bluuebunny/crossref_metadata_2025_split huggingface dataset:
Finite element methods for one‐dimensional combustion problems
Authors: Ramos J. I. 
Published: October 2005

AbstractThree adaptive finite element methods based on equidistribution, elliptic grid generation and hybrid techniques are used to study a system of reaction–diffusion equations. It is shown that these techniques must employ sub‐equidistributing meshes in order to avoid ill‐conditioned matrices and ensure the convergence of the Newton method. It is also shown that elliptic grid generation methods require much longer computer times than hybrid and static rezoning procedures. The paper also includes characteristic, Petrov–Galerkin and flux‐corrected transport algorithms which are used to study a linear convection–reaction–diffusion equation that has an analytical solution. The flux‐corrected transport technique yields monotonic solutions in good agreement with the analytical solution, whereas the Petrov–Galerkin method with quadratic upstream‐weighted functions results in very diffused temperature profiles. The characteristic finite element method which uses a Lagrangian–Eulerian formulation overpredicts the flame front location and exhibits overshoots and undershoots near the temperature discontinuity. These overshoots and undershoots are due to the interpolation of the results of the Lagrangian operator onto the fixed Eulerian grid used to solve the reaction–diffusion operator, and indicate that characteristic finite element methods are not able to eliminate numerical diffusion entirely.
Numerical studies of fluid flow through tubes with double constrictions
Authors: Lee T. S. 
Published: October 2005

AbstractThe flow fields in the neighbourhood of double constrictions in a circular cylindrical tube were studied numerically. The effects on the streamline, velocity and vorticity distributions as the flow passes through the constrictions in the tube were studied in the Reynolds number range 5–200. Double constrictions with dimensionless spacing ratios of 1, 2, 3 and ∞ were studied for a 50% constriction.It is noted that when the Reynolds number is below 10, no recirculation region is formed in the above constricted flow. For Reynolds numbers greater than 10, a recirculation region forms downstream of each of the constrictions. For constriction spacing ratios of 1, 2, and 3, when the Reynolds number is high, a recirculation region spreads between the valley of the constrictions. The recirculation region formed between the two constrictions has a diminishing effect on the generation of wall vorticity near the second constriction area. In general, the peak value of wall vorticity is found slightly upstream of each of the constrictions. When the Reynolds number is increased, the peak wall vorticity value increases and its location is moved upstream. Maximum wall vorticity generated by the first constriction is found to be always greater than the maximum wall vorticity generated by the second constriction. The extent of this spreading of the recirculation region from the first constriction and its effects on the second constriction depend on the constriction spacing ratio and the flow Reynolds number.
A multigrid solver for the vorticity‐velocity Navier‐Stokes equations
Authors: Napolitano M. , Catalano L. A. 
Published: October 2005

AbstractThis paper provides a multigrid incremental line‐Gauss‐Seidel method for solving the steady Navier‐Stokes equations in two and three dimensions expressed in terms of the vorticity and velocity variables. The system of parabolic and Poisson equations governing the scalar components of the vector unknowns is solved using centred finite differences on a non‐staggered grid. Numerical results for the two‐dimensional driven cavity problem indicate that the spatial discretization of the equation defining the value of the vorticity on the boundary is extremely critical to obtaining accurate solutions. In fact, a standard one‐sided three‐point second‐order‐accurate approximation produces very inaccurate results for moderate‐to‐high values of the Reynolds number unless an exceedingly fine mesh is employed. On the other hand, a compact two‐point second‐order‐accurate discretization is found to be always satisfactory and provides accurate solutions for Reynolds number up to 3200, a target impossible heretofore using this formulation and a non‐staggered grid.
The PROSPER General Circulation Model, an adapted form of the Sandia Ocean Modelling method: A numerical description
Authors: Zuur E. A. H. 
Published: October 2005

