bluuebunny/crossref_metadata_2025 huggingface dataset:
Computations for a jet impinging obliquely on a flat surface
Authors: Chuang Shu‐Hao , Wei Ching‐Yuan
Published: August 2005

A SIMPLE‐C algorithm and Jones‐Launder k‐ε two‐equation turbulence model are used to simulate a two‐dimensional jet impinging obliquely on a flat surface. Both the continuity and momentum equations for the unsteady state are cast into suitable finite difference equations. The pressure, velocity, turbulent kinetic energy and turbulent energy dissipation rate distributions are solved and show good agreement with various experimental data. The calculations show that the flow field structure of the jet impinging obliquely on a flat surface is strongly affected by the oblique impingement angle. The maximum pressure zone of the obliquely impinging jet flow field moves towards the left as the oblique impingement angle is decreased.
Simulation of two‐ and three‐dimensional internal subsonic flows using a finite element method
Authors: Buffat Marc
Published: August 2005

In this paper a finite element method is presented to predict internal subsonic flows. Using a low‐Mach‐number approximation, the pressure is decomposed into a mean thermodynamic contribution and a dynamic fluctuation to deal with the complex role of the pressure in internal aerodynamics. A semi‐implicit time integration and a finite element method with a moving mesh are described to take into account complex geometries and moving boundaries. An Uzawa algorithm accelerated by a preconditioned residual method is introduced to solve the coupled non‐symmetric linear system for the velocity components and the pressure. An efficient conjugate gradient method combined with an incomplete LU preconditioning is used to solve the non‐symmetric linear systems arising from the discretization. The implementation of the numerical scheme on parallel supercomputers is also discussed. Efficient algorithms for the finite element assembly phase and for the solution of linear systems are described which take advantage of the parallel architecture of the new generation of supercomputers. With this technique a global speed‐up of 10 is achieved on a supercomputer with eight processors. To illustrate the capabilities of the numerical method, 2D and 3D simulations of flows in the combustion chamber of a reciprocating engine and around the combustor dome of a gas turbine engine are presented.
Heat transfer during melting in rectangular enclosures—a finite element analysis
Authors: Sarkar A. , Sastri V. M. K.
Published: August 2005

This paper is devoted to the finite element analysis of heat transfer during melting in rectangular enclosures. The effects of aspect ratio and subcooling on the motion of the interface and the Nusselt number have been investigated. The different schemes employed in the present work throw useful light on the choice of the appropriate method for dealing with such phase change problems.
Domain decomposition methods in computational fluid dynamics
Authors: Gropp William D. , Keyes David E.
Published: August 2005

The divide‐and‐conquer paradigm of iterative domain decomposition or substructuring has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi‐uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the non‐linear iteration. Multiple discretizations (second‐order in the operator and first‐order in the preconditioner) and locally uniform mesh refinement pay dividends separately and can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.
A numerical method for the determination of slip characteristics between the layers of a two‐layer slurry flow
Authors: Nassehi V. , Khan A. R.
Published: August 2005

The observed phenomenon of slip between the layers of a flowing slurry is modelled mathematically by a finite‐element‐based numerical technique. This technique enables us to quantify variables such as the slip velocity and shear stress distribution at the interlayer boundary and the pressure drop within the flow domain.
A fire field model implemented in a parallel computing environment
Authors: Ierotheou C. S. , Galea E. R.
Published: August 2005

This paper describes the implementation of a fire field model in the parallel computing environment offered by multiple transputers. The fire model is built into the general purpose SIMPLE‐based CFD code HARWELL‐FLOW3D. The technique of domain decomposition has been applied tb convert the conventional serial version of FLOW3D into a code capable of efficiently utilizing an arbitrary number of transputers. Fire simulations consisting of up to 24 000 computational cells are performed on parallel systems with up to 15‐processors. The run time for this simulation has been reduced from over 4 days on a single processor to just over 8 h on the 15‐processor system. An interactive graphics system has also been developed which runs in parallel with the main computations.
A slope modification method for shallow water equations
Authors: Rao V. Subba , Latha G.
Published: August 2005

