bluuebunny/crossref_metadata_2025 huggingface dataset:
A new outflow boundary condition
Authors: Papanastasiou T. C. , Malamataris N. , Ellwood K.
Published: August 2005

Boundary conditions come from Nature. Therefore these conditions exist at natural boundaries. Often, owing to limitations in computing power and means, large domains are truncated and confined between artificial synthetic boundaries. Then the required boundary conditions there cannot be provided naturally and there is a need to fabricate them by intuition, experience, asymptotic behaviour and numerical experimentation. In this work several kinds of outflow boundary conditions, including essential, natural and free boundar conditions, are evaluated for two flow and heat transfer model problems. A new outflow boundary condition, called hereafter the free boundary condition, is introduced and tested. This free boundary condition is equivalent to extending the validity of the weak form of the governing equations to the synthetic outflow instead of replacing them there with unknown essential or natural boundary conditions. In the limit of zero Reynolds number the free boundary condition minimizes the energy functional among all possible choices of outflow boundary conditions. A review of results from applications of the same boundary conditions to several other flow situations is also presented and discussed.
Flux difference splitting for 1D open channel flow equations
Authors: Alcrudo Francisco , Garcia‐Navarro Pilar , Saviron Jose‐Maria
Published: August 2005

An upwind finite difference scheme based on flux difference splitting is presented for the solution of the equations governing unsteady open channel hydraulics. An approximate Jacobian needed for splitting the flux differences is defined that satisfies the conditions required to construct a first‐order upwind conservative discretization of the equations. Added limited second‐order corrections make the resulting scheme robust and accurate for the computation of all regimes of open channel flow. Some numerical results and comparisons with other classical schemes under exacting conditions are presented.
Calculation of two‐dimensional shear‐driven cavity flows at high reynolds numbers
Authors: Huser A. , Biringen S.
Published: August 2005

The time‐dependent Navier–Stokes equations are numerically integrated for two‐dimensional incompressible viscous flow in a shear‐driven square cavity. Using a time‐splitting method and finite differences on a staggered mesh, the momentum and pressure equations are directly solved by a tensor product method where one finite difference direction is diagonalized by eigenvalue decomposition. The effects of increasing Reynolds number are studied and the developing boundary layer is captured by using a finely clustered mesh. At Re = 30000 the flow is in a continuously developing unsteady regime. Power spectrum plots indicate that the unsteady flow oscillates with one fundamental frequency and exhibits some characteristics of transition between laminar and turbulent states.
Application of a vortex method to free surface flows
Authors: Chen Liyong , Vorus William S.
Published: August 2005

Vortex methods have found wide applications in various practical problems. The use of vortex methods in free surface flow problems, however, is still very limited. This paper demonstrates a vortex method for practical computation of non‐linear free surface flows produced by moving bodies. The method is a potential flow formulation which uses the exact non‐linear free surface boundary condition at the exact location of the instantaneous free surface. The position of the free surface, on which vortices are distributed, is updated using a Lagrangian scheme following the fluid particles on the free surface. The vortex densities are updated by the non‐linear dynamic boundary condition, derived from the Euler equations, with an iterative Lagrangian numerical scheme.

The formulation is tested numerically for a submerged circular cylinder in unsteady translation. The iteration is shown to converge for all cases. The results of the unsteady simulations agree well with classical linearized solutions. The stability of the method is also discussed.
A new decoupled finite element algorithm for viscoelastic flow. Part 2: Convergence properties of the algorithm
Authors: Swarbrick S. J. , Nassehi V.
Published: August 2005

We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper.
A boundary element formulation using the simple method
Authors: Grigor'Ev M. M.
Published: August 2005

A new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well‐known SIMPLE algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and Spalding.32However, the new method demands a much larger computer strorage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two‐dimensional domain are found analytically. To preserve the stability in the iteration process, under‐relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates atRe= 20 andRe= 200, the flows in a square cavity with a moving upper lid atRe= 1 andRe= 100 and the flow in a plane channel with sudden symmetric expansion atRe=46·6.
Finite element modelling of sheared flow effects on the radiation characteristics of acoustic sources in a circular duct
Authors: Steck James E. , Eversman Walter
Published: August 2005

