bluuebunny/crossref_metadata_2025 huggingface dataset:
A two‐phase, two‐component model for natural convection in a porous medium
Authors: Forsyth P. A. , Simpson R. B.
Published: August 2005

A numerical study of natural convection in a two‐phase, two‐component flow in a porous medium heated from below is presented. Interphase mass and energy transfer, latent heat and bouyancy effects are major physical features. This study extends earlier studies of natural convection based on single‐phase, saturated porous medium models. The appearance of two‐phase heat pipe zones in the flow has a marked effect on the fluid and heat flows as well as on the performance of the numerical methods. The numerical techniques for handling phase change, Jacobian construction and time step selection are discussed.
Three‐dimensional streamlined finite elements: Design of extrusion dies
Authors: Ellwood Kevin R. J. , Papanastasiou T. C. , Wilkes J. O.
Published: August 2005

A method to determine three‐dimensional die shapes from extrudate swell and vice versa is presented using a three‐dimensional Galerkin finite element method based on a streamlined formulation with the fluid velocities and pressures represented by triquadratic and trilinear basis functions respectively. The three‐dimensional streamlined method, an extension of the two‐dimensional formulation, uses successive streamsurfaces to form a boundary‐conforming co‐ordinate system. This produces a fixd, computational domain leaving the spatial location of the elements as unknowns to be determined with the standard primary variables (u, v, w, p). The extrudate produced by a die of a given shape is considered for moderate Reynolds numbers. Finally, the method is extended to address the problem of die design, where a die profile is sought to produce a target extrudate shape.
A one‐dimensional moving grid solution for the coupled non‐linear equations governing multiphase flow in porous media. 1: Model development
Authors: Gamliel Amir , Abriola Linda M.
Published: August 2005

A straightforward moving grid finite element method is developed to solve the one‐dimensional coupled system of non‐linear partial differential equations (PDEs) governing two‐ and three‐phase flow in porous media. The method combines features from a number of self‐adaptive grid techniques. These techniques are the equidistribution, the moving grid finite element and the local grid refinement/coarsening methods. Two equidistribution criteria, based on solution gradient and curvature, are employed and nodal distributions are computed iterativcly. Using the developed approach, an intermingle‐free nodal distribution is guaranteed. The method involves examination of a single representative gradient to facilitate the application of moving grid algorithms to solve a non‐linear coupled set of PDEs and includes a feature to limit mass balance error during nodal redistribution. The finite element part of the developed algorithm is verified against an existing finite difference model. A numerical simulation example involving a single‐front two‐phase flow problem is presented to illustrate model performance. Additional simulation examples are given in Part 2 of this paper. These examples include single and double moving fronts in two‐ and three‐phase flow systems incorporating source/sink terms. Simulation sensitivity to the moving grid parameters is also explored in Part 2.
A one‐dimensional moving grid solution for the coupled non‐linear equations governing multiphase flow in porous media. 2: Example simulations and sensitivity analysis
Authors: Gamliel Amir , Abriola Linda M.
Published: August 2005

This paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non‐linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single‐ and double‐front simulations for two‐ and three‐phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non‐linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non‐zero value for the repulslive force to avoid development of an ill‐conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested.
A comparison of spatial grids for numerical modelling of flows in near‐coastal seas
Authors: Lardner R. W. , Song Y.
Published: August 2005

Three‐dimensional algorithms for the numerical computation of flows caused by tides or meteorological forcing are developed for four of Arakawa's spatial grid types using a spectral method in the vertical dimension. Three of the grids, in which the velocity components are computed at the same grid points, offer potential advantages over the commonly used C‐grid. The computed results from the four grids are compared for three test problems based on the linearized hydrodynamical equations. It is concluded that the B‐grid provides a viable alternative to the C‐grid, with significant advantages when a spectral method is used.
Surface tension and buoyancy‐driven flow in a non‐isothermal liquid bridge
Authors: Zhang Yiqiang , Alexander J. Iwan D.
Published: August 2005

The Navier–Stokes–Boussinesq equations governing the transport of momentum, mass and heat in a non‐isothermal liquid bridge with a temperature‐dependent surface tension are solved using a vorticity‐stream‐function formulation together with a non‐orthogonal co‐ordinate transformation. The equations are discretized using a pseudo‐unsteady semi‐implicit finite difference scheme and are solved by the ADI method. A Picard‐type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary‐driven flow situations and mixed thermocapillary‐ and bouyancy‐driven flow.
A numerical study of bifurcation in laminar flow in curved ducts
Authors: Jayanti S. , Hewitt G. F.
Published: August 2005