A slope modification method is proposed for non‐oscillatory schemes based on the Lax‐Friedrich solver. The modified scheme is proved to be total‐variation‐diminishing (TVD) and second‐order accurate. Application of the scheme to the shallow water equations produces sharp profiles for shocks and achieves high accuracy in the smooth regions of the solution.
Orthogonal arrays: An introduction and their application in optimizing underrelaxation factors in ‘simple’‐based algorithm
Authors: Gopinath R. , Ganesan V.
Published: August 2005

The primary aim of this paper is to demonstrate how the ‘design‐of‐experiments’ techniques which are successful in physical experiments could also be adapted to a numerical simulation code.

As an example this technique is applied to a general finite difference code used for predicting three‐dimensional turbulent recirculating flows. Here the equations for velocities and continuity are solved using the algorithm called SIMPLE, which stands for semi‐implicit method for pressure‐linked equations. Physical modelling of turbulence is taken care of by means of kinetic energy and turbulence dissipation rate equations.

The objective is to optimize the underrelaxation factors of primary and secondary flow variables so that the number of iterations required for convergence is minimum. This is done by the orthogonal array technique (a particular type of design‐of‐experiment technique).

The geometry considered for this purpose is that of a simple gas turbine can combustor and the study is restricted to the isothermal non‐reacting condition.

Tests are carried out on three different grid configurations. In each case the underrelaxation factor for velocities contributed most to speed up the rate of convergence. Also, for each grid configuration the underrelaxation factor settings for minimum iterations for convergence was found to be same. Hence it is proposed that when doing grid independence tests for any similar flow situation, all the underrelaxation factors could be optimized on coarse grids.
Spectral element‐FCT method for scalar hyperbolic conservation laws
Authors: Giannakouros John , Karniadakis George Em
Published: August 2005

A new algorithm based on spectral element discretizations and flux‐corrected transport (FCT) ideas is developed for the solution of discontinuous hyperbolic problems. A conservative formulation is proposed, based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss–Chebyshev and Gauss–Lobatto–Chebyshev discretizations. In addition, high‐order time‐differencing schemes, a flux limiter and a general spectral filter are employed to improve the quality of the solution. It is demonstrated through model problems of linear advection and examples of one‐dimensional shock formation that the proposed algorithm leads to stable, non‐oscillatory solutions of high accuracy away from discontinuities. Typically, spectral or spectral element methods perform very poorly in the presence of even weak discontinuities, although they produce only exponentialy small errors for smooth solutions. Spectral element–FCT methods can provide spectral properties (i.e. minimum dispersion and diffusion errors) as well as great flexibility in the discretization, since a variable number of macroelements or collocation points per element can be employed to accommodate both accuracy and geometric requirements.
A hybrid method for computing the flow of viscoelastic fluids
Authors: Ariel P. D.
Published: August 2005

A hybrid method for computing the flow of viscoelastic and second‐order fluids is presented. It combines the features of the finite difference technique and the shooting method. The method is accurate because it uses central differences. Its convergence is at least superlinear.

The method is applied to obtain the solutions to three problems of flow of Walters' B' fluid: (a) flow near a stagnation point, (b) flow over a stretching sheet and (c) flow near a rotating disk. Numerical results reveal some new characteristics of flows which are not easy to demonstrate using the perturbation technique.
Energy flux equalization: An open boundary condition for non‐linear free surface flows
Authors: Jagannathan Sridhar
Published: August 2005

In the simulation of non‐linear free surface flows in a finite domain a major concern is with the radiation condition to be applied at the ‘open’ boundary. No general theoretical radiation conditions are known to exist. In this paper a new open boundary condition is formulated based on energy flux equalization between the non‐linear inner domain and a linear outer domain. The non‐linear flow in the inner domain is solved numerically using a semi‐Lagrangian procedure. The energy flux arriving at the open boundary is removed using a new open boundary condition which acts as a linear wave absorber. For the cases studied the performance of this boundary condition is found to be quite good.
A structured tri‐tree search method for generation of optimal unstructured finite element grids in two and three dimensions
Authors: Wille S. Ø.
Published: August 2005

