bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical simulation of vortex shedding past triangular cylinders at high Reynolds number using a k‐ε turbulence model
Authors: Johansson Stefan H. , Davidson Lars , Olsson Erik
Published: August 2005

Calculations of unsteady turbulent flow around and behind triangular‐shaped flameholders using a finite volume code with a k‐ε model of turbulence are presented.

The flow behind the flameholders is found to be unsteady (a von Kármán vortex street appears) with a well defined Strouhal frequency (predicted Sr=0·27 compared with an experimental value of 0·25). The predicted profiles of velocity and fluctuating kinetic energy agree well with experiments. The periodic motions in the vortex street are shown to be far more important than the turbulent stochastic motions in exchanging momentum in the transversal direction.

The pressure‐velocity coupling is handled with the SIMPLEC pressure correction procedure. The discretization in time is fully implicit and 90 times steps are used to resolve one time cycle. It was found that to capture the vortex street it is very important that the grid spacing is sufficiently fine (180 × 100).
Three‐dimensional vortex method for parachutes
Authors: Humi Mayer
Published: August 2005

We describe the implementation of a new 3D vortex algorithm for the computation of the drag and flow field around parachutes. Among its novel features, the algorithm couples large eddy simulation methodology with the vortex method, away from the wall region. Furthermore, boundary conditions for a wall (no‐slip) and compliant boundaries were implemented. The results of several simulations using this algorithm are analysed and discussed. The spectral contents of the vortex method are also considered.
Transient simulation of 2–3D stratified and intermittent two‐phase flows. Part II: Applications
Authors: Moe Randi
Published: August 2005

In this paper a new type of transient multidimensional two‐fluid model has been applied to simulate intermittent or slug flow problems. Three different approaches to modelling interfacial friction, including an interfacial tracking scheme, have been investigated. The numerial method is based on an implicit finite difference scheme, solved directly in two steps applying a separate equation for the pressure. 2D predictions of Taylor bubble propagation in horizontal and inclined channels have been compared with experimental data and analytical solutions. The 2D model has also been applied to investigate a number of special phenomena in slug flow, including slug initiation, bubble turning in downflow and the bubble centring process at large liquid flow rates.
p‐version least squares finite element formulation for two‐dimensional, incompressible fluid flow
Authors: Winterscheidt Daniel , Surana Karan S.
Published: August 2005

A p‐version least squares finite element formulation for non‐linear problems is applied to the problem of steady, two‐dimensional, incompressible fluid flow. The Navier‐Stokes equations are cast as a set of first‐order equations involving viscous stresses as auxiliary variables. Both the primary and auxiliary variables are interpolated using equal‐order C0 continuity, p‐version hierarchical approximation functions. The least squares functional (or error functional) is constructed using the system of coupled first‐order non‐linear partial differential equations without linearization, approximations or assumptions. The minimization of this least squares error functional results in finding a solution vector {δ} for which the partial derivative of the error functional (integrated sum of squares of the errors resulting from individual equations for the entire discretization) with respect to the nodal degrees of freedom {δ} becomes zero. This is accomplished by using Newton's method with a line search. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method.
Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions
Authors: Barakos G. , Mitsoulis E. , Assimacopoulos D.
Published: August 2005

Numerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 1010. The k‐ϵ model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non‐uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra‐values. ADI and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra‐values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k‐ϵ model with logarithmic wall functions, which gives significant overpredictions.
Generalized integral transform solution for boundary layer flow over a sphere
Authors: Lage P. L. C. , Rangel R. H.
Published: August 2005

The generalized integral transform technique is applied to the boundary layer equations for flow over a sphere in their primitive variables. Even though a diffusion‐based eigenvalue problem is used, the velocity profile, shear stress and separation point have been calculated with high accuracy. Low‐order approximations are shown to be accurate near the surface and the predictions of the separation point is very good. Comparison with finite difference results shows the better convergence behaviour of the integral transform method.
Comparison of variants of the bi‐conjugate gradient method for compressible Navier‐Stokes solver with second‐moment closure
Authors: Chuang C. C. , Chieng C. C.
Published: August 2005