The bifurcation phenomenon whereby multiple‐vortex secondary flow occurs in place of the normal two‐vortex flow in laminar flow in curved ducts has previously been studied numerically by several researchers. However, the various results have been conflicting on many points. The present paper describes a set of numerical experiments conducted to study the effect of numerical accuracy on the solution. The results show that the transition from two‐ to four‐vortex structure depends strongly on the differencing scheme and to a lesser extent on the grid size. The study also shows that as the Reynolds number of the flow increases, a two‐vortex structure is re‐established via a path which involves strongly asymmetric secondary flow patterns. These results are in agreement, at least qualitatively, with recent experimental theoretical and numerical results.
Compressible gas flow between closely spaced plates
Authors: Mourelatos Zissimos P.
Published: August 2005

A theoretical analysis is presented to solve numerically the steady state Navier–Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non‐choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.
Numerical prediction of vortex shedding behind a square cylinder
Authors: Kelkar Kanchan M. , Patankar Suhas V.
Published: August 2005

It is common knowledge that flow around bluff bodies exhibits oscillatory behaviour. The aim of the present study is to compute the steady two‐dimensional flow around a square cylinder at different Reynolds numbers and to determine the onset of unsteadiness through a linear stability analysis of the steady flow. Stability of the steady flow to small two‐dimensional perturbations is analysed by computing the evolution of these perturbations. An analysis of various time‐stepping techniques is carried out to select the most appropriate technique for predicting the growth of the perturbations and hence the stability of the flow. The critical Reynolds number is determined from the growth rate of the perturbations. Computations are then made for periodic unsteady flow at a Reynolds number above the critical value. The predicted Strouhal number agrees well with experimental data. Heat transfer from the cylinder is also studied for the unsteady laminar flow.
An accurate computation for rapidly varied flow in an open channel
Authors: Yang Jinn‐Chuang , Chen Kun‐Nan , Lee Hong‐Yuan
Published: August 2005

A new method combining the Preissmann four‐point scheme and the Holly–Preissmann reach‐back scheme is introduced to solve the rapidly varied flow problem in an open channel. The Preissmann four‐point scheme is well known for the computation of one‐dimensional unsteady flow. The Holly–Preissmann reach‐back scheme integrates the Holly‐Preissmann two‐point scheme with the concept of reach‐back characteristics, which allows the characteristics to project several time steps beyond the current time level. A spontaneous surge formation case is used to demonstrate and evaluate the applicability of the new method. It has been found that the results from this method are quite compatible with those of Preissmann four‐point scheme. In addition, with the appropriate choice of the number of reach‐back time steps, this new method can always avoid the numerical oscillation which usually exists when one uses the Preissmann four‐point scheme for the condition of Courant number not close to unity.
Computation of two‐dimensional dam‐break flood flows
Authors: Soulis Johannes Vassiliou
Published: August 2005

Sudden total collapse of a dam holding back a reservoir of water, whenever it occurs, becomes formidably impressive in the extent of destruction with which it is associated. The movement on a dry bed of a two‐dimensional flood wave resulting from the break of a dam has been one of the most important and challenging subjects in rapidly varied unsteady flows from the computational point of view. An implicit time‐marching finite volume numerical scheme was developed and subsequently applied for the solution of the two‐dimensional unsteady open channel flow equations written in conservation form. In order to avoid the problems associated with a conventional grid system, a body‐fitted non‐orthogonal local co‐ordinate system was utilized. The proposed numerical technique was applied to determine the stage hydrographs, water surface profiles and velocities of flood flows resulting from suddenly breached storage dams. Predictions were compared with an analytical solution, with available numerical solutions using MacCormack's two‐step explicit scheme and with experimental measurements. Agreement between predictions and measurements regarding the wave front advancement and stage hydrographs is considered to be satisfactory.
Numerical method for unsteady viscous hydrodynamical problem with free boundaries
Authors: Shopov Peter J. , Minev Peter D. , Bazhlekov Ivan B.
Published: August 2005

A finite element method for the transient incompressible Navier–Stokes equations with the ability to handle multiple free boundaries is presented. Problems of liquid–liquid type are treated by solving two coupled Navier–Stokes problems for two separate phases. The possibility to solve problems of liquid–gas, liquid–liquid–gas or liquid–liquid–liquid type is demonstrated too. Surface tension effects are included at deformable interfaces.