A new method for generating finite element grids in two and three dimensions is developed. The method is based on a new search tree structure. The search tree is built upon triangles in two dimensions and tetrahedra in three dimensions. The density of elements can be varied throughout the computational domain. Efficient search algorithms for finding points in space and for finding the boundary of the domain have been developed. The speed of the grid algorithm will permit adaptive gridding during computation. The grid algorithm is generally applicable to both hydrodynamic as well as aerodynamic finite element computations. The technique has been used with success for gridding the North Sea‐Skagerrak area.
Simulating two‐dimensional turbulent flow by using the κ–ϵ model and the vorticity–streamfunction formulation
Authors: Elkaim D. , Reggio M. , Camarero R.
Published: August 2005

A numerical procedure to solve turbulent flow which makes use of the κ–ϵ model has been developed. The method is based on a control volume finite element method and an unstructured triangular domain discretization. The velocity‐pressure coupling is addressed via the vorticity‐streamfunction and special attention is given to the boundary conditions for the vorticity. Wall effects are taken into account via wail functions or a low‐Reynolds‐number model. The latter was found to perform better in recirculation regions. Source terms of the κ and ε transport equations have been linearized in a particular way to avoid non‐realistic solutions. The vorticity and streamfunction discretized equations are solved in a coupled way to produce a faster and more stable computational procedure. Comparison between the numerical predictions and experimental data shows that the physics of the flow is correctly simulated.
Boundary‐conforming mapping applied to computations of highly deformed solidification interfaces
Authors: Tsiveriotis K. , Brown R. A.
Published: August 2005

A new boundary‐conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational fomulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.
River and reservoir flow modelling using the transformed shallow water equations
Authors: Borthwick A. G. L. , Barber R. W.
Published: August 2005

This paper describes a versatile finite difference scheme for the solution of the two‐dimensional shallow water equations on boundary‐fitted non‐orthogonal curvilinear meshes. It is believed that this is the first non‐orthogonal shallow water equation model incorporating the advective acceleration terms to have been developed in the United Kingdom.

The numerical scheme has been validated against the severe condition of jet‐forced flow in a circular reservoir with vertical side walls, where reflections of the initial free surface waves pose major problems in achieving a stable solution. Furthermore, the validation exercises are designed to test the computer model for artificial diffusion, which may be a consequence of the numerical scheme adopted to stabilize the shallow water equations. The model is shown to be capable of simulating the flow conditions in an irregularly shaped domain typical of the geometries frequently encountered in civil engineering river basin management.
A coding error elimination procedure for validating isotropic turbulent convection numerical calculations in axisymmetric flows with Eulerian and Lagrangian descriptions
Authors: Blank David A.
Published: August 2005

A procedure which ensures the elimination of discretization and coding errors in the numerical solution of a set of governing equations describing internal turbulent convection flows is given and illustrated. The governing equations investigated in the validation analysis are of general form. The equations for the turbulence model (k‐8) assume the turbulence to be isotropic. In the analysis a portion of the solution region uses a Lagrangian description while a Eulerian description is used elsewhere. The work was originally motivated by the need to validate numerical calculations performed in the modelling of cornbusting fluid flow within symmetric piston engines. Thus the procedure is demonstrated for an axisymmetric formulation. The same methodology can be even more easily applied to Cartesian‐based problems using the guidelines given in this work. Details of the procedure are presented in a very practical format, making it possible to consider both simpler and more complex governing equation sets with little additional effort. Thus the implementation of this procedure by researchers to a variety of both turbulent and laminar internal flow problems should prove to be easy.
An inviscid/viscous coupling approach for vortex flow field calculations
Authors: Lee K. D. , Brandt S. A.
Published: August 2005

