Three-step multi-domain BEM for solving transient multi-media heat conduction problems

In this paper, a three-step BEM analysis technique is proposed for solving 2D and 3D transient heat conduction problems consisting of multiple non-homogeneous media. The discretized boundary element formulation is written for each medium. The first step is to eliminate internal variables at the individual medium level; the second step is to eliminate boundary unknowns defined over nodes used only by the medium itself; and the third step is to establish the system of equations according to the continuity conditions of the temperature and heat flux at common interface nodes. Based on the central finite difference technique, an implicit time marching solution scheme is developed for solving the time-dependent system of equations. Three numerical examples are given to demonstrate the accuracy and effectiveness of the presented method.     

Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media

The discrete-ordinates method is formulated to solve transient radiative transfer with the incorporation of a transient term in the transfer equation in two-dimensional rectangular enclosures containing absorbing, emitting, and anisotropically scattering media subject to diffuse and/or collimated laser irradiation. The governing equations resulting from the discrete-ordinates discretization of the angular directions are further discretized in the spatial and the temporal domains by the finite-volume approach. The current formulation is suitable for solving transient laser transport in turbid media as well as for steady-state radiative transfer in many engineering problems. The method is applied to several example problems and compared with existing steady-state solutions and Monte Carlo transient solutions. Good agreement is found in all cases. Short-pulsed laser interaction and propagation in a turbid medium with high scattering albedo are studied. The imaging of an inhomogeneous zone inside a turbid medium is demonstrated.     

A block iterative finite element algorithm for numerical solution of the steady–state,compressible Navier–Stokes equations

An iterative method for numerically solving the time independent Navier–Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss–Seidel principle in block form to the systems of the non-linear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C⁰-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.     

Hybrid BEM for the early stage of unsteady transport process

This paper presents a new approach for solving the early stage of 3D time‐dependent transport problems in non‐homogeneous fractured porous media in which the initial distribution of concentration presents discontinuous jump at the interface of two regions of transport properties differing in several orders of magnitude. The goal of this formulation is to overcome the problems of different scales and apparent large flux during early time by combining the 3D dual reciprocity boundary element method and a semi‐analytical solution of the time‐dependent advection–diffusion equation, employing a two‐level finite difference time integration scheme. Theoretical background, validation results and practical applications for the advection–diffusion equation in fractured and continuous porous media are reported. The results show advantages for relatively large‐scale models and complex geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

The finite element method applied to ideal gaseous mixtures

The finite element technique is extended to an ideal gaseous mixture to study diffusion of several gaseous species in a carrier gas under various geometries and flow conditions. This is accomplished by obtaining the finite element analog of the balance of mass for each species, along with the corresponding equations for the balance of mass, momentum and energy for the mixture. Numerical results are obtained for a steady-state, incompressible, isothermal, viscous mixture of two gases for several boundary conditions. Favourable agreement is obtained between the finite element results and analytical solutions.     

Densification Rates of Ceramic Matrix Composites with Initial Matrix Inhomogeneity

A viscoelastic finite element method is developed to analyze the effect of non-homogeneous matrix compaction on densification of ceramic matrix composites. The heterogeneous matrix of the composite is represented by a system of two or more co-axial cylinders of different initial matrix density. The sintering potential can be expressed in terms of a free strain rate. The free strain rate is derived from the relationship of relative density versus sintering time, measured from the neat matrix sample. The knowledge of free strain rate is a prerequisite for conducting the finite element analysis. For the heterogeneous matrix, two different density-time relationships are assumed, based on the concepts of neck formation and neck growth between contacting particles, and pore coarsening. The results of the finite element analysis show that a nonuniform compaction of the composite generally has a detrimental effect on the densification process.     

Magnetic resonance imaging gradient coil design by combiningoptimization techniques with the finite element method

In this paper, the optimization techniques of complex method, steepest descent, and conjugate gradient are investigated in terms of their convergence behaviors. The conjugate gradient method is then combined with finite element analysis techniques to develop a magnetic resonance imaging (MRI) G_z gradient coil design strategy which maximizes the field linearity within a specified region of interest. It is found that conjugate gradient optimization in conjunction with the finite element method is a powerful and flexible coil design approach with the potential to incorporate complex coil geometries, inhomogeneous media, and transient current excitation     

Transient fields of pulsed transducers in solids

The radiation and propagation of elastic waves in solid media are of fundamental importance in ultrasonic NDE. Due to the limitation of analytical approaches, numerical procedures are most appropriate for solving the governing equations. In this paper, the finite element method is used to predict the transient fields of pulsed transducers in a solid medium with axisymmetric geometry. Comparisons with other models are performed. The transducer field interactions with spherical voids are also presented.     