The method is of Lagrangian type with mesh redefinition. A predictor‐corrector scheme is used to compute the position of the deformable interface with automatic control of its accuracy and smoothness. The method is provided with an automatic choice of the time integration step and an optional spline filtration of the truncation error at the free surface. In order to show the accuracy of the method, tests and comparisons are presented. Numerical examples include motion of bubbles and multiple drops.
A modified adaptive grid method for recirculating flows
Authors: Lee D. , Tsuei Y. M.
Published: August 2005

In this study a method of equidistribution of a weight function for grid adaption is modified to produce a smoother grid which yields a more accurate solution. In the original scheme the weight function was estimated on each grid independently and a large variation in the values of the, weight function could generate a highly skewed and non‐uniform grid which produced large errors. In this study the weight function is smoothed by coupling neighbouring weight functions. Abrupt changes in the weight function are alleviated and a smoother grid distribution is obtained. With relatively minor modifications of the original weight function it is demonstrated in this study that the solution can be improved. The test cases presented are the one‐dimensional convection‐diffusion equation, a laminar polar cavity flow, a laminar backwardfacing step flow and a turbulent reacting sudden expansion pipe flow. Numerical efficiencies ranging from factors of five to 10 are achieved over uniform grid methods.
A finite element solutionof three‐dimensional mixed convection gas flows in horizontal chnnels using preconditioned iterative metrix methods
Authors: Einset Erik O. , Jensen Klavs F.
Published: August 2005

An algorithm is presented for the finite element solution of three‐dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMERS), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centered around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain‐renumbering scheme that enhances the overall algorithm performance is proposed on the basis of and analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly f the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three‐dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.
Influence of skirt radius on performance of circular clarifier with density stratification
Authors: Zhou Siping , McCorquodale John A.
Published: August 2005

A numerical model for predicting the velocity field and suspended solids distribution in a secondary circular clarifier with density difference is evaluated. The density effects are characterized by the inlet densimetric Froude number. This study focuses on the role of the reaction baffle position in the performance of the clarifiers. For a large‐radius baffle and low densimetric Froude number an important phenomenon known as the density waterfall occurs in the inlet zone of the clarifiers. This was predicted by the numerical model and confirmed by the physical model tests. This model consists of a series of conservation equations for fluid mass and momentum and sediment concentration. The turbulent stresses are calculated by use of the eddy viscosity concept and the κ–ϵ. turbulence model. The study showed that the density waterfall results in high entrainment and high recirculation. A comparison of the solids concentration distribution for a tank with a small skirt radius to that with a large skirt radius shows that small skirt radius reduces the density waterfall effect and significantly improves the clarifier performance at low densimetric Froude numbers.
An extension of Osher's Riemann solver for chemical and vibrational non‐equilibrium gas flows
Authors: Abgrall R. , Fezoui L. , Talandier J.
Published: August 2005

In this paper we study an extension of Osher's Riemann solver to mixtures of perfect gases whose equation of state is of the form encountered in hypersonic applications. As classically, one needs to compute the Riemann invariants of the system to evaluate Osher's numerical flux. For the case of interest here it is impossible in general to derive simple enough expressions which can lead to an efficient calculation of fluxes. The key point here is the definition of approximate Riemann invariants to alleviate this difficulty.

Some of the properties of this new numerical flux are discussed. We give 1D and 2D applications to illustrate the robustness and capability of this new solver. We show by numerical examples that the main properties of Osher's solver are preserved; in particular, no entropy fix is needed even for hypersonic applications.
A numerical simulation of boundary layer effects in a shock tube
Authors: Badcock K. J.
Published: August 2005

A numerical scheme is used to investigate boundary layer effects in a shock tube. The method consists of a mixture of Roe's approximate Riemann solver and central differences for the convective fluxes and central differences for the viscous fluxes and is implicit in one space dimension. Comparisons are made with experimental data and with solutions obtained via boundary layer equations. Examination of the calculated flow field explains the observed behaviour and highlights the approximate nature of boundary layer solutions.
A general numerical method for solution of gravity wave problems. Part 2: Steady nonlinear gravity waves
Authors: Liao S. J.
Published: August 2005