A new computational approach is developed for the analysis of vortex‐dominated flow fields around highly swept wings at high angles of attack. In this approach an inviscid Euler technology is coupled with viscous models, similar to inviscid/boundary layer coupling. The viscous nature of the vortex core is represented by an algebraic model derived from the Navier–Stokes equations. The approach also accounts for the effects of the viscous shear layer near a wing surface through a modified surface boundary condition. The inviscid/viscous coupling consistently provides improved predictions of leading edge separation, vortex bursting and secondary vortex formation at relatively low computational cost. Results for several cases are compared with wind tunnel tests and other Euler and Navier‐Stokes solutions.
Numerical simulation of jet‐forced flow in a circular reservoir using discrete and random vortex methods
Authors: Borthwick A. G. L. , Barber R. W.
Published: August 2005

This paper describes a Biot–Savart discrete vortex model for simulating the flow patterns which occur when a single high‐velocity inflow jet is used to stir the fluid within a circular container. The first stage of the model consists of conformally mapping the circular perimeter of the container onto a rectangle by means of a Schwarz–Christoffel transformation. A potential flow solution is then obtained for the flow inside the rectangle and this is transformed to give the potential flow inside the circle. In the second stage of the simulation, discrete vortices are added at the inlet of the physical system in order to model the inflow shear layers. Velocity components resulting from the discrete vortices and their images in the walls of the cylinder are superimposed on the uniform potential flow solution. The positions of the vortices are updated using a Lagrangian tracking procedure. Viscous effects are incorporated through the use of random walks. From the results it is shown that the discrete vortex method does predict qualitatively the important features of jet‐forced reservoir flow.
Numerical investigation of confined wakes behind a square cylinder in a channel
Authors: Mukhopadhyay A. , Biswas G. , Sundararajan T.
Published: August 2005

The structure of confined wakes behind a square cylinder in a channel is investigated via the numerical solution of the unsteady Navier–Stokes equations. Vortex shedding behind the cylinder induces periodicity in the flow field. Details of the phenomenon are simulated through numerical flow visualization. The unsteady periodic wake can be characterized by the Strouhal number, which varies with the Reynolds number and the blockage ratio of the channel. The periodicity of the flow is, however, damped in the downstream region of a long duct. This damping may be attributed to the influence of side walls on the flow structure.
A study of laminar air flow through cracks by numerical solution of the differential equations
Authors: Mokhtarzadeh‐Dehghan M. R. , Ward‐Smith A. J. , Walker R. N.
Published: August 2005

This paper describes a numerical study of laminar flow through building cracks such as those found around doors or windows. The mathematical model is based on the solution of the two‐dimensional conservation equations of mass and momentum by a finite volume method. The results are presented for two crack geometries, namely double‐bend and four‐bend cracks. The variation in local pressure coefficient along the crack walls and the velocity and pressure distributions within the cracks are described. The overall predicted pressure coefficient for the double‐bend crack for the double‐bend crack is compared with the results obtained using a correlation given by Baker et al.5.
Computing brine transport in porous media with an adaptive‐grid method
Authors: Trompert R. A. , Verwer J. G. , Blom J. G.
Published: August 2005

An adaptive‐grid finite‐difference method is applied to a model for non‐isothermal, coupled flow and transport of brine in porous media. In the vicinity of rock salt formations the salt concentration in the fluid becomes large, giving rise to disparate scales in the salt concentrations profiles. A typical situation one encounters is that of a sharp freshwater‐saltwater interface that moves in time. In such situations adaptive‐grid methods are more effective than standard fixed‐grid methods, since they refine the space grid locally and, hence, provide for substantial reduction in the number of grid points, memory use and CPU time. The adaptive‐grid method of this paper is a static, local uniform grid refinement method. Its main feature is that it integrates on nested sequences of locally uniformly refined Cartesian space grids, which are automatically adjusted in time to follow rapid spatial transitions. Variable time steps are used to cope with rapid temporal transitions, including a fast march to possible steady‐state solutions. For time stepping, the implicit, second‐order BDF scheme is used. Two specific example problems are numerically illustrated. The main physical properties involved here are advection and dispersion and in case of dominant advection sharp freshwater‐saltwater interfaces arise.
A complete boundary integral formulation for steady compressible inviscid flows governed by non‐linear equations
Authors: Zuosheng Yang
Published: August 2005