FDM and FEM solutions to linear dynamics of porous media: stabilised,monolithic and fractional schemes

A number of methods have been developed for solving the dynamics of saturated porous media. However, most solutions are based on the finite element method, and only a few employ finite differences (FDM). One problem with the FDM is the difficulty in fulfilling the inf‐sup (Lady?enskaja‐Babu?ka‐Brezzi) condition. This paper explores solutions with the FDM, including the development of new schemes aiming at stabilised formulations. The efficiency, accuracy and stability of several FDM and finite element method algorithms are thoroughly investigated as well. A combination of primary variables from the theory of porous media is considered, including the so‐called up and uvp formulations. Six numerical schemes are produced and quantitatively studied. Simulations of 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

The quasi-linear method of fundamental solution applied to non-linear wave equations

This paper presents a new meshless method developed by combining the quasi-linear method of fundamental solution (QMFS) and the finite difference method to analyze wave equations. The method of fundamental solution (MFS) is an efficient numerical method for solution Laplace equation for both two- and three-dimensional problems. The method has also been applied for the solution of Poisson equations and transient Poisson-type equations by finding the particular solution to the non-homogeneous terms. In general, approximate particular solutions are constructed using the interpolation of the non-homogeneous terms by the radial basis functions (RBFs). The interpolation in terms of RBFs often leads to a badly conditioned problem which demands special cares. The current work suggests a linearization scheme for the non-homogeneous term in terms of the dependent variable and finite differencing in time resulting in Helmholtz-type equations whose fundamental solutions are available. Consequently, the particular solution is no longer needed and the MFS can be directly applied to the new linearized equation. The numerical examples illustrate the effectiveness of the presented method.     

Application of the Laplace transform dual reciprocity boundary element method in the modelling of laser heat treatments

The Laplace Transform Dual Reciprocity Boundary Element Method (LTDRM or LT-DRBEM) provides with an alternative numerical technique to finite difference (FDM) or finite element methods (FEM) for solving transient diffusion problems. With this method, solutions are calculated directly at any specific time thus avoiding the use of time-stepping schemes. Besides, domain integrals are removed from the problem formulation.In this work we study the applicability of the LT-DRBEM method for laser heat treatment modelling purposes. A simple model was developed based on a two dimensional transient heat conduction equation, in which the laser beam is included as a heat flux boundary condition of gaussian shape. Results corresponding to a stationary and a moving beam are presented and discussed. Non-linear formulations of the problem as those given by temperature dependent material properties are also considered. Good accuracy results were obtained for the stationary beam approach, whereas severe limitations were found for the moving beam case.     

Temperature distribution in cylindrical packed beds

The heat transfer problem in a cylindrical packed bed with continuous flow of gases has been studied by treating the solid phase as a pseudo-homogeneous substance. A set of finite difference equations governing the temperature distributions in the solid and gaseous phases have been obtained using a mixing-cells model, to account for the turbulent mixing phenomenon. Numerical solutions are obtained by solving this set of equations of temperature distributions using relaxation method.     

Dynamic analysis of large-scale SSI systems for layered unbounded media via a parallelized coupled finite-element/boundary-element/scaled boundary finite-element model

An algorithm for a parallelized coupled model based on finite element method (FEM), boundary element method (BEM), and scaled boundary FEM (SBFEM) for harmonic and transient dynamic response of large-scale 2D structures embedded in or on layered soil media is presented. The BEM and SBFEM are used for modelling the dynamic response of the unbounded media. The standard FEM is used for modelling the finite region and the embedded structure. The objective of the development of this parallelized coupled model is to use the power of high performance computing, and to take into account the advantages and evade the disadvantages of the above mentioned numerical methods for modelling of the unbounded media in soil-structure interaction (SSI) systems. The development of the parallel algorithm for this model is essential for solving arbitrarily shaped large-scale SSI problems, which cannot be solved within reasonable elapsed times by a serial algorithm. The efficiency of the proposed parallel algorithm and the validity of the coupled model are shown by means of three numerical examples, indicating the excellent accuracy and applicability of the parallel algorithm with considerable time-savings in large-scale problems.     