Variants of the bi‐conjugate gradient (Bi‐CG) method are used to resolve the problem of slow convergence in CFD when it is applied to complex flow field simulation using higher‐order turbulence models. In this study the Navier‐Stokes and Reynolds stress transport equations are discretized with an implicit, total variation diminishing (TVD), finite volume formulation. The preconditioning technique of incomplete lower‐upper (ILU) factorization is incorporated into the conjugate gradient square (CGS), bi‐conjugate gradient stable (Bi‐CGSTAB) and transpose‐free quasi‐minimal residual (TFQMR) algorithms to accelerate convergence of the overall itertive methods. Computations have been carried out for separated flow fields over transonic bumps, supersonic bases and supersonic compression corners. By comparisons of the convergence rate with each other and with the conventional approximate factorization (AF) method it is shown that the Bi‐CGSTAB method gives the most efficient convergence rate among these methods and can speed up the CPU time by a factor of 2·4–6·5 as compared with the AF method. Moreover, the AF method may yield somewhat different results from variants of the Bi‐CG method owing to the factorization error which introduces a higher level of convergence criterion.
A numerical study of pulsatile laminar flows in a pipe with a ring‐type constriction
Authors: Shi Z. D. , Lee T. S. , Winoto S. H.
Published: August 2005

Numerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non‐zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non‐staggered grid and a modified Crank‐Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer (Re) is 100. The Womersley number (Nw) ranges from 0 to 50, with the corresponding Strouhal number (St) ranging from 0 to 3·98. The constriction opening ratio (d/D) and thickness ratio (h/D) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. For Nw ≤ 1 and St≤ 1·56 x 10−3 the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δp) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing Nw and St, the phase angle between the flow rate and the dp/dz becomes larger and has its maximum value of 90° at Nw = 50 and St = 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non‐zero mean velocity sinusoidal flow has the smallest. For larger Nw and St the fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases for Nw ranging from 0 to 4·2, while this length becomes very small at Nw = 50 and St = 3·98. The deceleration tends to enlarge the recirculation region and this effect appears for Nw ≥ 3 and St ≥ 1·43×10−2. Linear relations exist between the flow rate and the instantaneous maximum values of velocity, vorticity and shear stress.
Time‐dependent liquid metal flows with free convection and a deformable free surface
Authors: McClelland Matthew A.
Published: August 2005

The finite element method is employed to investigate time‐dependent liquid metal flows with free convection, free surfaces and Marangoni effects. The liquid circulates in a two‐dimensional shallow trough with differentially heated vertical walls. The spatial formulation incorporates mixed Lagrangian approximations to the velocity, pressure, temperature and free surface position. The time integration is performed with the backward Euler and trapezoid rule methods with step size control. The Galerkin method is used to reduce the problem to a set of non‐linear equations which are solved with the Newton–Raphson method. Calculations are performed for conditions relevant to the electron beam vaporization of refractory metals. The Prandtl number is 0·015 and Grashof number are in the transition range between laminar and turbulent flow. The results reveal the effects of flow intensity, surface tension gradients, mesh refinement and time integration strategy.
Applied mathematics and turbulence modelling
Authors: Mohammadi B. , Pironneau O.
Published: August 2005

Turbulence modelling is done traditionally in fluid mechanics departments. However, mathematical tools such as frame invariance, multiple scale expansions and the like are of great help.

We shall demonstrate these facts by applying mathematical and numerical tools to the K–ε model. We shall investigate wall laws. Reynolds hypothesis, positivity of k and ε and flows with multiple scales.

We shall also take this opportunity to review some mathematical results relevant to turbulence modelling.
A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme
Authors: Zienkiewicz O. C. , Codina R.
Published: August 2005

The paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier‐Stokes or Euler equations. Full incompressibility can be dealt with if the algorithm is used in its semi‐explicit form and its structure permits arbitrary interpolation functions to be used avoiding the Babuška‐Brezzi restriction. In a fully explicit version it introduces a rational form of balancing dissipation avoiding the use of arbitrary parameters and forms for this.
Triphasic finite element model for swelling porous media
Authors: Snijders H. , Huyghe J. M. , Janssen J. D.
Published: August 2005

The equations describing the mechanical behaviour of intervertebral disc tissue and other swelling porous media are three coupled partial differential equations in which geometric and physical non‐linearities occur. The boundary conditions are deformation‐dependent. To solve the equations for an arbitrary geometry and arbitrary boundary conditions, we use the finite element (FE) method. The differential equations are rewritten in an integral form by means of the weighted residual method. The domain of the integral is defined via a set of shape functions (i.e. finite elements). By applying the Gauss theorem and rewriting with respect to the reference state (total Lagrange), non‐linear equations are obtained. These are solved by means of the Newton‐Raphson technique. In order to get a finite set of equations, the weighted residual equations are discretized. The shape functions are chose as weighting functions (Galerkin method). This discretization results in a non‐symmetric stiffness matrix. A general description is given for the elements implemented into the commercial FE package DIANA (DIANA Analysis B.V., Delft, Netherlands). The numerical results of unconfined compression of a schematic intervertebral disc with varying proteoglycan concentration are given.
Reproducing kernel particle methods
Authors: Liu Wing Kam , Jun Sukky , Zhang Yi Fei
Published: August 2005