A type of numerical scheme for 2D and 3D steady non‐linear water wave problems is described. It is based on the finite process method and is insensitive to initial solutions. The relationship between the finite process method and iterative techniques is discussed. As a numerical example the flow past a submerged vortex is solved and the results are compared with those of other authors.
Improved artificial dissipation schemes for the Euler equations
Authors: Thomadakis M. P. , Tsangaris S.
Published: August 2005

The influence of artificial dissipation schemes on the accuracy and stability of the numerical solution of compressible flow is extensively examined. Using an implicit central difference factored scheme, an improved form of artificial dissipation is introduced which highly reduces the errors due to numerical viscosity. A function of the local Mach number is used to scale the amount of numerical damping added into the solution according to the character of the flow in several flow regimes. The resulting scheme is validated through several inviscid flow test cases.
Adaptive h‐refinement on 3D unstructured grids for transient problems
Authors: Löhner Rainald , Baum Joseph D.
Published: August 2005

An adaptive finite element scheme for transient problems is presented. The classic h‐enrichment/coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every n time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre‐sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements arc realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock‐shock and shock‐object interaction runs in a production mode. A typical example of this class of problems is given.
Navier‐Stokes computations past a prolate spheroid at incidence. II: High incidence case
Authors: Piquet J. , Queutey P.
Published: August 2005

The computation of incompressible three‐dimensional viscous flow is investigated. An iterative fully decoupled technique based on the fully elliptic mode is applied to the Reynolds‐averaged‐Navier‐Stokes equations (RANSE) written down in a non‐orthogonal curvilinear body‐fitted co‐ordinate system. Results of the computations are compared with experimental data past a prolate spheroid at 30° incidence.
An efficient three‐dimensional semi‐implicit finite element scheme for simulation of free surface flows
Authors: Li Y. S. , Zhan J. M.
Published: August 2005

An efficient semi‐implicit finite element model is proposed for the simulation of three‐dimensional flows in stratified seas. The body of water is divided into a number of layers and the two horizontal momentum equations for each layer of water are first integrated vertically. Nine‐node Lagrangian quadratic isoparametric elements are employed for spatial discretization in the horizontal domain. The time derivatives are approximated using a second‐order‐accurate semi‐implicit time‐stepping scheme. The distinguishing feature of the proposed numerical scheme is that only nodal values on the same vertical line are coupled. Two test cases for which analytic solutions are available are employed to test the proposed scheme. The test results show that the scheme is efficient and stable. A numerical experiment is also included to compare the proposed scheme with a finite difference scheme.
Computation of turbulent asymmetric wake
Authors: Tulapurkara E. G. , Vengadesan S. , Lakshminarasimhan J.
Published: August 2005

The development of asymmetric wake behind an aerofoil in turbulent incompressible flow has been computed using finite volume scheme for solving two‐dimensional Navier‐Stokes equations along with the k‐ε model of turbulence. The results are compared with available experimental data. It is observed that the computed shift of the point of minimum velocity with distance is sensitive to the prescribed value of the normal component of velocity at the trailing edge of the aerofoil. Making the model constant Cu as a function of streamline curvature and changing the production term in the equation for ε, has only marginal influence on the results.
Analysis of erosion behaviour in a turbocharger radial turbine
Authors: Benim A. C. , Neuhoff H. G.
Published: August 2005

An analysis of the erosion behaviour of a turbocharger radial turbine is presented. The solution domain includes both sides of the radial turbine scroll with double intake and the rotor channel. In the analysis a dilute gas‐particle flow assumption is employed. The gas turbulence is defined by the k‐ε model. In solving the gas phase equation, the computer code Harwell‐FLOW3D is employed, which is based on a finite volume formulation using non‐orthogonal body‐fitted structured gridding and a pressure correction method. The particle phase is described by a Lagrangian approach, while particle paths are computed deterministically, neglecting the turbulent dispersion. For the computation of particle trajectories the code PTRACK is employed, which has been developed at ABB. Computations are carried out for several particle size classes. The results show that particles are thrown back into the scroll by the rotor at high rates. This seems to be the main source of erosion effects in the scroll. It has been observed that particles are unequally distributed between the scroll sides on their re‐entry, resulting in greater erosion on one of the scroll sides. The maximum erosion along the scroll is found to be likely to occur near the scroll end.
Transient simulation of 2D and 3D stratified and intermittent two‐phase flows. Part I: Theory
Authors: Moe Randi , Bendiksen Kjell H.
Published: August 2005