A perturbation method for stochastic meshless analysis in elastostatics

A stochastic meshless method is presented for solving boundary‐value problems in linear elasticity that involves random material properties. The material property was modelled as a homogeneous random field. A meshless formulation was developed to predict stochastic structural response. Unlike the finite element method, the meshless method requires no structured mesh, since only a scattered set of nodal points is required in the domain of interest. There is no need for fixed connectivities between nodes. In conjunction with the meshless equations, classical perturbation expansions were derived to predict second‐moment characteristics of response. Numerical examples based on one‐ and two‐dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method. A good agreement is obtained between the results of the proposed method and Monte Carlo simulation. Since mesh generation of complex structures can be a far more time‐consuming and costly effort than the solution of a discrete set of equations, the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems. Copyright © 2001 John Wiley & Sons, Ltd.     

Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution

This paper is concerned with the development of a numerical procedure for solving complex boundary value problems in plane elastostatics. This procedure—the displacement discontinuity method—consists simply of placing N displacement discontinuities of unknown magnitude along the boundaries of the region to be analyzed, then setting up and solving a system of algebraic equations to find the discontinuity values that produce prescribed boundary tractions or displacements. The displacement discontinuity method is in some respects similar to integral equation or ‘influence function’ techniques, and contrasts with finite difference and finite element procedures in that approximations are made only on the boundary contours, and not in the field. The method is illustrated by comparing computed results with the analytical solutions of two boundary value problems: a circular disc subjected to diametral compression, and a circular hole in an infinite plate under a uniaxial stress field. In both cases the numerical results are in excellent agreement with the exact solutions.     

The PE2D package for transient eddy current analysis

The PE2D package is a suite of programs for solving, by the finite element method, the electro-magnetic and electrostatic problems which are described by the Laplace, Poisson, Helmholtz or diffusion equation in two dimensions. This paper describes the package and illustrates its use in solving transient eddy-current problems.     

Application of the finite element iterative method to the eigenvalue problem of a crack between dissimilar media

The finite element iterative method is applied to the eigenvalue problem of a crack between dissimilar media. In this case the transfer matrix is non-symmetric, which leads to complex eigenvalues. The singularity obtained agrees with the analytical results of r^(?1/2+ie). The method of evaluating the eigenfunctions is general and can be applied to more complex cases of material and geometry, which are frequently encountered in composite materials. A powerful method for evaluating stress intensities in dissimilar media is given in the Appendix. The method is also reduced for homogeneous media to give stress intensity factors for modes I, II and III.     

Time‐dependent shape functions for modeling highly transient geothermal systems

This paper presents new time‐dependent finite element shape functions suitable for modeling high‐gradient transient conductive heat flow in geothermal systems. The shape functions are made adaptive by enhancing the approximation functions with time‐dependent variables, which may vary according to the transient process without adding extra degrees of freedom or applying mesh adaptation. Two different approaches are presented. First, an iterative method is proposed, in which an exponential approximation function, which is optimized continually during the transient process, is incorporated in the shape function. Second, an analytical method is suggested, in which an analytical solution of a simplified process is incorporated in the shape function, enabling an explicit update of the shape functions in each time step. A methodology for modeling the variation of temperature in one and two dimensions is introduced. The ability of the method to capture high‐gradient temperature profiles using relatively large elements is illustrated with numerical examples of cases in which equally large standard finite elements fail. Copyright © 2008 John Wiley & Sons, Ltd.     

基于ANSYS软件对SiCp/A1(ZL102)复合材料铸造渗流过程多孔介质结构的有限元处理

采用统计平均的方法描述多孔介质微观结构的影响,根据多孔介质的连续介质模型及有限元方法对多孔介质内的铝液的渗流行为进行数值模拟,给出了可视化的瞬态温度场分布,并且初步预测了不同时刻的渗流有效高度.     

Hygrothermomechanical evaluation of porous media under finite deformation. Part I - finite element formulations

The coupled thermomechanical responses of fluid-saturated porous continua subjected to finite deformation are investigated. Field equations governing the transient response of the media are derived from a continuum thermodynamics mixture theory based on mass balance, momentum balance and energy balance laws as well as the Clausius-Duhem inequality. Finite element procedures for the two-dimensional response, employing updated Lagrangian formulations for the solid skeleton deformation and the weak formulations for fluid and thermal transport equations, are implemented in a fully implicit form. Temperature-dependent mechanical properties for the non-linear solid matrix, characterized by Perzyna's viscoplastic model, are assumed. An iterative scheme based on the full Newton-Raphson method is presented for simultaneously solving the coupled non-linear equations.