bluuebunny/crossref_metadata_2025_split huggingface dataset:
Transient simulation of 2D and 3D stratified and intermittent two‐phase flows. Part I: Theory
Authors: Moe Randi , Bendiksen Kjell H. 
Published: August 2005

AbstractStratified 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

AbstractThis 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

AbstractContinuity 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

AbstractBased 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

AbstractThis 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

AbstractA 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

AbstractThe 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

AbstractAn 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

AbstractIn 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

AbstractThe 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

AbstractIn 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

AbstractIn 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

AbstractA 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

AbstractThe 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

AbstractWe 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

AbstractBoundary 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

AbstractA 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

AbstractThe 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

AbstractThe 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

AbstractA 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

AbstractRecently, 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.
Entropy correcting schemes and non‐hierarchical auto‐adaptive dynamic finite element‐type meshes: Applications to unsteady aerodynamics
Authors: Richter Roland , Leyland Pénélope 
Published: August 2005

AbstractThis paper discusses the different sources of non‐physical entropy production which occur in the numerical resolution of the Euler equations for compressible inviscid flow and proposes several ways of correcting these effects. In particular a hybrid corrected centred, augmented by an accurate upwind scheme near singular boundaries is proposed which satisfies the mathematical entropy condition, and which solves the flow accurately within regions near non‐smooth boundaries of the computational domain. A coupled new dynamic auto‐adaptive mesh algorithm which produces highly accurate solutions is also introduced. This algorithm is non‐hierarchical. i.e. it does not depend on a fixed background mesh, which allows structural and geometrical changes and generates extremely precise discretizations for steady and unsteady flow.
Hopf bifurcation in annular liquid jets with mass transfer
Authors: Ramos J. I. 
Published: August 2005

AbstractA numerical study of Hopf bifuractions in annular liquid jets with mass transfer is presented. The study is based on the asymptotic equations which govern the dynamics of inviscid, incompressible, thin, annular liquid jets and on equilibrium conditions for mass transfer at the jet's inner and outer interfaces. It is shown that the amplitude of the time‐periodic motion that results from the Hopf bifurcation increases whereas its frequency decreases as the solubility ratio is increased.