A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time‐frequency and space‐wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element‐free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two‐dimensional examples of advection‐diffusion equations and compressible Euler equations are also presented together with 2D multiple‐scale decompositions.
Simulation of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique
Authors: Shen Wen‐Zhong , Loc Ta Phuoc
Published: August 2005

Two‐dimensional external viscous flows are numerically approximated by means of a domain decomposition method which combines a vortex method and a finite difference method. The vortex method is used in the flow region which is dominated by convective effects, whereas the finite difference method is used in the flow region where viscous diffusion effects are dominant. An influence matrix technique combined with the uniformity condition of the pressure is used to enforce the tangential velocity boundary condition. Comparisons between numerical and experimental data show that the method is well adapted for simulating two‐dimensional flows.
A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations
Authors: Li Ming , Tang Tao , Fornberg Bengt
Published: August 2005

We note in this study that the Navier‐Stokes equations, when expressed in streamfunction‐vorticity form, can be approximated to fourth‐order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth‐order scheme is that it allows direct iteration for low‐to‐medium Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re ⩽ 7500 point‐SOR iteration is used and the convergence is fast.
Finite element computations of two‐dimensional arterial flow in the presence of a transverse magnetic field
Authors: Sharma G. C. , Kapoor Jaya
Published: August 2005

A finite element solution of the Navier‐Stokes equations for steady flow under the magnetic effect through a double‐branched two‐dimensional section of a three‐dimensional model of the canine aorta is discussed. The numerical scheme involves transforming the physical co‐ordinates to a curvilinear boundary‐fitted co‐ordinate system. The shear stress at the wall is calculated for a Reynolds number of 1000 with the branch‐to‐main aortic flow rate ratio as a parameter. The results are compared with earlier works involving experimental data and found to be in reasonable qualitative agreement. The steady flow, shear stress and branch flow under the effect of a magnetic field have been discussed in detail.
Finite element solution of the equations governing the flow of electrolyte in charged microporous membranes
Authors: James A. E. , Stillman J. D. , Williams D. J. A.
Published: August 2005

Electrical double‐layer effects are unimportant in flows through porous media except when the Debye length k−1 is comparable in magnitude with the pore radius a. Under these conditions the equations governing the flow of electrolyte are those of Stokes, Nernst‐Planck and Poisson. These equations are non‐linear and require numerical solution. The finite element method provides a useful basis for solution and various algorithms are investigated. The numerical stability and errors of each scheme are analysed together with the development of an appropriate finite element mesh. The electro‐osmotic flow of a typical electrolyte (barium chloride) through a uniformly charged cylindrical membrane pore is investigated and the ion fluxes are post‐computed from the numerical solutions. The ion flux is shown to be strongly dependent on both zeta potential and pore radius, ka, indicating the effects of overlapping electrical double layers.
The development of a structured mesh grid adaption technique for resolving shock discontinuities in upwind Navier‐Stokes codes
Authors: Patel M. K. , Pericleous K. A. , Baldwin S.
Published: August 2005

A technique is described for the adaptation of a structured control volume mesh during the iterative solution process of the Navier‐Stokes equations. The scalar equidistribution method is adopted, in conjunction with a Laplace‐like grid solver to make a curvilinear body‐fitted grid sensitive to local flow gradients. Hence, whilst the total number of grid nodes remains constant during a computation, their relative position is continuously adjusted to promote clustering of cells in regions where gradients are high. The focus of this work is in compressible aerodynamics, where such clustering would be desirable in regions containing shocks but also in boundary layers. The technique is three‐dimensional and operates in a series of user‐defined grid subdomains or patches. These patches act as reference frames within which grid activity takes place. Bi‐cubic splines are extensively used to define the aerodynamic surfaces forming the calculation boundaries and to ensure that grid movement does not compromise surface integrity. The technique is applied to aerofoils, wing surfaces, transonic ducts and nozzles and a supersonic wedge cascade. Significant sharpening of both normal and oblique shock discontinuities is demonstrated over static grid simulations and with fewer overall grid nodes. The technique is successful in both inviscid and viscous (turbulent) simulations.
Advection of axisymmetric interfaces by the volume‐of‐fluid method
Authors: Mashayek F. , Ashgriz N.
Published: August 2005