The recent interest in propeller noise generation, stimulated by development of new propeller types for commerical propjets, has generated a need for the ability of measure the noise characteristics of propellers. However, wind tunnel noise measurements are affected by reflections from the wind tunnel walls. Computer codes predicting the free‐field noise of a propeller and its noise field in a circular wind tunnel allow validating the use of wind tunnel measurements to predict free‐field noise characteristics. A wind tunnel contains flow which is uniform in the duct axial direction, but can vary in the radial direction. It can be shown that a third‐order differential equation governs the acoustic pressure field for such a duct containing radially sheared subsonic flow. This third‐order problem is then posed as a coupled pair of equations which are second‐order in terms of acoustic density and first‐order in terms of an artificial variable which represents the effects of the flow being sheared. It is shown that this form of the problem allows a natural extension of the existing numerical solution techniques for non‐sheared flow. The sheared flow problem is presented, and a finite element method is developed to yield a solution for propeller‐type acoustic forces. The finite element code and method are refined with numerical experiments, and results are presented for a specific propeller and duct geometry. Good agreement is shown between this method and an alternate approach to the sheared flow problem using a piecewise constant representation of the velocity in the boundary layer. This validates both the numerical methods.
Flux difference splitting for open‐channel flows
Authors: Glaister P.
Published: August 2005

A finite difference scheme based on flux difference splitting is presented for the solution of the one‐dimensional shallow‐water equations in open channels, together with an extension to two‐dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second‐order scheme which avoids non‐physical, spurious oscillations. The scheme is applied to a one‐dimensional dam‐break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two‐dimensional dam‐break problem. The numerical results are compared with the exact solution, or other numerical results, where available.
The analysis of unsteady incompressible flows by a three‐step finite element method
Authors: Jiang Chun Bo , Kawahara Mutsuto
Published: August 2005

This paper describes a three‐step finite element method and its applications to unsteady incompressible fluid flows. Stability analysis of the one‐dimensional pure convection equation shows that this method has third‐order accuracy and an extended numerical stability domain in comparison with the Lax‐‐Wendroff finite element method. The method is cost‐effective for incompressible flows because it permits less frequent updates of the pressure field with good accuracy. In contrast with the Taylor‐Galerkin method, the present method does not contain any new higher‐order derivatives, which makes it suitable for solving non‐linear multidimensional problems and flows with complicated boundary conditions. The three‐step finite element method has been used to simulate unsteady incompressible flows. The numerical results obtained are in good agreement with those in the literature.
A second‐order upwind finite‐volume method for the Euler solution on unstructured triangular meshes
Authors: Pan Dartzi , Cheng Jen‐Chieh
Published: August 2005

A scheme for the numerical solution of the two‐dimensional (2D) Euler equations on unstructured triangular meshes has been developed. The basic first‐order scheme is a cell‐centred upwind finite‐volume scheme utilizing Roe's approximate Riemann solver. To obtain second‐order accuracy, a new gradient based on the weighted average of Barth and Jespersen's three‐point support gradient model is used to reconstruct the cell interface values. Characteristic variables in the direction of local pressure gradient are used in the limiter to minimize the numerical oscillation around solution discontinuities. An Approximate LU (ALU) factorization scheme originally developed for structured grid methods is adopted for implicit time integration and shows good convergence characterisitics in the test. To eliminate the data dependency which prohibits vectorization in the inversion process, a black‐gray‐white colouring and numbering technique on unstructured triangular meshes is developed for the ALU factorization scheme. This results in a high degree of vectorization of the final code. Numerical experiments on transonic Ringleb flow, transonic channel flow with circular bump, supersonic shock reflection flow and subsonic flow over multielement aerofoils are calculated to validate the methodology.
Linear and non‐linear iterative methods for the incompressible Navier‐Stokes equations
Authors: Clift Simon S. , Forsyth Peter A.
Published: August 2005

In this study, the discretized finite volume form of the two‐dimensional, incompressible Navier‐Stokes equations is solved using both a frozen coefficient and a full Newton non‐linear iteration. The optimal method is a combination of these two techniques. The linearized equations are solved using a conjugate‐gradient‐like method (CGSTAB). Various types of preconditioning are developed. Completely general sparse matrix methods are used. Investigations are carried out to determine the effect of finite volume cell anisotropy on the preconditioner. Numerical results are given for several test problems.
A conservative and shape‐preserving semi‐Lagrangian method for the solution of the shallow water equations
Authors: Garcia‐Navarro P. , Priestley A.
Published: August 2005

Semi‐Lagrangian methods are now perhaps the most widely researched algorithms in connection with atmospheric flow simulation codes. In order to investigate their applicability to hydraulic problems, cubic Hermite polynomials are used as the interpolant technique. The main advantage of such an approach is the use of information from only two points. The derivatives are calculated and limited so as to produce a shape‐preserving solution. The lack of conservation of semi‐Lagrangian methods, however, is widely regarded as a serious disadvantage for hydraulic studies, where non‐linear problems in which shocks may develop are often encountered. In this work we describe how to make the scheme conservative using an FCT approach. The method proposed does not guarantee an unconditional shock‐capturing ability but is able to correctly reproduce the discontinuous flows common in open channel simulation without any shock‐fitting algorithm. It is a cheap way to improve existing 1D semi‐Lagrangian codes and allows stable calculations beyond the usual CFL limits. A basic semi‐Lagrangian method is presented that provides excellent results for a linear problem: the new techniques allow us to tackle non‐linear cases without unduly degrading the accuracy for the simpler problems. Two one‐dimensional hydraulic problems are used as test cases, water hammer and dam break. In the latter case, because of the non‐linearity, special care is needed with the low‐order solution and we show the advantages of using Leveque's large‐time step version of Roe's scheme for this purpose.
Numerical simulation of free shear flows and far‐field sound pressure directivity
Authors: Soh W. Y.
Published: August 2005