AbstractThe PROSPER General Circulation Model (PGCM) is a three‐dimensional model based on the incompressible Navier‐Stokes equations, an equation of state and the heat equation. The hydrostatic approximation and the rigid lid approximation are used. The system of equations is converted into an equivalent form in which the surface pressure is more directly expressed in terms of a two‐dimensional Poisson equation. The finite difference method is described and analysed. In particular, the iteration method within every time step to determine the new surface pressure and velocity components, and numerical diffusion aspects due to the use of the staggered Arakawa‐C grid are looked at. Since part of the development of the PGCM code is a result of studying the Sandia Ocean Modelling System (SOMS), a comparison is made with respect to the concepts used in both models.
A quadratic‐element formulation of the complex variable boundary element method
Authors: Bailey Robert T. , Hsieh C. K. 
Published: October 2005

AbstractThe complex variable boundary element method (CVBEM) for simply connected domains is extended to include the use of quadratic elements and interpolating functions. The derivation follows the format for linear elements given in the literature, with second‐degree Lagrange polynomials taken as the interpolating functions. The quadratic‐element CVBEM nodal‐ and interior‐point equations are given in detail, and the resulting formulation is successfully tested by solving example problems with available analytical solutions. Comparisons of computational efficiency and accuracy are made between the solutions obtained using linear and quadratic elements. Additional comparisons are made using published results from other boundary element methods.
Segmented multigrid domain decomposition procedure for incompressible viscous flows
Authors: Srinivasan Kumar , Rubin Stanley G. 
Published: October 2005

AbstractThe application of grid stretching or grid adaptation is generally required in order to optimize the distribution of nodal points for fluid‐dynamic simulation. This is necessitated by the presence of disjoint high gradient zones, that represent boundary or free shear layers, reversed flow or vortical flow regions, triple deck structures, etc. A domain decomposition method can be used in conjunction with an adaptive multigrid algorithm to provide an effective methodology for the development of optimal grids. In the present study, the Navier‐Stokes (NS) equations are approximated with a reduced Navier‐Stokes (RNS) system, that represents the lowest‐order terms in an asymptotic Re expansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and ensures mass conservation in all subdomain grid interfaces, as well as at the outflow boundary. The higher‐order (NS) diffusion terms are included through a deferred corrector, in selected subdomains, when necessary. Adaptivity in the direction of refinement is achieved by grid splitting or domain decomposition in each level of the multigrid procedure. Normalized truncation error estimates of key derivatives are used to determine the boundaries of these subdomains. The refinement is optimized in two co‐ordinate directions independently. Multidirectional adaptivity eliminates the need for grid stretching so that uniform grids are specified in each subdomain. The overall grid consists of multiple domains with different meshes and is, therefore, heavily graded. Results and computational efficiency are discussed for the laminar flow over a finite length plate and for the laminar internal flow in a backward‐facing step channel.
Numerical simulation of cooling‐induced convective currents on a littoral slope
Authors: Horsch G. M. , Stefan H. G. , Gavali S. 
Published: October 2005

AbstractThe transient development of cooling‐induced flow in a triangular domain filled with water is studied by means of numerical simulation as a model for flow developing in the littoral region of lakes or coasts. The domain is fitted in polar co‐ordinates; solutions are obtained for different values of the independent parameters of the model, which are the Rayleigh number (Ra), the Prandtl number (Pr) and the slope of the domain (S). Within the ranges examined, as Ra is increased, different regimes of the developing flow are observed; these are found qualitatively to be insignificantly influenced by changes in S, whereas the flow is found to be quantitatively insensitive to Pr for high enough values of Pr. Several interesting features of the flow are depicted and integral values useful in the analysis of flow in lakes are extracted.
Space‐time finite element computation of compressible flows between moving components
Authors: Wren G. P. , Ray S. E. , Aliabadi S. K. , Tezduyar T. E. 
Published: October 2005