A criterion is proposed for the advection of axisymmetric interfaces. The location of an interface is followed by a volume‐tracking technique wherein a volume fraction parameter is assigned to each of the cells in a Eulerian grid system. The interface is discretized into a set of line segments fitted at the boundary of every pair of neighbouring computational cells. The orientation of a line segment is obtained by inspecting the volume fractions of two neighbouring cells. The volume fractions are then advected using the velocity components at the boundary of the two cells. The following advection criterion is proposed: for advection in the axial direction the axial velocity u is assumed constant in the vicinity of each cell face; for advection in the radial direction the radial velocity v times the radial distance r is assumed constant in the vicinity of each cell face, i.e. rβv = const., where β = 0 for Cartesian and β = 1 for axisymmetric systems. The above criterion is used to develop an algorithm for the advection of axisymmetric interfaces which is referred to as the ‘axisymmetric flux line segment model for advection and interface reconstruction’ or A‐FLAIR.
A hybrid finite‐element–volume‐of‐fluid method for simulating free surface flows and interfaces
Authors: Mashayek F. , Ashgriz N.
Published: August 2005

A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume‐of‐fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid‐size‐dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM‐VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break‐up of a capillary jet and the coalescence collision of two liquid drops.
Transmission‐line modelling of nonlinear reactive components and mutual inductances
Authors: Wong Chi‐Chung
Published: August 2005

Transmission‐line models (TLMs) for nonlinear reactive components and mutual inductances are derived. The model for nonlinear reactive components is shown to be an improvement on the previous one. TLM results with the mutual inductance model are compared with the exact solution, and good agreement is found.
Time domain absorbing boundary condition in Layered media
Authors: Lin C. C. , Mei K. K.
Published: August 2005

An absorbing boundary condition for simple layered media is presented. The method enables the modelling of open space radiation and scattering problems when the source (or scatterer) and a plane interface between two media are both located within the finite‐difference or finite‐element region. The projection operator method is used to take into account the presence of reflected waves at the media interface. The derivation of the projection operator is presented for one, two and three dimensions. Examples of electromagnetic radiation and scattering in two dimensions are presented to illustrate the numerical implementation and validity of the new absorbing boundary condition.
A hybrid modelling technique for underwater acoustic scattering
Authors: Orme E. A. , Johns P. B. , Arnold J. M.
Published: August 2005

A numerical method using impulse analysis of a transmission‐line matrix is used to model the scattering of underwater acoustic waves. The method is demonstrated by observation of plane and curved wavefronts travelling through the medium, and by plane wavefronts being scattered by a reflecting boundary.
Radar cross‐section reduction studies of partially open cavity structures
Authors: Chou Ri‐Chee , Lee Shung‐Wu
Published: August 2005

Shooting and bouncing rays (SBR) is a numerical method based on geometric optics developed to compute the electromagnetic scattering from jet inlets and partially open cavity structures. This method is used to study the effects of shaping on the radar cross‐section (RCS) of cavities. Two cylindrical cavity structures are analysed: one with a uniform circular cross‐section, and the other with a non‐uniform cross‐section varying from a triangular shape to a circular shape. By bending the longitudinal axis of a cylindrical cavity, a significant reduction in RCS at near axial incidence can be achieved.
The use of orthogonal curvilinear meshes in TLM models
Authors: Meliani H. , De Cogan D. , Johns P. B.
Published: August 2005

The development of numerical models to describe physical problems with irregular boundaries frequently involves the use of very fine or variable Cartesian meshes when a more descriptive mesh might be appropriate. This paper describes the application of the transmission line matrix (TLM) technique to the analysis of orthogonal curvilinear mesh problems. Although very high levels of accuracy are possible, the computational efficiency may be reduced owing to the stub admittance factor, S, and the need for an accurate evaluation of the transmission line parameters.
A self‐consistent model for short‐channel mosfets
Authors: Banna M. El , Nokali M. El
Published: August 2005

A de model for short‐channel MOSFETs is presented in this paper. Several second‐order effects associated with small‐geometry MOSFETs such as mobility degradation, carrier velocity saturation and channel length modulation are included in the model. The analysis emphasizes the modeling of the output conductance and the transconductance which are important in analogue circuit simulation. The theoretical predictions of the model are in good agreement with the experimental data available in the literature.
The 3D transmission‐line matrix method: Theory and comparison of the processes
Authors: Saguet P.
Published: August 2005