Stratified and intermittent stratified‐bubble (slug) flows are complex phenomena, often requiring transient 2D and 3D descriptions. This paper presents the physical basis of a new type of multidimensional two‐fluid model, particularly suited for transient flow problems. Important constitutive relations for wall shear stress and interfacial momentum transfer with necessary assumptions and simplifications are discussed. The numerical method is based on an implicit finite difference scheme, solved directly in two steps applying a separate equation for the pressure. The model has been verified through extensive comparisons with available experimental data as well as through comparisons with other models.
Calculation of quasi‐three‐dimensional incompressible viscous flows by the finite element method
Authors: Sedlář M.
Published: August 2005

This paper discusses the calculation of quasi‐three‐dimensional incompressible viscous flow by FEM. The Reynolds‐averaged Navier‐Stokes equations are solved in curvilinear co‐ordinates by the reduced integration and penalty method (RIP). Streamline upwind artificial viscosity (SUAV) and the Baldwin‐Lomax algebraic model of turbulence are used. Time discretization is by the general implicit θ‐method.
Numerical analysis of saltwater intrusion using B‐spline boundary elements
Authors: Cabral J. J. S. P. , Wrobel L. C.
Published: August 2005

Continuity of the derivatives of the main variable is an important feature to obtain an accurate representation of moving boundaries with discrete numerical methods, since the value and direction of the velocity are normally used to relocate the nodal points in a time‐marching scheme. A recently developed formulation of the boundary element method using cubic B‐splines provides up to C2 continuity between adjacent elements. This formulation is applied in this work to saltwater intrusion problems in confined, leaky and unconfined aquifers.
Turbulent free surface flow simulation using a multilayer model
Authors: Lai C. J. , Yen C. W.
Published: August 2005

Based on the steady hydrodynamic equations, a multilayer (ML) model has been formulated for simulating turbulent flow in open channels. The model is imposed on a general curvilinear co‐ordinate system with non‐staggered finite volume discretization. The turbulent quantities in the model are described by the layer‐averaged K‐ε turbulence model with standard coefficients. Assuming a vertical hydrostatic pressure distribution, a depth correction scheme, originating in the Rhie and Chow approach for confined flows, is incorporated into the SIMPLE procedure to compute the water surface.

Using the multilayer model, flows in a 180° channel bend, near a groin, and in straight open channels are computed. The results are compared with experimental data and with calculations of a depth‐averaged model (DAV) having three‐dimensional effect corrections. The comparisons show that the predictions of the ML model on mean flow values are in good agreement with the available data and are better than those of the DAV model. The vertical distribution of the turbulent energy dissipation rate is also shown to agree well with the open‐channel measurements.
p‐version least squares finite element formulation for two‐dimensional, incompressible, non‐Newtonian isothermal and non‐isothermal fluid flow
Authors: Bell Brent C. , Surana Karan S.
Published: August 2005

This paper presents a p‐ version least squares finite element formulation (LSFEF) for two‐dimensional, incompressible, non‐Newtonian fluid flow under isothermal and non‐isothermal conditions. The dimensionless forms of the diffential equations describing the fluid motion and heat transfer are cast into a set of first‐order differential equations using non‐Newtonian stresses and heat fluxes as auxiliary variables. The velocities, pressure and temperature as well as the stresses and heat fluxes are interpolated using equal‐order, C0‐continuous, p‐version hierarchical approximation functions. The application of least squares minimization to the set of coupled first‐order non‐linear partial differential equations results in finding a solution vector {δ} which makes the partial derivatives of the error functional with respect to {δ} a null vector. This is accomplished by using Newton's method with a line search.

The paper presents the implementation of a power‐law model for the non‐Newtonian Viscosity. For the non‐isothermal case the fluid properties are considered to be a function of temperature. Three numerical examples (fully developed flow between parallel plates, symmetric sudden expansion and lid‐driven cavity) are presented for isothermal power‐law fluid flow. The Couette shear flow problem and the 4:1 symmetric sudden expansion are used to present numerical results for non‐isothermal power‐law fluid flow. The numerical examples demonstrate the convergence characteristics and accuracy of the formulation.
On the difficulties and remedies in enforcing the div = 0 condition in the finite element analysis of thermal plumes with strongly temperature‐dependent viscosity
Authors: Coulliette D. L. , Koch M.
Published: August 2005