AbstractA numerical simulation capability for the injector flow of a regenerative liquid propellant gun (RLPG) is presented. The problem involves fairly complex geometries and two pistons in relative motion; therefore a stabilized space‐time finite element formulation developed earlier and capable of handling flows with moving mechanical components is used. In addition to the specifics of the numerical method, its application to a 30 mm RLPG test firing is discussed. The computational data from the simulation of this test case are interpreted to provide information on flow characteristics, with emphasis on the tendency of the flow to separate from the injection orifice boundary of the test problem. In addition, the computations provided insight into the behaviour of the flow entering the combustion chamber.
Gene expression by human monocytes from peripheral blood in response to exposure to metals
Authors: Jost‐Albrecht Katrin , Hofstetter Willy 
Published: October 2005

AbstractWith increasing life expectancy and active lifestyles, the longevity of arthroplasties has become an important problem in orthopaedic surgery and will remain so until novel approaches to joint preservation have been developed. The sensitivity of the recipient to the metal alloys may be one of the factors limiting the lifespan of implants. In the present study, the response of human monocytes from peripheral blood to an exposure to metal ions was investigated, using the method of real‐time polymerase chain reaction (PCR)–based low‐density arrays. Upon stimulation with bivalent (Co2+ and Ni2+) and trivalent (Ti3+) cations and with the calcium antagonist LaCl3, the strength of the elicited monocytic response was in the order of Co2+ ≥ Ni2+ > Ti3+ ≥ LaCl3. The transcriptional regulation of the majority of genes affected by the exposure of monocytes to Co2+ and Ni2+ was similar. Some genes critically involved in the processes of inflammation and bone resorption, however, were found to be differentially regulated by these bivalent cations. The data demonstrate that monocytic gene expression is adapted in response to metal ions and that this response is, in part, specific for the individual metals. It is suggested that metal alloys used in arthroplasties may affect the extent of inflammation and bone resorption in the peri‐implant tissues in dependence of their chemical composition. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2006
An in vivo study of tricalcium phosphate and glutaraldehyde crosslinking gelatin conduits in peripheral nerve repair
Authors: Chen Ming‐Hong , Chen Pei‐Ru , Chen Mei‐Hsiu , Hsieh Sung‐Tsang , Huang Jing‐Shan , Lin Feng‐Huei 
Published: October 2005

AbstractIn order to modulate the mechanical properties of gelatin, we previously developed a biodegradable composite composed by tricalcium phosphate and glutaraldehyde crosslinking gelatin (GTG) feasible for surgical manipulation. In this study, we evaluated the in vivo applications of GTG conduit for peripheral nerve repair. The effect of sciatic nerve reconstruction was compared between resorbable permeable GTG conduits and durable impermeable silicone tubes. Traditional methods of assessing nerve recovery following peripheral nerve repair including histomorphometric and electrophysiologic features were conducted in our study. In addition, autotomy score and sciatic function index (SFI) in walking tract analysis were used as additional parameters for assessing the return of nerve function. Twenty‐four weeks after sciatic nerve repair, the GTG conduits were harvested. Microscopically, regeneration of nerves was observed in the cross‐section at the mid portion of all implanted GTG conduits. The cross‐sectional area of regenerated nerve of the GTG group was significant larger than that of the silicone group. In the compound muscle action potentials (CMAP), the mean recovery index of CMAP amplitude was 0.24 ± 0.02 for the silicone group, 0.41 ± 0.07 for the GTG group. The mean SFI increased with time in the GTG group during the evaluation period until 24 weeks. Walking tract analysis showed a higher SFI score in the GTG group at both 12 and 24 weeks. The difference reached a significant level at 24 weeks. Thus, the histomorphometric, electrophysiologic, and functional assessments demonstrate that GTG can be a candidate for peripheral nerve repair. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2006
Low‐frequency asymptotics for dissipative Maxwell's equations in bounded domains
Authors: Weck Norbert , Witsch Karl J. 
Published: October 2005

AbstractConsider a bounded domain Ω surrounded by a perfect conductor and containing a conducting cavity D. The behaviour of the solutions of the time harmonic Maxwell problem as frequency tends to 0 is analysed in this situation. Necessary and sufficient conditions on the excitations are given which guarantee the existence of a limit. This limit turns out to be the solution of some static problem.
Asymptotic expansions for hyperbolic–parabolic systems with a small parameter
Authors: Kreiss Gunilla 
Published: October 2005