This paper presents an overview of the 3D transmission‐line matrix method of analysis, describing the various nodes which are available to date: expanded node, asymmetrical condensed node, symmetrical condensed node. The most general scattering matrices of these nodes are given. The various techniques used to implement irregularly graded meshes are also described. A comparison of all the processes applied to the same structure is made. Conclusions on their use are then discussed.
The discrete time domain Green's function or Johns matrix — A new powerful concept in transmission line modelling (TLM)
Authors: Hoefer Wolfgang J. R.
Published: August 2005

A new TLM‐based concept analogous to the Green's function approach in classical electromagnetic theory is presented. It employs the procedure known as time domain diakoptics. The response of a TLM mesh to a unit impulse excitation at selected input points is interpreted as a discrete Green's function in the time domain, and the term ‘Johns matrix’ is proposed for this characteristic response. As in classical theory, the response of the mesh to an arbitrary excitation is found by convolving the excitation with its Johns matrix. This concept extends the generalized scattering parameter concept into the time dimension, opens unprecedented possibilities for partioning time domain problems at the field level, and permits large‐scale preprocessing of substructures for computer‐aided design. It also represents and elegant way of modelling broadband absorbing boundary conditions, imperfectly conducting walls and general frequency dispersive boundaries in the time domain.
The calculation of radar cross‐section (RCS) using the TLM method
Authors: German Fred J. , Gothard Griffin K. , Riggs Lloyd S. , Goggans Paul M.
Published: August 2005

The calculation of the radar cross‐section (RCS) of complex bodies using the symmetrical condensed TLM method is presented. The technique is based on a near‐to‐far field transformation of the TLM calculated near fields. Several two‐dimensional examples are presented which validate the method. The main advantage of utilizing techniques such as TLM for RCS computation lies in the ability to model arbitrary bodies with complex material compositions.
The modelling of networks with frequently changing topology whilst maintaining a constant system matrix
Authors: Hui S. Y. R. , Christopoulos C.
Published: August 2005

This paper describes a novel technique with which a system with changing topology can be modelled whilst maintaining a constant system matrix. This technique employs a new transmission‐line switch model which has a constant characteristic impedance, irrespective of its state. The method is explained, compared with the switched‐resistance method and demonstrated by two examples. It has been found that the proposed method offers substantial advantages in the formulation of the problems and in the efficiency of computation.
Analysis of acoustic radiation patterns of array transducers using the TLM method
Authors: Saleh A. H. M. , Blanchfield P.
Published: August 2005

The paper describes the application of the TLM numerical method for the analysis of acoustic wave propagation. It presents a general scattering algorithm for modelling homogeneous and inhomogeneous mediums where both the density and compressibility of the propagation space are varied. The method is used to obtain the acoustic radiation patterns of discrete transducer arrays. The effect of the spacing and the number of transducer elements on the radiation pattern are demonstrated by numerical results obtained using a two‐dimensional TLM mesh. The results also show the effect of array shading on the radiation pattern. Beam steering by delayed excitation of the transducer elements is also demonstrated here. In addition the paper presents two simple techniques for detecting the direction of wave propagation in the TLM mesh.
Numerical aspects of the boundary residual method
Authors: Bunch K. J. , Grow R. W.
Published: August 2005

The boundary residual method is a powerful technique for solving EM boundary‐value problems. This technique produces matrices difficult to solve using many of the standard numerical techniques. This paper discusses lesser‐known numerical aspects of this method, and it shows efficient and well‐conditioned methods to solve both the homogeneous and non‐homogeneous boundary residual problem.
Modelling of the generation of Ga interstitials during the diffusion of Zn into GaAs
Authors: Harrison I.
Published: August 2005

The diffusion of Zn into a GaAs crystal is modelled using numerical techniques similar to those of Zahari and Tuck.1 This technique does not directly solve any differential equations, the physical processes are directly modelled. The diffusion of Zn is assumed to be by the kick‐out mechanism. In this mechanism the Zn atoms diffuse into the crystal interstitially with a constant diffusion coefficient. The interstitial Zn atoms transfer to the substitutional lattice site by kicking out a Ga atom. The incorporation of the Zn atoms on to the lattice sites is assumed to take place at a rate much greater than the diffusion of the interstitial Zn. The diffusion of the generated Ga interstitial is also contained in the model. The effect on the Zn concentration profile and Ga interstitial concentration of varying both the Ga interstitial diffusivity and equilibrium concentration has been examined. Finally, the implications of these results on Zn induced disordering of GaAs/AlAs superlattices is discussed.
Modelling of electrically thick cylindrical antennas
Authors: Tan Soon Hie
Published: August 2005