An implicit spatial differencing technique with fourth‐order accuracy has been developed based on the Pade compact scheme. A dispersion‐relation‐preserving concept has been incorporated into the numerical scheme. Two‐dimensional Euler computation of a spatially developing free shear flow with and without external excitation has been performed to demonstrate the capability of the numerical scheme developed. Results are in good agreement with theory and experimental observation regarding the growth rate of the fluctuating velocity, the convective velocity and the vortex‐pairing process. The far‐field sound pressure generated by the computed shear flow solution using Lighthill's acoustic analogy shows a strong directivity with a zone of silence at the flow angle.
A comparison of second‐order and fourth‐order pressure gradient algorithms in a σ‐co‐ordinate ocean model
Authors: McCalpin John D.
Published: August 2005

In stratified three‐dimensional models the use of a boundary‐fitted vertical co‐ordinate is known to produce errors in the horizontal pressure gradient calculation near steep topography. The error is due to the splitting of the horizontal pressure gradient term in each of the momentum equations into two parts and the subsequent incomplete cancellation of the truncation errors of those parts. In order to minimize these pressure gradient errors, a fourth‐order‐accurate pressure gradient calculation has been implemented and installed in SPEM, a three‐dimensional primitive equation ocean model. The stability and accuracy of the new scheme are compared with those of the original second‐order‐accurate model in a series of calculations of unforced flow in the vicinity of an isolated seamount. The new scheme is shown to have much smaller pressure gradient errors over a wide range of parameter space as well as a greater parametric domain of numerical stability.
Solution of the axisymmetric inverse problem by higher‐order line doublets
Authors: Zedan M. F.
Published: August 2005

The axial singularity inverse method for designing bodies of revolution has been improved by using higher‐order doublet elements. The performance of the method for various element orders and other solution parameters is presented in detail. The results indicate that the method is generally more robust, less sensitive to insets and has a better‐conditioned coefficient matrix compared with the source method of the same order. The condition number of the matrix is shown to increase with the thickness of the body, the order of the method, the number of elements and the degree of stretching of the node distribution. In general, good performance is attained for most bodies even with ƒr as low as 2 by using 10–12 second‐order doublet elements with insets greater than 0.02L from rounded ends. Increasing the insets to 0.06L appears to improve the accuracy of the method for most bodies but slows its convergence.
A numerical method for 3D viscous incompressible flows using non‐orthogonal grids
Authors: He P. , Salcudean M.
Published: August 2005

This paper presents a numerical method for fluid flow in complex three‐dimensional geometries using a body‐fitted co‐ordinate system. A new second‐order‐accurate scheme for the cross‐derivative terms is proposed to describe the non‐orthogonal components, allowing parts of these terms to be treated implicitly without increasing the number of computational molecules. The physical tangential velocity components resulting from the velocity expansion in the unit tangent vector basis are used as dependent variables in the momentum equations. A coupled equation solver is used in place of the complicated pressure correction equation associated with grid non‐orthogonality. The co‐ordinate‐invariant conservation equations and the physical geometric quantities of control cells are used directly to formulate the numerical scheme, without reference to the co‐ordinate derivatives of transformation. Several two‐ and three‐dimensional laminar flows are computed and compared with other numerical, experimental and analytical results to validate the solution method. Good agreement is obtained in all cases.
A contribution to the great Riemann solver debate
Authors: Quirk James J.
Published: August 2005

The aims of this paper are threefold: to increase the level of awareness within the shock‐capturing community of the fact that many Godunov‐type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very‐high‐resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
On the approximation of horizontal gradients in sigma co‐ordinates for bathymetry with steep bottom slopes
Authors: Stelling Guus S. , Van Kester Jan A. Th. M.
Published: August 2005

Nowadays the simulation of free surface flow and transport in rivers, estuaries and seas is often based upon three‐dimensional modelling systems. Most of these three‐dimensional modelling systems use sigma co‐ordinates in the vertical. By the use of the sigma transformation the water column can be divided into the same number of layers independently of the water depth. Especially for steep bottom slopes combined with vertical stratification of the density, sigma‐transformed grids impose numerical problems for the accurate approximation of horizontal gradients. This paper deals with algorithms for the approximation in sigma co‐ordinates of the horizontal diffusive fluxes of temperature and salinity and for the approximation of the horizontal pressure gradients. The approximation of the horizontal diffusive fluxes is based upon a finite volume method. The approximation of the pressure gradients is directly related to the approximation of the diffusive fluxes. Artificial vertical diffusion and artificial flow due to truncation errors are minimized. The method described in this paper is not hampered by the so‐called ‘hydrostatic consistency condition’. This will be illustrated by numerical experiments.
Application of streamwise diffusion to time‐dependent free convection of liquid metals
Authors: McClelland Matthew A.
Published: August 2005

