulation for eigenvalue problems built up from a new quotient R_s which is defined on a load space. From R_s properties, upper and lower bounds for the exact eigenfrequencies are proved. The application of the method requires the solution of an eigenvalue problem of finite dimension and the computation of a constant which is characteristic of the discretization subspace. Results of numerical tests are given for the vibration problem of an elastic clamped membrane.     

Calculations of J integrals around fractal defects in plates

This paper presents a method of analyzing fractal defects based on numerical calculations of J integrals. Two different constructions of fractal approximations are taken into consideration together with a comparison of the stability of the numerical simulations in both cases. The value of J integral provides information about the energy concentrated on the defect. The result was used to examine the relation between the energy and the measure of the defect. The simplest model indicates this relation to be linear. Nonetheless, the presented results suggest that not only the measure of the defect but also its orientation and configuration play a significant role in the energy distribution on the defect boundaries.     

On the analytical expressions of mass and stiffness matrices for linear triangular finite elements for lateral sloshing of liquid in axisymmetric tanks

The analytical expressions of mass and stiffness matrices for a triangular finite element with piecewise linear basis functions are presented for the lateral sloshing of the liquid in axisymmetric tanks, for a circumferential wave number m=1, antisymmetric. Finite element numerical results of the eigenvalue problem for the free vibration of liquid-filled axisymmetric tanks are compared favorably with previous numerical and experimental results, and therein a good agreement is achieved.     

Investigation of diffusion in p-version ‘LSFE’ and ‘STLSFE’ formulations

This paper deals with investigation of diffusion for p-version least squares finite element formulation (LSFEF) and p-version space-time coupled least squares finite element formulation (STLSFEF) for steady-state and transient problems. Convection dominated flows result in hyperbolic system of equations which leads to ill-conditioned matrices when using Galerkin formulation. Various techniques (SUPG, SUPG-with discontinuity capturing operator etc.) have been devised to overcome the difficulties arising primarily due to hyperbolic terms and sharp gradients. In this paper, it is demonstrated that when using p-version STLSFEF or LSFEF, no such difficulties are encountered in formulation as well as in the solution procedure. Almost all numerical processes suffer from numerical diffusion to some extent, however, it is demonstrated in this paper that in p-version STLSFE and LSFE formulations numerical diffusion can be completely eliminated by mesh refinement and p-level increase and the formulations are free of inherent diffusion. Several model problems are considered with dominant convective terms to investigate diffusion in p-version LSFEF and STLSFEF. Two dimensional convection-diffusion problems are used as steady state representative cases. One dimensional transient problems considered in this paper include pure advection, convection-diffusion and Burgers' equation. Numerical results are also compared with exact solutions and those reported in the literature.     

Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation

When applying numerical methods for the computation of stationary waves from the Helmholtz equation, one obtains ‘numerical waves’ that are dispersive also in non-dispersive media. The numerical wave displays a phase velocity that depends on the parameter k of the Helmholtz equation. In dispersion analysis, the phase difference between the exact and the numerical solutions is investigated. In this paper, the authors' recent result on the phase difference for one-dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic. It is then shown that previous error estimates in H¹-norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only. On the other hand, recently proven error estimates for constant resolution contain a pollution term. With certain assumptions on the exact solution, this term is of the order of the phase difference. Thus a link is established between the results of dispersion analysis and the results of numerical analysis. Throughout the paper, the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems. Special attention is given to the performance of the Galerkin method with a higher order of polynomial approximation p(h-p-version).     

Software packages for determining the dynamic characteristic of printed components in radio-electronic apparatus

The use of numerical modeling for solving the problem of analyzing the dynamic characteristics of the printed components of radio-electronic apparatus is considered. A method is proposed for constructing models for the numerical solution of various problems based on the method of finite differences. Software packages are described and examples of the solution of problems of investigating the dynamics of printed circuits of radioelectronic apparatus on a computer are given.Translated from Izmeritel'naya Tekhnika, No. 5, pp. 57–60, May, 1994.     

Weighted residual solutions in the time domain

The Galerkin and subdomain forms of the weighted residual method are used to generate recursive equations in time for the numerical solution of a system of ordinary differential equations. The single-step methods that result from a linear interpolation equation match currently available methods whose stability and oscillation properties are known. A three-level scheme developed by combining two linear elements is shown to be unconditionally unstable. Two of the three schemes obtained using a quadratic interpolation equation and quadratic weighting functions are also shown to be unconditionally unstable. The third scheme is unconditionally stable, but the calculated values for a numerical solution of u? + u = 0, u(0) = 1 are not as accurate as the values obtained using the single-step central difference method.