A complete boundary integral formulation for steady compressible inviscid flows governed by non‐linear equations is established by using the specific mass flux as a dependent variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain. It is shown that the boundary integral formulation developed in this paper is equivalent of the results of distributions of the fundamental solutions of the Laplacian operator equation with a different order along the boundaries of the domain. Hence, we have succeeded in establishing the fundamental‐solution method for compressible inviscid flows governed by non‐linear equations.
Influence of particle diameter distribution on the downstream particle turbulence in a two‐phase, turbulent, round jet
Authors: Sargianos N. P. , Anagnostopoulos J. S. , Bergeles G.
Published: August 2005

A numerical algorithm is used to study the ‘fan‐spreading’ mechanism of axial particle turbulence acquisition and the effects on it of the inlet particle diameter distribution, downstream of a particle‐laden, turbulent, round jet. The algorithm is based on the particle‐source‐in‐cell numerical technique for two‐phase flows. Eulerian equations are used for the description of the gas‐phase dynamics, whilst the solid particles are treated within the Lagrangian framework. The turbulent particle dispersion is simulated with the aid of the stochastic separated flow model. It was found that the ‘fan‐spreading’ turbulence is very much affected by the mean and standard deviation of the particle size distribution; in particular, it was found that the ‘fan‐spreading’ mechanism becomes weaker when the standard deviation of the particle diameter distribution is higher and the mean particle diameter smaller. An analytical expression describing the axial particle turbulence due to ‘fan‐spreading’ is proposed and tested, along with a similarity profile valid for the particles of bigger size.
Use of characteristics method with cubic interpolation for unsteady‐flow computation
Authors: Yang Jinn‐Chuang , Chiu Kuang‐Ping
Published: August 2005

The specified‐time‐interval (STI) scheme has been used commonly in applying the method of characteristics (MOC) to unsteady open‐channel flow problems. However, with the use of STI scheme, the numerical error for the simulation results can always be induced due to the interpolation used to approximate the characteristics trajectory. Hence, in order to remedy the numerical errors caused by the interpolation, one needs to seek some kind of interpolation technique with higher‐order accuracy. Instead of the linear interpolation technique, which has been used very commonly and can induce serious numerical diffusion, the Holly‐‐Preissmann two‐point, method, which is a cubic interpolation technique with fourth‐order of accuracy, is proposed here to integrate with the method of characteristics for the computation of one‐dimensional unsteady flow in open channel. The concept of reachback and reachout in space and time directions for the characteristics is also introduced to assure the model stability. The computed results from this new model are compared with those computed by using the Preissmann four‐point scheme and the multimode method of characteristics with linear interpolation.
A high‐resolution Godunov‐type scheme in finite volumes for the 2D shallow‐water equations
Authors: Alcrudo Francisco , Garcia‐Navarro Pilar
Published: August 2005

A high‐order Godunov‐type scheme based on MUSCL variable extrapolation and slope limiters is presented for the resolution of 2D free‐surface flow equations. In order to apply a finite volume technique of integration over body‐fitted grids, the construction of an approximate Jacobian (Roe type) of the normal flux function is proposed. This procedure allows conservative upwind discretization of the equations for arbitrary cell shapes. The main advantage of the model stems from the adaptability of the grid to the geometry of the problem and the subsequent ability to produce correct results near the boundaries. Verification of the technique is made by comparison with analytical solutions and very good agreement is found. Three cases of rapidly varying two‐dimensional flows are presented to show the efficiency and stability of this method, which contains no terms depending on adjustable parameters. It can be considered well suited for computation of rather complex free‐surface two‐dimensional problems.
Employment of second‐moment closure for calculation of turbulent recirculating flows in complex geometries with collocated variable arrangement
Authors: Farhanieh Bijan , Davidson Lars , Sundén Bengt
Published: August 2005