A finite element (FE) analysis of experimentally observed creeping thermal plumes in a medium whose viscosity is strongly temperature‐dependent is performed. Such plumes are considered to play an important role in numerous geological processes and numerical modelling is often the only option to study their physics. Initial simulations by means of the general‐purpose Galerkin finite element package NACHOS‐II demonstrated serious deficiencies of the method in modelling plumes with large viscosity contrasts, in spite of several options for the solution (mixed or penalty formulation) and the elements (continuous or discontinous pressure). In agreement with observations from FE simulations of isothermal Stokes flow in other studies, we have isolated the violation of the div = 0 or incompressibility constraint as the major culprit in the failure of the FE method. It is demonstrated that the a posteriori computed discrete divergence (DDIV) can be used as a diagnostic tool to evaluate the reliability of the FE solution and to rank the solution and element options provided in the NACHOS code. On the basis of these considerations, the combination of the mixed method with a Q2‐P1 (discontinuous pressure) element turns out to be the most suitable for the present plume problem but is still unable to sufficiently enforce the div = 0 condition. With a goal to remedy this detrimental behaviour, several FE modifications and new approaches have been taken. These include: (i) use of a new scaling option for the governing equations which has the effect of equilbrating the stiffness matrices and thus improving their condition; (ii) implementation of several iterative solution techniques such as the iterated penalty and the Uzawa algorithm for the augmented Langrangian to better accommodate the dual role of the pressure; (iii) use of a multistep Newton method to better handle the high non‐linearity of the coupled flow/transport problem. Although each of these options (or a combination of them) is able to improve on the quality of FE solution, the most startling amelioration has been gained with option (iii). Use of the latter resulted in very satisfactory modelling of the experimentally observed plumes.
Adaptive panel methods and their integration with CAD
Authors: David Tim , Lewis Robert
Published: August 2005

The work outlined below presents simple but effective adaptive meshing algorithms for boundary integral methods modelling inviscid flows (panel method) using the IGES standard for describing geometry. By using certain IGES entities in describing the boundary, CAD‐derived geometry may be used such that the geometric integrity of the boundary is maintained after an adaptive redistribution of the mesh. Three types of error estimators are tested and all are shown to produce a more accurate representation of the flow phenomena for the same number of panels as compared with a uniform mesh distribution.
An algebraic multigrid solver for Navier‐Stokes problems
Authors: Webster R.
Published: August 2005

An efficient numerical method is presented for solving the equations of motion for viscous fluids. The equations are discretized on the basis of unstructured finite element meshes and then solved by direct iteration. Advective fluxes are temporarily fixed at each iteration to provide a linearized set of coupled equations which are then also solved by iteration using a fully implicit algebraic multigrid (AMG) scheme. A rapid convergence to machine accuracy is achieved that is almost mesh‐independent. The scaling of computing time with mesh size is therefore close to the optimum.
A finite volume scheme for two‐phase compressible flows
Authors: Saurel R. , Forestier A. , Veyret D. , Loraud J.‐C.
Published: August 2005

In gas‐particle two‐phase flows, when the concentration of the disperesed phase is low, certain assumptions may be made which simplify considerably the equations one has to solve. The gas and particle flows are then linked only via the interaction terms. One may therefore uncouple the full system of equations into two subsystems: one for the gas phase, whose homogeneous part reduces to the Euler equations; and a second system for the particle motion, whose homogeneous part is a degenerate hyperbolic system. The equations governing the gas phase flow may be solved using a high‐resolution scheme, while the equations describing the motion of the dispersed phase are treated by a donor‐cell method using the solution of a particular Riemann problem. Coupling is then achieved via the right‐hand‐side terms. To illustrate the capabilities of the proposed method, results are presented for a case specially chosen from among the most difficult to handle, since it involves certain geometrical difficulties, the treatment of regions in which particles are absent and the capturing of particle fronts.
Finite element analysis of multicomponent two‐phase flows with interphase mass and momentum transport
Authors: Schunk P. R. , Rao R. R.
Published: August 2005

The application of the finite element method to multiphase flow problems with interphase mass and heat transfer is described. A general forinulation is used that determines the position of the interfacial boundary and allows for multiple solvents, differential volatilities and concentration‐ and temperature‐dependent thermophysical properties. Species phase change and the dramatic volume change that acompanies interphase mass transfer make implementation of the theory challening, since these events lead to discontinuous velocities and concentrations at phase boundaries. These discontinuities are especially large in processes involving rapid evaporation or condensation. As examples we examine the effects of rapid drying on film and fibre formation of sol‐‐gel materials, which are often laden with volatile species.
On the implementation of symmetric and antisymmetric periodic boundary conditions for incompressible flow
Authors: Segal Guus , Vuik Kees , Kassels Kees
Published: August 2005