A numerical analysis is given for the application of streamwise diffusion to high‐intensity flows with marginal spatial resolution. Terms are added to the momentum equation which are similar to those used in the Petrov‐Galerkin, Taylor‐Galerkin and balancing tensor diffusivity methods. Values for the streamwise viscosity are obtained from mesh refinement studies. An illustration is given for the time‐dependent free convection of a liquid metal in a cavity with differentially heated sided walls. The spatial problem is solved with the Galerkin finite element method and the time integration is performed with the backward Euler method. Solution quality and computation time are compared for results with and without added streamwise diffusion. For the cases presented, streamwise diffusion eliminates spurious oscillations and saves computation time without compromising the solution.
Comparison of finite element methods for the St. Venant equations
Authors: Hicks F. E. , Steffler P. M.
Published: August 2005

Finite element schemes for hyperbolic systems are applied to the St. Venant equations for one‐dimensional, unsteady, open channel flow. The comparative performances of the characteristic‐dissipative‐Galerkin, Taylor‐Galerkin and least squares finite element schemes are assessed by means of linear Fourier analysis and solution of idealized non‐linear wave propagation problems. Of particular interest is the behaviour of these schemes for the regressive wave component in both subcritical and supercritical flows. To assess the quality of the basic solution, the methods are compared without any additional artificial diffusion or shock‐capturing formulations. The balanced treatment of both wave components in the characteristic‐dissipative‐Galerkin method is illustrated. Also, the method displays little sensitivity to parameters variations. The Taylor‐Galerkin scheme provides good solutions, although oscillations due to wave dispersion and minimal diffusion of the regressive wave are displayed. Also, this method is somewhat sensitive to the time step increment. The least squares method is considered unsuitable for unsteady, open channel flow problems owing to its inability to propagate a regressive wave in a supercritical flow.
A Eulerian/Lagrangian model to calculate the evolution of a water droplet spray
Authors: Creismeas Paul
Published: August 2005

We introduce a Eulerian/Lagrangian model to compute the evolution of a spray of water droplets inside a complex geometry. To take into account the complex geometry we define a rectangular mesh and we relate each mesh node to a node function which depends on the location of the node. The time‐dependent incompressible and turbulent Navier‐Stokes equations are solved using a projection method. The droplets are regarded as individual entities and we use a Lagrangian approach to compute the evolution of the spray. We establish the exchange laws related to mass and heat transfer for a droplet by introducing a mass transfer coefficient and a heat transfer coefficient. The numerical results from our model are compared with those from the literature in the case of a falling droplet in the atmosphere and from experimental investigation in a wind tunnel in the case of a polydisperse spray. The comparison is fairly good. We present the computation of a water droplet spray inside a complex and realistic geometry and determine the characteristics of the spray in the vicinity of obstacles.
Approximation of shallow water equations by Roe's Riemann solver
Authors: Ambrosi D.
Published: August 2005

The inviscid shallow water equations provide a genuinely hyperbolic system and all the numerical tools that have been developed for a system of conservation laws can be applied to them. However, this system of equations presents some peculiarities that can be exploited when developing a numerical method based on Roe's Riemann solver and enhanced by a slope limiting of MUSCL type. In the present paper a TVD version of the Lax‐Wendroff scheme is used and its performance is shown in 1D and 2D computations. Then two specific difficulties that arise in this context are investigated. The former is the capability of this class of schemes to handle geometric source terms that arise to model the bottom variation. The latter analysis pertains to situations in which strict hyperbolicity is lost, i.e. when two eigenvalues collapse into one.
A transport approach to the convolution method for numerical modelling of linearized 3D circulation in shallow seas
Authors: Xu Zhigang
Published: August 2005

A new method for solving the linearized equations of motion is presented in this paper, which is the implementation of an outstanding idea suggested by Welander: a transport approach to the convolution method. The present work focuses on the case of constant eddy viscosity and constant density but can be easily extended to the case of arbitrary but time‐invariant eddy viscosity or density structure. As two of the three equations of motion are solved analytically and the main numerical ‘do‐loop’ only updates the sea level and the transport, the method features succinctness and fast convergence.

The method is tested in Heaps' basin and the results are compared with Heaps' results for the transient state and with analytical solutions for the steady state. The comparison yields satisfactory agreement. The computational advantage of the method compared with Heaps' spectral method and Jelesnianski's bottom stress method is analysed and illustrated with examples.