This paper addresses the implementation of second‐moment closure into a collocated variable arrangement body‐fitted‐finite‐volume scheme in which Cartesian velocity components are used. The methods for avoiding instability in the solution procedure are described. A new method for the treatment of the near‐wall regions for the momentum equations, as well as the prescription of the stresses at the wall, is described in detail. The performance of the methodology is assessed by applying it to two flow situations, where experimental data are available: the flow over a backward step, and the flow through a sinusoidal pipe constriction. The results are very promising.
Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake
Authors: Sun J. , Li J. , Roux B.
Published: August 2005

This paper describes flow around a pair of cylinders in tandem arrangement with a downstream cylinder being fixed or forced to oscillate transversely. A sinusoidal parietal velocity is applied to simulate cylinder oscillation. Time‐dependent Navier‐Stokes equations are solved using finite element method. It is shown that there exist two distinct flow regimes: ‘vortex suppression regime’ and ‘vortex formation regime’. Averaged vortex lengths between the two cylinders, pressure variations at back and front stagnant points as well as circumferential pressure profiles of the downstream cylinder are found completely different in the two regimes and, thus, can be used to identify the flow regimes. It is shown that frequency selection in the wake of the oscillating cylinder is a result of non‐linear interaction among vortex wakes upstream and downstream of the second cylinder and its forced oscillation. Increasing cylinder spacing results in a stronger oscillatory incident flow upstream of the second cylinder and, thus, a smaller synchronization zone.
Evaluation of various high‐order‐accuracy schemes with and without flux limiters
Authors: Tamamidis Panos , Assanis Dennis N.
Published: August 2005

Conventional high‐order schemes with reduced levels of numerical diffusion produce results with spurious oscillations in areas where steep velocity gradients exist. To prevent the development of non‐physical oscillations in the solution, several monotonic schemes have been proposed. In this work, three monotonic schemes, namely Van Leer's scheme, Roe's flux limiter and the third‐order SHARP scheme, are compared and evaluated against schemes without flux limiters. The latter schemes include the standard first‐order upwind scheme, the second‐order upwind scheme and the QUICK scheme. All the above schemes are applied to four two‐dimensional problems: (i) rotation of a scalar ‘cone’ field, (ii) transport of a scalar ‘square’ field, (iii) mixing of a cold with a hot front and (iv) deformation of a scalar ‘cone’ field. These problems test the ability of the selected schemes to produce oscillation‐free and accurate results in critical convective situations. The evaluation of the schemes is based on several aspects, such as accuracy, economy and complexity. The tests performed in this work reveal the merits and demerits of each scheme. It is concluded that high‐order schemes with flux limiters can significantly improve the accuracy of the results.
Unstructured volume‐agglomeration MG: Solution of the Poisson equation
Authors: Koobus Bruno , Lallemand Marie‐Hélène , Dervieux Alain
Published: August 2005

We are interested in solving second‐order PDEs with multigrid and unstructured meshes. The multigrid strategy we present here is adapted from the generalized finite volume agglomeration multigrid algorithm we have developed recently for the solution of the Euler equations. We now focus on Poisson's equation. A strategy is defined by introducing a correction factor for the diffusive terms, and some illustrating results are given.
Tools for simulating non‐stationary incompressible flow via discretely divergence‐free finite element models
Authors: Turek Stefan
Published: August 2005

We develop simulation tools for the non‐stationary incompressible 2D Navier‐‐Stokes equations. The most important components of the finite element code are: the fractional step ϑ‐scheme, which is of second‐order accuracy and strongly A‐stable, for the time discretization; a fixed point defect correction method with adaptive step length control for the non‐linear problems (stationary Navier‐Stokes equations); a modified upwind discretization of higher‐order accuracy for the convective terms. Finally, the resulting nonsymmetric linear subproblems are treated by a special multigrid algorithm which is adapted to the quadrilateral non‐conforming discretely divergence‐free finite elements. For the graphical postprocess we use a fully non‐stationary and interactive particle‐tracing method. With extensive test calculations we show that our method is a candidate for a ‘black box’ solver.
An efficient shock‐capturing algorithm for compressible flows in a duct of variable cross‐section
Authors: Glaister P.
Published: August 2005