Hallen's integral equation has been used as the basis for the formulation of cylindrical antenna theories for many years. Being a Fredholm integral equation of the first kind, its solution is mathematically an ill‐posed problem. The stability of the numerical methods based on this integral equation is dependent on the singularity and the non‐smoothness of the kernel function. For electrically thick cylindrical antennas, the dominance of the singular part of the kernel (logarithmic) is weakened and the kernel function becomes relatively smooth. This observation implies possible deteriorations of the stability of the numerical methods based on Hallen's integral equation. This paper describes the development of an alternative formulation for the electrically thick cylindrical antennas based on the singular integral equation of the first kind with a Cauchy‐type kernel which eliminates the potential instability problem. A numerical method based on this formulation of the antenna problem has been implemented and case studies show that it is very stable and efficient for the numerical modelling of electrically thick cylindrical antennas.
Radiation losses in microstrip antenna feed networks printed on multilayer substrates
Authors: Harokopus W. P. , Katehi P. B.
Published: August 2005

The effect of the substrate structure on the radiation properties of microstrip array feed networks is investigated with the space‐domain integral equation approach. Numerical and analytical techniques are employed to produce efficient computer algorithms. Results for space and surface wave losses are presented for corner discontinuities printed on substrate/superstrate, and two‐layer substrate structures. Comparisons are made with the single‐layer case.
An investigation of the numerical properties of the mode‐matching technique
Authors: Sorrentino R. , Mongiardo M. , Alessandri F. , Schiavon G.
Published: August 2005

A new insight into the numerical properties of the mode‐matching (MM) technique is given at the example of capacitive and inductive diaphragms in rectangular waveguide. The presence of two sources of error is pointed out and the existence is demonstrated of an optimum modal ratio which produces the best compensation between the two errors. The MM technique is formulated in a generalized form as an integral equation for either the electric field on the aperture or the current on the diaphragm. This allows the edge condition to be incorporated into the basis functions in order to improve the numerical efficiency of the method. An extensive investigation of the numerical properties of the various formulations in different cases is presented, including the frequency behaviour of the numerical error.
Comprehensive MoL analysis of a class of semiconductor‐based transmission lines suitable for microwave and optoelectronic application
Authors: Wu Ke , Vahldieck Ruediger
Published: August 2005

A comprehensive analysis procedure is presented to investigate mode propagation in a class of semiconductor‐based transmission lines suitable for application in microwave or optoelectronic circuits. The method of lines (MoL) has been used to investigate single or multiconductor planar transmission line structures printed on a combination of insulating and semiconducting substrate. Homogeneous as well as inhomogeneous doping areas in the semiconductor are included in the theoretical formulation. Numerical results are presented for III–V semiconductor travelling wave electro‐optic modulators in double‐rib, multilayer strip waveguide configuration, microslabTMtransmission lines with partial and full strip cover and slow‐wave MIS microstrip/coplanar transmission lines on thick and thin film semiconductor substrate with gradually inhomogeneous doping layer.
Improvements in the analysis of a TH0mp cavity for precise complex permittivity measurements
Authors: Marchildon Louis , Akyel Cevdet , Abdulnour Jawad , Gauthier Sylvain
Published: August 2005

An analysis of the relationship between complex permittivity and complex resonance frequency is proposed for a cylindrical cavity oscillating in a TM0mp mode. Effects of wall conductivity, coupling loops, and holes for the insertion of dielectric samples are fully taken into account. With dielectric samples of small radii, insertion holes produce the most important corrections. Their effect is modelled through a finite difference solution of the field equations in the neighbourhood of the holes. A computer program is described for the analysis, the use of which is illustrated with results of measurements.
An efficient velocity–space model of carrier transport in Gallium Arsenide
Authors: Dunn Douglas E. , de Araujo Carlos A. Paz
Published: August 2005