Attention is also paid to the recent efforts made in the spectral method to accelerate the convergence of the velocity profile. This study suggests that an efficient way to accelerate the convergence is to extract both the windinduced surface Ekman spiral and the pressure‐induced bottom Ekman spiral as a prespecified part of the profile.

The present work also provides a direct way to find the eigenfunctions for arbitrary eddy viscosity profile. In addition, mode‐trucated errors are analysed and tabulated as functions of mode number and the ratio of the Ekman depth to the water depth, which allows a determination of a proper mode number given an error tolerance.
Analysis of finite element schemes for convection‐type problems
Authors: Comini Gianni , Manzan Marco , Nonino Carlo
Published: August 2005

Various finite element schemes of the Bubnov–Galerkin and Taylor–Galerkin types are analysed to obtain the expressions of truncation errors. This way, dispersion errors in the transient, and diffusion errors both in the transient and in the steady state, are identified. Then, with reference to the transient advection–diffusion equation, stability limits are determined by means of a general von Neumann procedure. Finally, the operational equivalence between Taylor–Galerkin methods, utilized for pseudo‐transient calculations, and Petrov–Galerkin methods, derived for the steady state forms of the advection–diffusion equation, is illustrated. Theoretical conclusions are supported by the results of numerical experiments.
A revised numerical model to predict heat transfer in turbulent flow
Authors: Visser J. A. , Cilliers J. P.
Published: August 2005

The accurate modelling of heat transfer to turbulent flow and the prediction of the temperature distribution in the flow remain one of the problem areas of numerical simulations. Traditional turbulence closure models, like the k–ε model, effectively only increase the viscosity of the fluid and introduce wall functions close to boundaries to obtain the correct velocity distribution. These turbulence models do not model the small‐scale mixing that occurs in turbulent flow. When solving the energy equation these small‐scale mixings dominate the heat transfer rate at the boundaries as well as the temperature distribution in the flow. This paper outlines a revised method, based on the k–ε turbulence model, that can be used to predict heat transfer in turbulent flow. A single turbulent conductivity term is introduced that can be used over the complete flow field including the boundaries. A detailed description of the mathematical model and boundary conditions used for the turbulence model are included in the paper. The effective turbulent conductivity method was evaluated in several finite difference simulations of water flowing through a smooth pipe while being heated. Simulation and verification were performed over a range of Reynolds numbers. Verification of the model is accomplished by comparing the numerically predicted centre temperature of the fluid as well as the heat flux to the fluid to measured temperatures in a similar pipe. From these results it is concluded that the revised turbulent conductivity model holds great potential to obtain accurate simulated heat transfer rates for general applications.
Efficient mould filling simulation in castings by an explicit finite element method
Authors: Lewis R. W. , Usmani A. S. , Cross J. T.
Published: August 2005

A model for simulating the process of mould filling in castings is presented. Many defects in a casting have their origins at the filling stage. Numerical simulation of this process can be of immense practical benefit to the foundry industry, however a rigorous analysis of this process must model a wide range of complex physical phenomena. In order to contain the costs and complexity that would be necessary for such a model, certain simplifying assumptions have been made. These assumptions limit the scope of this model to only predicting realistic thermal fields during the filling process.

A laminar regime has been assumed for the flow field, which is obtained by solving the incompressible Navier–Stokes equations using a velocity–pressure segregated semi‐implicit finite element method. The free metal surface is predicted by advecting a pseudo‐concentration function via the computed flow field. This involves an explicit finite element solution of a pure advection equation. The thermal field is calculated by solving the convective–diffusive energy equation by an explicit finite element method using the computed flow field and the location of the free surface. All the advection terms are discretized using a Taylor–Galerkin method. The interface between the metal and mould is modelled using special interface elements.

The model is demonstrated by solving practical example problems. The results show that a sharp thermal front is maintained during the course of filling without excessive diffusion. The heat diffusion in the mould can be controlled by varying the metal mould heat transfer coefficient.
Thermo‐hygro‐mechanical analysis of concrete
Authors: Baggio Paolo , Majorana Carmelo E. , Schrefler Bernhard A.
Published: August 2005

The computational analysis of thermohygrometric and mechanical behaviour of concrete structures is carried out by means of the finite element method. To evaluate the thermal and hygral performance of this material together with the damage and creep effects, the knowledge of the heat and moisture transfer processes taking place inside the medium is first required and then the consequent mechanical behaviour can be analysed. The theoretical approach used to obtain the governing differential equations for heat and moisture tansfer is based on the procedure of averaging continuum equations applied to heat and mass transfer and drying processes. According to that model the same set of equations is used to represent both the saturated zone (if present), the unsaturated one and the water‐vapour phase changes. The mechanical formulation is based on the virtual work principle and incorporates Prony–Dirichlet series expansion to represent the relaxation or creep functions, avoiding the memorization of the whole strain or stress history. Damage effects are taken into account within a coupled formulation, following a procedure presented in a previous paper. At this preliminary stage the analysis is performed in two stages (first the heat and mass transfer and then the mechanical analysis) using two FEM computer codes in sequence to apply the proposed approach to structures of any shape.
The influence of the stabilization parameter on the convergence factor of iterative methods for the solution of the discretized Stokes problem
Authors: Vincent C.
Published: August 2005

This paper discusses the influence of the stabilization parameter on the convergence factor of various iterative methods for the solution of the Stokes problem discretized by the so‐called locally stabilized Q1‐P0 finite element. Our objective is to point out optimal parameters which ensure rapid convergence.