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co‐ordinate. This includes flow in a duct of variable cross‐section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two‐dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two‐dimensional problem with no sources.
Modelling the non‐linear interaction of wind and tide: Its influence on current profiles
Authors: Davies A. M. , Lawrence J.
Published: August 2005

A single‐point model in the vertical is used to examine the coupling between tidal currents and wind‐driven flows in shallow near‐coastal regions. Calculations using both a linear slip and a no‐slip condition at the sea bed clearly show that coupling between tidal and wind‐driven currents cannot occur in a linear model with a time‐independent eddy viscosity. However with a physically more realistic time‐varying viscosity related to the flow field, coupling does occur, the magnitude of this non‐linear interaction depending upon the change in eddy viscosity over a tidal cycle and the intensity of shear in the vertical. A point model in the vertical with flow induced by an oscillatory pressure gradient and an additional constant wind stress is used to examine the influence of viscosity parametrization and water depth upon this coupling.

The solution in the vertical is accomplished using both a functional approach and a finite difference method. Some conclusions as to the relative merits of these approaches, particularly the use of a transformed grid in the case of high‐shear surface and bed boundary layers, are made in the paper.
A new general‐purpose least‐squares finite element model for steady incompressible low‐viscosity laminar flow using isoparametric C1‐continuous Hermite elements
Authors: Nassehi V. , Petera J.
Published: August 2005

This paper deals with a critical evaluation of various finite element models for low‐viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least‐squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low‐viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least‐squares method in conjunction with C1‐continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping of C1 Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least‐squares method in combination with isoparmetric Hermite elements offers a new general‐purpose modelling technique which can accurately simulate all types of low‐viscosity incompressible laminar flow in complex domains.
Numerical investigations of radial jet reattachment flows
Authors: Laschefski H. , Braess D. , Haneke H. , Mitra N. K.
Published: August 2005

A finite volume computational scheme to solve the Navier‐Stokes equations for the laminar flow fields of partially enclosed axial and radial jets impinging on a flat plate has been devised and tested. This scheme is based on the SIMPLEC technique. However, because of the backflow at the ‘outflow’ boundary, the SIMPLEC pressure correction technique has to be modified. The need for this modification, necessitated by the convergence failure, showed the ‘hidden’ pressure boundary condition of SIMPLE‐type techniques. Test computations with the present scheme for flows in a channel with a built‐in cylinder show that the location of the exit boundary affects very slightly the separated flow behind the cylinder. Computed Squire jet flows compare quite well with the available analytical solution. Finally, impinging radial jets have been computed for different Reynolds numbers. The results show the critical Reynolds number below which a steady solution is obtained and above which periodic and eventually chaotic flows result.
Implicit schemes for unsteady Euler equations on triangular meshes
Authors: Sens A. S. , Mortchelewicz G. D.
Published: August 2005

An implicit finite element method is presented for the solution of steady and unsteady inviscid compressible flows on triangular meshes under transonic conditions. The method involves a first‐order time‐stepping scheme with a finite element discretization that reduces to central differencing on a rectangular mesh. On a solid wall the slip condition is prescribed and the pressure is obtained from an approximation of the normal momentum equation. With this solver no artificial viscosity is added to ensure the success of the calculation. Numerical examples are given for steady and unsteady cases.
A net inflow method for incompressible viscous flow with moving free surface
Authors: Wang S. P. , Wang K. K.
Published: August 2005