In this paper we consider symmetric and antisymmetric periodic boundary conditions for flows governed by the incompressible Navier‐Stokes equations. Classical periodic boundary conditions are studied as well as symmetric and antisymmetric periodic boundary conditions in which there is a pressure difference between inlet and outlet. The implementation of this type of boundary conditions in a finite element code using the penalty function formulation is treated and also the implementation in a finite volume code based on pressure correction. The methods are demonstrated by computation of a flow through a staggered tube bundle.
Numerical simulation of coextrusion and film casting
Authors: Fortin A. , Carrier P. , Demay Y.
Published: August 2005

In the first part of this paper a numerical strategy is developed for the numerical simulation of the coextrusion process. Coextrusion consists of extruding many polymers in the same die in order to combine their respective properties. The die is generally flat and quite large and consequently a two‐dimensional approximation is sufficient. The main difficulty is to accurately predict the interfaces between the different layers of polymers. A finite element method based on a pseudoconcentration function is developed to calculate these fluid interfaces. Numerical results are presented for the coextrusion of up to five fluids.

In the second part of the paper the above strategy is slightly modified to simulate the film‐casting process. In this case a polymer is stretched (with a draw velocity UL) at the exit of the die in order to produce a very thin layer of polymer that is cooled in contact with a chill roll. Only one polymer‐air interface has to be computed. The draw ratio is defined as Dr = UL/U, where U is the mean velocity of the polymer at the exit of the die. As the draw ratio is increased, instabilities appear and numerical results put in evidence the draw resonance phenomenon.
Transonic Euler computation in streamfunction co‐ordinates
Authors: An C.‐F. , Barron R. M.
Published: August 2005

A new approach has been developed to calculate two‐dimensional steady transonic flows past aerofoils using the Euler equations in streamfunction co‐ordinates. Most existing transonic computation codes require the use of a grid generator to determine a suitable distribution of grid points. Although simple in concept, the grid generation may take a considerable proportion of the CPU time and storage requirements. However, this grid generation step can be avoided by introducing the von Mises transformation, which produces a formulation in streamwise and natural body‐fitting co‐ordinates. In this work a set of Euler equivalent equations in streamfunction co‐ordinates is formulated, consisting of three equations with three unknowns; one is a geometric variable, the streamline ordinate y, and the other two are physical quantities, the density ρ and the vorticity ω. To solve these equations, typedependent differencing, development of a shock point operator, marching from a non‐characteristic boundary and successive line overrelaxation are applied. Particular attention has been paid to the supercritical case where a careful treatment of the shock is essential. It is shown that the shock point operator is crucial to accurately capture shock waves. The computed results show excellent agreement with existing experimental data and other computations.
Implementation and performance of the time integration of a 3D transport model
Authors: Sommeijer B. P. , Kok J.
Published: August 2005

The total solution of a three‐dimensional model for computing the transport of salinity, pollutants, suspended material (such as sediment or mud), etc. in shallow seas involves many aspects, each of which has to be treated in an optimal way in order to cope with the tremendous computational task involved. In this paper we focus on one of these aspects, i.e. on the time integration, and discuss two numerical solution methods. The emphasis in this paper is on the performance of the methods when implemented on a vector/parallel, shared memory computer such as a Cray‐type machine. The first method is an explicit time integrator and can straightforwardly be vectorized and parallelized. Although a stabilizing technique has been applied to this method, it still suffers from a severe time step restriction. The second method is partly implicit, resulting in much better stability characteristics; however, as a consequence of the implicitness, it requires in each step the solution of a large number of tridiagonal systems. When implemented in a standard way, the recursive nature would prevent vectorization, resulting in a very long solution time. Following a suggestion of Golub and Van Loan, this part of the algorithm has been tuned for use on the Cray C98/4256. On the basis of a large‐scale test problem, performance results will be presented for various implementations.
The compressible Newtonian extrudate swell problem
Authors: Georgiou G. C.
Published: August 2005

We solve the compressible Newtonian extrudate swell problem in order to investigate the effect of compressiblity on the shape of the extrudate. We employ a first‐order equation of state relating the density to the pressure and use finite elements for the numerical solution of the problem. Our results show that the shape of the extrudate and the final extrudate swell ratio are not significanlty affected even at high compressibility values.
Navier‐Stokes equations with imposed pressure and velocity fluxes
Authors: Conca C. , Pares C. , Pironneau O. , Thiriet M.
Published: August 2005