The first part of the paper is concerned with the dual formulation of the problem. It gives the theoretical precision and practical developments of our stabilized context Uzawa‐type algorithm. We assert that the convergence factor of such a method is majored independently of the mesh size by a function of the stabilization parameter. Moreover, we point out that there exists an optimal value of this parameter that minimizes this upper bound. This gives a theoretical justification of pre‐existing numerical results. We show that the optimal parameter can be determined a priori. This is a key point when the method has to be implemented. Finally, we base an interpretation of the iterated penalty method numerical behaviour on some theoretical results about the minimum eigenvalue of the stabilized dual operator. This algorithm involves a penalty parameter and a stabilization parameter and we discuss a strategy for choosing optimal parameters.

The mixed formulation of the problem is dealt with in the second part of the paper, which proposes several preconditioned conjugate‐gradient‐type methods. The indefinite character of the problem makes it intrinsically hard. However, if one chooses a suitable preconditioner, this difficulty is overcome, since the preconditioned operator becomes positive definite. We study the eigenvalue spectrum of the preconditioned operator and thereby the convergence factor of the algorithm. In contrast with the two previous formulations, we show that this convergence factor is majored independently of the stabilization parameter. More precisely, we point out convergence factors comparable with those obtained for Poisson‐type problems. Finally, we present a variant of the latter method which uses our so‐called macroblock‐type preconditioner. A comparison with the simple case of diagonal preconditioning is addressed and the improved performance of the macroblock‐type preconditioner is evidenced.

Various 2D numerical experiments are given to corroborate the theories presented herein.
Operator‐splitting methods for the incompressible Navier‐Stokes equations on non‐staggered grids. Part 1: First‐order schemes
Authors: Churbanov Alexander G. , Pavlov Andrei N. , Vabishchevich Peter N.
Published: August 2005

New implicit finite difference schemes for solving the time‐dependent incompressible Navier‐Stokes equations using primitive variables and non‐staggered grids are presented in this paper. A priori estimates for the discrete solution of the methods are obtained. Employing the operator approach, some requirements on the difference operators of the scheme are formulated in order to derive a scheme which is essentially consistent with the initial differential equations. The operators of the scheme inherit the fundamental properties of the corresponding differential operators and this allows a priori estimates for the discrete solution to be obtained. The estimate is similar to the corresponding one for the solution of the differential problem and guarantees boundedness of the solution. To derive the consistent scheme, special approximations for convective terms and div and grad operators are employed. Two variants of time discretization by the operator‐splitting technique are considered and compared. It is shown that the derived scheme has a very weak restriction on the time step size. A lid‐driven cavity flow has been predicted to examine the stability and accuracy of the schemes for Reynolds number up to 3200 on the sequence of grids with 21 × 21, 41 × 41, 81 × 81 and 161 × 161 grid points.
Viscous‐inviscid coupling in free surface ship flows
Authors: Campana E. , Di Mascio A. , Esposito P. G. , Lalli F.
Published: August 2005

An application of multidomain decomposition to the computation of the steady free surface flow past a ship hull is presented. Viscous effects are taken into account in the neighbourhood of solid walls and in the wake by the Reynolds averaged Navier‐Stokes equations, whereas the assumption of irrotationality in the external flow allows a description by a potential model. Free surface boundary conditions have been implemented in a linearized form at the undisturbed waterplane. Suitable matching conditions are enforced at the interface between the viscous and the potential regions. The numerical results obtained for two merchant ship forms (the HSVA tanker and the Series 60 hull) are compared with experimental data available in the literature.
Mastering Sulfonation of Aromatic Polysulfones: Crucial for Membranes for Fuel Cell Application
Authors: Iojoiu C. , Maréchal M. , Chabert F. , Sanchez J.‐Y.
Published: August 2005