A new GaAs carrier transport modelling methodology is presented, designed to address the competing needs of microscopic detail and of computational efficiency. The rationale for advanced semiclassical models based on the Boltzmann transport equation (BTE) are reviewed and discussed in terms of the unique properties of GaAs. A new methodology is then presented, formulated around a one‐dimensional velocity–space variable. It includes a realistic description of the GaAs band structure including multiple valleys, non‐parabolicity, and anisotropy, which is used to explicitly evaluate the scattering distributions, and rates, for different scattering mechanisms. These in turn allow a direct evaluation of the BTE scattering inegral, which is solved iteratively with the non‐scattering terms. Based on this methodology, a prototype model is shown to reproduce the GaAs velocity–field relationship in homogeneous, undoped material. Band structure and forward‐scattering effects are clearly visible in the model's solutions for the carrier velocity distribution. The model's computational simplicity, combined with a finer level of detail, makes it suitable for device simulation without invoking Monte Carlo or other computationally intensive methods.
Computational models for laminated magnetic materials
Authors: Silvester Peter P.
Published: August 2005

The permeability tensor of the homogeneous bulk material externally equivalent to a laminated packet of non‐linear, anisotropic, non‐hysteretic sheets is derived by symbolic computation. The composite permeability bears a surprisingly simple algebraic relationship to the local permeabilities of its component materials even in the general case. Several special cases of common interest, where the tensor permeability assumes symmetric or diagonal form, are examined. Results are presented both as algebraic expressions and as brief optimized Fortran subroutines suitable for fitting into field analysis programs.
Application of the TLM method to two‐dimensional scattering problems
Authors: Simons N. R. S. , Bridges E.
Published: August 2005

In this paper the application of the TLM method to electromagnetic scattering problems is investigated. To achieve the full computational benefits of using a time‐domain numerical method, pulse excitation can be applied together with Fourier transformation of an output impulse response to yield frequency‐domain results over a wide bandwidth. The configuration of the mesh is the same as that used in FD–TD scattering simulations (i.e., separation of the simulation space into total and scattered field regions). To terminate the exterior boundaries of the mesh, absorbing boundary conditions are applied to absorb the outward travelling waves. The effect of the absorbing boundaries on both time‐ and frequency‐domain results is investigated. Frequency‐domain scattered far‐field patterns are presented for perfectly conducting square and circular cylinders illuminated by an incident plane wave (TM case). Forward and back scattering cross‐section results obtained from a single TLM simulation indicate both the accuracy and efficiency of the method for calculating frequency‐domain results over a wide bandwidth.
Radiation and scattering of transient electromagnetic fields (invited paper)
Authors: Felsen Leopold B.
Published: August 2005

Under wideband and especially ultrawideband (short pulse) excitation, the electromagnetic fields, after encounters with a propagation or scattering environment, reveal features which range from highly resolved spikes or dips to smooth oscillations at early and late observation times, respectively. Time‐domain (TD) analytic modelling should be structured around wave objects which relate features (observables) in data to distinct features in the environment. A strategy to this end, named observable‐based parametrization (OBP), is proposed here. The rules are learned from frequency‐ and time‐domain asymptotics applies to spatial and spectral domain representations of tractable prototype problems. This leads to self‐consistent hybrid combinations OBP–TD travelling (wavefront) and oscillatory (resonant) synthesizing basis fields; the latter include novel TD leaky modes for guiding wave channels and TD Bragg modes for periodic arrays. These concepts are illustrated by examples.
Characteristics of a rectangular waveguide containing a magnetized cylindrical ferrite post
Authors: Diamandi Ioanna , Sahalos John N. , Vafiadis Elias
Published: August 2005

A rigorous formulation of the scattering by a magnetized ferrite in a rectangular waveguide is presented. The EM field depends on the dimension, the frequency and the internal static magnetic field of the ferrite post. For some special values of the above quantitites the reflection or the transmission coefficient becomes equal to zero. These values give a family of filters and the results which follow explain their characteristics.
An investigation of the different TLM configurations used in the modelling of diffusion problems
Authors: Ait‐sadi Rachida , Naylor Phillip
Published: August 2005

The commonly used transmission‐line modelling (TLM) network of one‐dimensional diffusion problems often results in unwanted oscillations. Two different TLM configurations (line boundary (LB) and resistance boundary (RB)), are investigated with some techniques necessary to reduce the oscillations. Comparisons between the various LB and RB models addressed in this paper, indicate that, in general, two‐dimensional TLM models produce consistently more accurate results.
TLM modelling using an SIMD computer
Authors: Tan C. C. , Fusco V. F.
Published: August 2005