Boundary value problems for Stokes and Navier‐Stokes equations with non‐standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux. First, a variational formulation is introduced which is shown to be equivalent to the Stokes equations with the non‐standard boundary conditions under consideration. The existence and uniqueness of the solution of the variational problem are studied. Secondly, most of the results obtained for the Stokes equations are extended to the case of the Navier‐Stokes equations. The final section is devoted to numerical experiments, flows in pipes and physiological flows.
Finite volume computation of incompressible turbulent flows in general co‐ordinates on staggered grids
Authors: Zijlema M. , Segal A. , Wesseling P.
Published: August 2005

A brief review of the computation of incompressible turbulent flow in complex geometries is given. A 2D finite volume method for the calculation of turbulent flow in general curvilinear co‐ordinates is described. This method is based on a staggered grid arrangement and the contravariant flux componets are chosen as primitive variables. Turbulence is modelled either by the standard k–ε model or by a k–ε model based on RNG theory. Convection is approximated with central differences for the mean flow quantities and a TVD‐type MUSCL scheme for the turbulence equations. The sensitivity of the method to the grid properties is investigated. An application of this method to a complex turbulent flow is presented. The results of computations are compared with experimental data and other numerical solutions and are found to be satisfactory.
Numerical computation of an impinging jet with uniform wall suction
Authors: Yang Yue‐Tzu
Published: August 2005

The paper presents numerical predictions of a turbulent axisymmetric jet impinging onto a porous plate, based on a finite volume method of solving the Navier‐Stokes equations for an incompressible air jet with the K–ε turbulence model. The velocity and pressure terms of the momentum equations are solved by the SIMPLE (semi‐implicit method for pressure‐linked equation) method. In this study, non‐uniform staggered grids are used. The parameters of interest include the nozzle‐to‐wall distance and the suction velocity. The results of the present calculations are compared with available data reported in the literature. It is found that suction effects reduce the boundary layer thickness and increase the velocity gradient near the wall.
An application of the capacitance matrix method to accommodate masked land areas and island circulations in a primitive equation ocean model
Authors: Wilkin John L. , Mansbridge James V. , Hedström Katherine S.
Published: August 2005

The capacitance matrix method has been implemented in a primitive equation ocean model to accommodate islands and portions of irregular coastal boundaries that cannot be treated adequately by boundary‐fitted orthogonal curvilinear co‐ordinates. The algorithm preserves the ability to solve the streamfunction equation using fast and accurate elliptic solvers that require a rectangular computational domain. By superposition of a set of island Green functions, the solution is adjusted to ensure continuity of pressure around each island. The implementation is tested by comparison with an analytic solution for wind‐driven flow in a closed basin similar to the southwest Pacific Ocean.
Finite element/finite volume solutions of full potential, Euler and Navier‐Stokes equations for compressible and incompressible flows
Authors: Hafez M.
Published: August 2005

A cell‐vertex finite volume formulation, using local finite element approximations to calculate fluxes through an auxiliary mesh (control volumes) is used to solve inviscid and viscous compressible flow equations on unstructured grids. Non‐linear artificial viscosity methods are adopted to avoid decoupling and capture shock waves. Artificial time‐dependent terms are augmented if needed, to guarantee convergence of common iterative procedures to a steady‐state solution. The incompressible limit of compressible flow equations is studied. A unified approach for solving both compressible and incompressible flow problems is proposed. Also some results of a zonal formulation with different governing equations in different regions are presented. Applications to the solution of Maxwell's equations for wave propagation and scattering are discussed in an appendix.
An hp adaptive strategy for finite element approximations of the Navier‐Stokes equations
Authors: Oden J. Tinsley , Wu Weihan , Legat Vincent
Published: August 2005

Recently, a rigorous a posteriori error estimate, based on the element residual method, for the steady‐state Navier‐Stokes equations has been derived. In this paper, by using this error estimate, we construct an hp adaptive strategy to minimize the total computation costs while achieving a targeted accuracy for steady incompressible viscous flow problems. The basic hp adaptive strategy is to solve the approximate problem in three consecutive stages corresponding to three different meshes, i.e. an initial mesh, an intermediate adaptive h‐mesh, and a final adaptive hp mesh. Our numerical result shows that the three‐step hp adaptive strategy for the incompressible flow problems indeed provides an accurate approximate solution while keeping the computational costs under control.