The publication deals with the sulfonation of aromatic polysulfones that results in ionomers intended to be used as membranes for Proton Exchange Membrane Fuel Cells. The mechanical properties and the lifespan of the membranes depend, in particular, on the mode of synthesis of the ionomers and on chemical degradations which can occur and cut the polymeric chains. This article gives a progress report on the various methods giving access to polysulfone ionomers based on sulfonic acid functions. Among these methods, particular attention has been paid to electrophilic substitution from commercially available polysulfone. Although electrophilic sulfonation of aromatic molecules has been known for about one century, its application to the sulfonation of polymers still raises problems, e.g. homogeneity and degradations. A mechanism of chemical degradation is proposed to explain the chain breakings occurring in the course of reaction. The difficulty in passing from the laboratory scale to an industrial production is illustrated from reactions carried out at the pilot scale.
Characterization of Sulfonated Poly(Ether Ether Ketone)/Polytetrafluoroethylene Composite Membranes for Fuel Cell Applications
Authors: Xing D. M. , Yi B. L. , Liu F. Q. , Fu Y. Z. , Zhang H. M.
Published: August 2005

The sulfonated poly(ether ether ketone) (SPEEK) / polytetrafluoroethylene (PTFE) composite membranes were produced to aid the swelling properties. The PTFE porous films were used as reinforcing material for the SPEEK/PTFE composite membranes. Scanning electron micrographs showed that SPEEK resin was distributed uniformly in the composite membrane and completely plugged the micropores; there is a continuous thin SPEEK film present on the PTFE surface. The dimensional stability and mechanical strength of the composite membranes were apparently improved. The composite membrane had a smaller oxygen permeability than the Nafion® membrane despite it being larger than that of the SPEEK homogenous membrane. The performance and stability of the PEMFC with SPEEK/PTFE composite membranes were also tested. Results showed that the fuel cell had a larger resistance than the SPEEK homogenous membrane or the Nafion® membrane, but these disadvantages are compensated for with the thinner composite membrane, because of its low gas permeability and high mechanical strength. Stability testing showed that the cell performance could be kept steady for more than 150 hours. The structure of the composite membrane didn't undergo any change and a tight bond remained between the composite membrane and the catalyst layers of electrode after more than 300 hours of intermittent operation.
Multilayer Sulfonated Polyaromatic PEMFC Membranes
Authors: Marrony M. , Rozière J. , Jones D. J. , Lindheimer A.
Published: August 2005

Sulfonated polyetheretherketone (sPEEK) membranes have been developed in which a hierarchical organisation into multilayers has been favoured during preparation using solvent casting. Bilayer membranes comprising sPEEK of different degrees of sulfonation (having ion exchange capacities between 1.1 and 1.6 meq g–1) have been characterised for their water uptake properties and proton conductivity. The composite membranes show no tendency to delaminate, even under prolonged operation in a hydrogen – oxygen fuel cell. By associating sPEEK of different water uptake characteristics, water back diffusion in an operating fuel cell is favoured, leading to a degree of control over the direction of water production at the anode or the cathode. Such a bilayer membrane has been operated at 110 °C without reactant gas hydration for over 900 h.
Bioactive and biocompatible pieces of HA/sol‐gel glass mixtures obtained by the gel‐casting method
Authors: Padilla S. , Sánchez‐Salcedo S. , Vallet‐Regí M.
Published: August 2005

Hydroxyapatite (HA)/glass mixtures have shown a faster bioactive behaviour than HA itself. On the other hand, the gel‐casting method is a simple and reproducible colloidal method to produce ceramic pieces with complex shapes. In this work, pieces of HA/glass mixtures were prepared by the gel‐casting method. A study for obtaining concentrated slurries of these mixtures is reported; the bioactivity and biocompatibility of the obtained pieces have been studied also. The influence of pH, dispersant concentration, the content and milling of glass, and the way to prepare the suspensions were investigated. The lowest viscosity and better rheological properties were achieved with the lowest glass content, when the glass was added after the dispersion of the HA powder and when the glass was not milled after calcination. Fluid suspensions with a high solid content (50 vol.%) could be prepared and well‐shaped pieces were obtained from these slurries. These pieces showed in vitro bioactive behavior in simulated body fluid; additionally, the proliferation and spreading assays with osteoblastic cells (HOS) showed that the pieces are biocompatible. The results obtained indicate that the gel‐casting of HA/glass mixtures produces bioactive and biocompatible pieces with the required shapes. Therefore, these materials could be good candidates for clinical applications and scaffolds for tissue engineering. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2005
Serum deprivation improves seeding and repopulation of acellular matrices with valvular interstitial cells
Authors: Cushing Melinda C. , Jaeggli Michael P. , Masters Kristyn S. , Leinwand Leslie A. , Anseth Kristi S.
Published: August 2005