AbstractIn this paper we consider initial‐boundary value problems for systems with a small parameter ϵ. The problems are mixed hyperbolic–parabolic when ϵ > 0 and hyperbolic when ϵ = 0. Often the solution can be expanded asymptotically in ϵ and to first approximation it consists of the solution of the corresponding hyperbolic problem and a boundary layer part. We prove sufficient conditions for the expansion to exist and give estimates of the remainder. We also examine how the boundary conditions should be choosen to avoid O(1) boundary layers.
Resonance phenomena in infinite strings with periodic ends
Authors: Werner P. 
Published: October 2005

AbstractWe study the propagation of linear waves, generated by a compactly supported time‐harmonic force distribution, in an infinite string under the assumption that the material properties are p1‐periodic for x > a and p2‐periodic for x < − a. As has been pointed out in two preceding papers devoted to related configurations ([4], [5]), the combination of a time‐periodic force and a periodic spatial structure may lead to resonance phenomena. We show that the present configuration also permits resonances of orders t and t1/2 for a discrete set of frequencies. The occurrence of resonances is closely related to the presence of non‐trivial solutions of the corresponding time‐independent homogeneous problem which satisfy certain asymptotic properties (‘standing waves’).
Full low‐frequency asymptotic expansion for second‐order elliptic equations in two dimensions
Authors: Kleinman R. , Vainberg B. 
Published: October 2005

AbstractThe present paper contains the low‐frequency expansions of solutions of a large class of exterior boundary value problems involving second‐order elliptic equations in two dimensions. The differential equations must coincide with the Helmholtz equation in a neighbourhood of infinity, however, they may depart radically from the Helmholtz equation in any bounded region provided they retain ellipticity. In some cases the asymptotic expansion has the form of a power series with respect to k2 and k2 (ln k + a)−1, where k is the wave number and a is a constant. In other cases it has the form of a power series with respect to k2, coefficients of which depend polynomially on In k. The procedure for determining the full low‐frequency expansion of solutions of the exterior Dirichlet and Neumann problems for the Helmholtz equation is included as a special case of the results presented here.
The sorption of mixtures under linear equilibrium partitioning and chemical transformation
Authors: Oppenheimer Seth F. 
Published: October 2005

AbstractWe consider the flow of a mixture, whose components are undergoing temporally and spatially varying linear equilibrium sorption partitioning and, possibly nonlinear, chemical transformations. We are able to generate an evolution system of parabolic type on the space of uniformly continuous functions and thus obtain classical solutions for arbitrary initial values.
New convergence results and preconditioning strategies for the conjugate gradient method
Authors: Kaporin I. E. 
Published: October 2005

AbstractInstead of the standard estimate in terms of the spectral condition number we develop a new CG iteration number estimate depending on the quantity B = 1/ntr M/(det M)1/n, where M is an n × n preconditioned matrix. A new family of iterative methods for solving symmetric positive definite systems based on B‐reducing strategies is described. Numerical results are presented for the new algorithms and compared with several well‐known preconditioned CG methods.
A simple hybrid stress element for shear deformable plates
Authors: de Miranda Stefano , Ubertini Francesco 
Published: October 2005

AbstractA new quadrilateral 4‐node element for shear deformable plates is developed based on the hybrid stress formulation. The element is designed to be simple, stable, free of locking and to pass all the patch tests. To this purpose, special attention is devoted to select displacement and stress approximations. The standard displacement interpolation is enhanced by linking the transverse displacement to the nodal rotations and an appropriate stress approximation is rationally derived. In particular, the assumed stress approximation is equilibrated within each element, co‐ordinate invariant and ruled by the minimum number of parameters. Excellent element performance is demonstrated by a wide experimental evaluation. Copyright © 2005 John Wiley & Sons, Ltd.
Mathematical analysis and numerical study to free vibrations of annular plates using BIEM and BEM
Authors: Chen J. T. , Lin S. Y. , Chen I. L. , Lee Y. T. 
Published: October 2005