A major limitation of the transmission‐line matrix (TLM) method used to solve Maxwell's equations is the long computation time required. The TLM scattering calculations involved can, however, be viewed as parallel in nature. This paper describes an effort to reduce computational time by using an SIMD, DAP multiprocessor computer employed to solve a two‐dimensional TLM electromagnetic field formulation. A parallel algorithm based on the TLM scattering algorithm is designed and implemented using FORTRAN‐ PLUS Enhanced on an AMT DAP 510 machine. Here the connectivity of the DAP is exploited to simulate the intrinsic scattering behaviour on which the TLM algorithm relies. The results show that parallel processing on an SIMD machine such as the DAP is advantageous, especially for higher‐order mesh sizes.
Integral equation formulation of radiation from rectangular waveguides and horns
Authors: Moheb H. , Shafai L.
Published: August 2005

The radiation field patterns of rectangular waveguides and horns of finite dimensions are obtained numerically. The electric field integral equation is formulated to relate their radiation patterns to the surface current distribution. These currents are determined numerically by reducing the integral equation to a matrix equation, using the moment method. The computed currents are then used to calculate the radiation patterns and cross‐polar fields of the finite wavegiudes and horns. The method is numerically efficient and can be applied to the computation and optimization of the antenna feed configurations.
Numerical simulation of two‐valley semiconductor device model based on an ENO shock capturing algorithm
Authors: Radunvić Desanka , Radunović Jovan
Published: August 2005

Simulation results for a n+−n−n+ two‐valley semiconductor device obtained by use of a shock capturing numerical agorithm are presented. The one‐dimensional problem is modelled by two systems of Euler equations connected by their source terms, and the Poisson equation. The resulting system of seven equations is hyperbolic and non‐linear, and it is a great problem to find an adequate numerical approximation of its time‐dependent discontinuities. There are additional complications due to the stiffness of the source terms.

The numerical method used in this paper is first‐order acurate in time but of high spatial order in regions of smoothness. Before the method is applied, the system has to be transformed to a characteristic form. The adopted shock capturing algorithm enables the choice of the order of the accuracy by the appropriate choice of the reconstruction polynomial. Reconstructions of the second and fourth order are tested and some numerical results are presented. Because of the stiffness of the source terms, the sixth‐order accurate scheme breaks down. The results presented, and especially the response obtained of the structure to the step and periodic applied voltage, prove the correctness of the used schemes.
On the responses of strip‐line interconnects with discontinuities excited by external fields
Authors: Sali S.
Published: August 2005

An algorithm is developed to evaluate the responses of discontinuous coplanar strip‐lines excited by external electromagnetic fields. The algorithm uses the cascade chain matrix method which employs the distributed circuit parameters to model the external field coupling to the line and it is applicable to most commonly encountered discontinuities in microwave integrated circuit interconnects on lossy substrates. A general CAD program is developed based on this model and it is applied to realistic coplanar strip‐line interconnections with geometric and resistive discontinuities to illustrate the capabilities of the algorithm. These interconnect models are selected from a practical microwave integrated circuit design. Simplicity and fast speed of the algorithm enable computer‐aided analysis of externally induced electromagnetic noise in integrated circuits to be carried out. The effects of dielectric losses in the integrated circuit substrates and the discontinuities in the conducting tracks on the wave coupling are investigated in isolation.
Parallel three‐dimensional finite difference beam propagation methods
Authors: Masoudi Husain M. , Arnold John M.
Published: August 2005

In this work, we show the implementation of two explicit three‐dimensional finite‐difference beam propagation methods (BPM) on two different parallel computers, namely a transputer array and a Connection Machine (CM). To assess the performance of using parallel computers, serial computer codes of the two methods have ben implemented and a comparison between the speed of the serial and paralledl codes has been made. Large gains in the speed of the paralled FD‐BPMs has been obtained compared to the serial implementations. In addition, a comparison between the performance of the transputer array and the CM in executing the two FD‐BPMs has been discussed. Finally, to assess and compare the two methods, three different rib waveguides and three different directional couplers have been analysed and the results compared with published results.
Adaptive finite element mesh generation program for electron gun simulation
Authors: Xia S. , Broers A. N.
Published: August 2005

This paper describes a computer program for generating finite element meshes for electron guns. Two new methods, the ‘projection’ and the ‘mesh density function’ methods, are used to generate the mesh. The new methods enable the mesh distribution to be set smothly and changed easily, and also enable the mesh distribution to be adjusted according to parameters associated with the gun configuration or by feedback from the electric field calculation. The new program, which can handle a large variety of complicated electron gun structures, has been used in conjunction with the SOGUN program which has been developed by Zhu and Munro for electron gun simulation.