Cell‐extracted valvular tissues (acellular scaffolds, or aScaffolds) offer unique advantages over synthetic polymers for cardiac valve engineering applications in that they retain extracellular matrix molecules to support cellular ingrowth. The extracellular matrix is important in directing many cellular pathways, such as adhesion, proliferation, migration, differentiation, and survival. However, repopulating this type of scaffold often requires high seeding densities or recurrent cell delivery. The optimization of valvular interstitial cell (VIC) seeding onto aScaffolds is reported herein. VICs (the most prevalent cell type in valve leaflets) have maximal growth in 15–20% serum concentrations on tissue‐culture polystyrene. Interestingly, after VIC seeding onto aScaffolds, a reduction of serum content, from 15% serum to 5% or less, was found to increase significantly the number of adherent cells, as well as induce transfer of VICs from a tissue‐culture polystyrene surface to the aScaffold. aScaffolds seeded and cultured with periods of reduced serum levels were shown to support and enhance VIC viability and attachment, as well as accelerate VIC migration into the aScaffold, leading to a uniformly repopulated valve leaflet construct after 4 weeks of static culture. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2005
Development of multifunctional polymer–mineral composite materials for bone tissue engineering
Authors: Vlakh Evgenia G. , Panarin Evgeniy F. , Tennikova Tatiana B. , Suck Kirstin , Kasper Cornelia
Published: August 2005

The main goal of this article is the development of a novel approach to construct multifunctional composite scaffolds for bone tissue engineering. For this purpose, different kinds of mineral macroporous supports, water‐soluble aldehyde‐containing copolymers of N‐vinylpyrrolidone, as well as different nonspecific and biospecific ligands governing cell adhesion and growth have been used. The composite materials were tested initially for cytotoxicity in cell culture experiments using a model cell line. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2005
Suppression of polyethylene particle–induced osteolysis by exogenous osteoprotegerin
Authors: von Knoch Fabian , Heckelei Anja , Wedemeyer Christian , Saxler Guido , Hilken Gero , Brankamp Jochen , Sterner Thomas , Landgraeber Stefan , Henschke Frank , Löer Franz , von Knoch Marius
Published: August 2005

Alterations of the key regulators of osteoclastogenesis, receptor activator of NF‐kappaB (RANK), RANK ligand (RANKL), and osteoprotegerin (OPG) have been implicated in wear particle–induced osteolysis, the most common cause for implant failure in total joint replacements. This study investigated the effect of exogenous OPG on ultra‐high‐molecular‐weight polyethylene (UHMWPE) particle–induced osteolysis. The murine calvarial osteolysis model was utilized in 28 C57BL/6J mice randomized to four groups. Group I underwent sham surgery only, group II received UHMWPE particles, and group III and IV particles and subcutaneous OPG starting from day 0 (group III) or day 5 (group IV) until sacrifice. After 2 weeks, calvaria were prepared for histology and histomorphometry. Bone resorption was measured within the midline suture using Giemsa staining and osteoclast numbers were determined using TRAP staining. UHMWPE particle implantation resulted in grossly pronounced osteoclastogenesis and bone resorption. Both immediate and delayed treatment with OPG counteracted these particle‐induced effects significantly, suppressing osteoclast formation and bone resorption (p < 0.001 and p < 0.001, respectively). In conclusion, exogenous OPG markedly suppressed UHMWPE particle–induced osteolysis in a murine calvarial model. This important finding underscores the crucial significance of the OPG‐RANKL‐RANK signaling in wear particle–induced osteolysis. Exogenous OPG may prove an effective treatment modality for wear debris‐mediated periprosthetic osteolysis after total joint arthroplasty. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2005
Prolonged duration local anesthesia with lipid–protein–sugar particles containing bupivacaine and dexamethasone
Authors: Colombo Gaia , Padera Robert , Langer Robert , Kohane Daniel S.
Published: August 2005

Glucocorticoids prolong block duration from polymeric microspheres containing bupivacaine, but not from unencapsulated drug. Here we investigate this effect applies to particles with much more rapid drug release and improved long‐term biocompatibility. Male Sprague‐Dawley rats were given sciatic nerve blocks with 75 mg of 3% or 60% (w/w) dipalmitoylphosphatidylcholine (DPPC) spray‐dried lipid–protein–sugar particles (LPSPs) containing 10% (w/w) bupivacaine and 0%, 0.05%, or 0.1% (w/w) dexamethasone. Sensory nerve block from bupivacaine‐containing 3% and 60% (w/w) DPPC particles without dexamethasone yielded blocks lasting 301 ± 56 and 321 ± 127 min, respectively. Addition of 0.05% (w/w) dexamethasone increased block durations to 610 ± 182 and 538 ± 222 min, respectively; increasing dexamethasone loading to 0.1% did not further increase duration. One day after injection, dexamethasone‐containing particles resulted in lower inflammation scores and capsule thickness than dexamethasone‐free particles, but the difference was gone by day 4. Excipient composition had prominent effects at all time points. For all groups, inflammation was largely resolved by 2 weeks after injection. Dexamethasone approximately doubled the duration of nerve block from bupivacaine‐loaded LPSPs, while maintaining excellent biocompatibility. Such formulations could be useful in clinical applications when nerve blockade is needed for 24 hours or less. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2005