AbstractIn this paper, the spurious eigenequations for annular plate eigenproblems by using BIEM and BEM are studied in the continuous and discrete systems. Since any two boundary integral equations in the plate formulation (4 equations) can be chosen, 6 (C) options can be considered instead of only two approaches (single‐layer and double‐layer methods, or singular and hypersingular equations) which are adopted for the eigenproblems of the membrane and acoustic problems. The occurring mechanism of the spurious eigenequation for annular plates in the complex‐valued formulations is studied analytically. For the continuous system, degenerate kernels for the fundamental solution and the Fourier series expansion for the circular boundary density are employed to derive the true and spurious eigenequations analytically. For the discrete system, the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the true and spurious eigenequations. True eigenequation depends on the specified boundary condition while spurious eigenequation is embedded in each formulation. It is found that the spurious eigenvalue for the annular plate is the true eigenvalue of the associated interior problem with an inner radius of the annular domain. Also, we provide three methods (SVD updating technique, Burton and Miller method and CHIEF method) to suppress the occurrence of the spurious eigenvalues. Several examples were demonstrated to check the validity of the formulations. Copyright © 2005 John Wiley & Sons, Ltd.
A mathematical framework of the bridging scale method
Authors: Tang Shaoqiang , Hou Thomas Y. , Liu Wing Kam 
Published: October 2005

AbstractIn this paper, we present a mathematical framework of the bridging scale method (BSM), recently proposed by Liu et al. Under certain conditions, it had been designed for accurately and efficiently simulating complex dynamics with different spatial scales. From a clear and consistent derivation, we identify two error sources in this method. First, we use a linear finite element interpolation, and derive the coarse grid equations directly from Newton's second law. Numerical error in this length scale exists mainly due to inadequate approximation for the effects of the fine scale fluctuations. An modified linear element (MLE) scheme is developed to improve the accuracy. Secondly, we derive an exact multiscale interfacial condition to treat the interfaces between the molecular dynamics region ΩD and the complementary domain ΩC, using a time history kernel technique. The interfacial condition proposed in the original BSM may be regarded as a leading order approximation to the exact one (with respect to the coarsening ratio). This approximation is responsible for minor reflections across the interfaces, with a dependency on the choice of ΩD. We further illustrate the framework and analysis with linear and non‐linear lattices in one‐dimensional space. Copyright © 2005 John Wiley & Sons, Ltd.
On the density of finite element matrices
Authors: George J. Alan 
Published: October 2005

AbstractExplicit formulae for the density of a class of finite element matrices are presented. The formulae are functions of the characteristics of the mesh and the element (piecewise polynomial) employed. Results are given for two‐dimensional triangular and quadrilateral elements and three‐dimensional tetrahedral and cuboid elements. These results are useful in the management of storage in finite element computer programmes.
A comparison of preconditioned iterative techniques using rapid operator application against direct solution methods
Authors: Foresti S. , Hassanzadeh S. , Murakami H. , Sonnad V. 
Published: October 2005

AbstractThe p‐version of the finite element method which uses high order hierarchic basis functions within an element allows for ease of adaptive computation, and high accuracy with relatively few degrees of freedom. However, the solution time and storage requirements for large 3‐D problems can be very high when direct methods are used to factor global matrices. Iterative techniques with rapid operator application have minimal storage requirements because neither element nor global matrices are formed, but may not converge rapidly enough. We study an approach that attempts to combine the two methods by using direct factorization of the matrix corresponding to low level polynomials as a preconditioner to an iterative method at a higher polynomial level. This resulting solution scheme converges more rapidly than an unpreconditioned scheme but has much lower storage requirements than direct methods. We illustrate the effectiveness of this scheme on some large three‐dimensional problems in structural analysis.