A new finite element procedure called the net inflow method has been developed to simulate time‐dependent incompressible viscous flow including moving free surfaces and inertial effects. As a fixed mesh approach with triangular element, the net inflow method can be used to analyse the free surface flow in both regular and irregular domains. Most of the empty elements are excluded from the computational domain, which is adjusted successively to cover the entire region occupied by the liquid. The volume of liquid in a control volume is updated by integrating the net inflow of liquid during each iteration. No additional kinetic equation or material marker needs to be considered. The pressure on the free surface and in the liquid region can be solved explicitly with the continuity equation or implicitly by using the penalty function method. The radial planar free surface flow near a 2D point source and the dam‐breaking problem on either a dry bed or a still liquid have been analysed and presented in this paper. The predictions agree very well with available analytical solutions, experimental measurements and/or other numerical results.
Finite volume methods for laminar and turbulent flows using a penalty function approach
Authors: Simoneau J. , Pollard A.
Published: August 2005

A penalty function, finite volume method is described for two‐dimensional laminar and turbulent flows. Turbulence is modelled using the k‐ϵ model. The governing equations are discretized and the resulting algebraic equations are solved using both sequential and coupled methods. The performance of these methods is gauged with reference to a tuned SIMPLE‐C algorithm. Flows considered are a square cavity with a sliding top, a plane channel flow, a plane jet impingement and a plane channel with a sudden expansion. A sequential method is employed, which uses a variety of dicretization practices, but is found to be extremely slow to converge; a coupled method, evaluated using a variety of matrix solvers, converges rapidly but, relative to the sequential approach, requires larger memory.
A multigrid method for predicting periodically fully developed flow
Authors: Bai L. , Mitra N. K. , Fiebig M. , Kost A.
Published: August 2005

The use of multigrid methods in complex fluid flow problems is still under development. In this paper a full multigrid procedure has been incorporated in a finite volume solution for predicting fully developed fluid flow in a streamwise periodic geometry. Steady computations in two‐dimensional body fitted co‐ordinates have shown considerable savings in computation time by this multigrid method.
Taylor‐Galerkin‐based spectral element methods for convection‐diffusion problems
Authors: Timmermans L. J. P. , Van De Vosse F. N. , Minev P. D.
Published: August 2005

Several explicit Taylor‐Galerkin‐based time integration schemes are proposed for the solution of both linear and non‐linear convection problems with divergence‐free velocity. These schemes are based on second‐order Taylor series of the time derivative. The spatial discretization is performed by a high‐order Galerkin spectral element method. For convection‐diffusion problems an operator‐splitting technique is given that decouples the treatment of the convective and diffusive terms. Both problems are then solved using a suitable time scheme. The Taylor‐Galerkin methods and the operator‐splitting scheme are tested numerically for both convection and convection‐diffusion problems.
The effects of flow split ratio and flow rate in manifolds
Authors: Fu H. , Watkins A. P. , Yianneskis M.
Published: August 2005

This paper reports a combined experimental and numerical investigation of three‐dimensional steady turbulent flows in inlet manifolds of square cross‐section. Predictions and measurements of the flows were carried out using computational fluid dynamics and laser Doppler anemometry techniques respectively. The flow structure was characterized in detail and the effects of flow split ratio and inlet flow rate were studied. These were found to cause significant variations in the size and shape of recirculation regions in the branches, and in the turbulence levels. It was then found that there is a significant difference between the flow rates through different branches.

The performance of the code was assessed through a comparison between predictions and measurements. The comparison demonstrates that all important features of the flow are well represented by the predictions.
A preconditioned alternating inner‐outer iterative solution method for the mixed finite element formulation of the Navier‐Stokes equations
Authors: Wille S. Ø.
Published: August 2005

In the present work a new iterative method for solving the Navier‐Stokes equations is designed. In a previous paper a coupled node fill‐in preconditioner for iterative solution of the Navier‐Stokes equations proved to increase the convergence rate considerably compared with traditional preconditioners. The further development of the present iterative method is based on the same storage scheme for the equation matrix as for the coupled node fill‐in preconditioner. This storage scheme separates the velocity, the pressure and the coupling of pressure and velocity coefficients in the equation matrix. The separation storage scheme allows for an ILU factorization of both the velocity and pressure unknowns. With the inner‐outer solution scheme the velocity unknowns are eliminated before the resulting equation system for the pressures is solved iteratively. After the pressure unknown has been found, the pressures are substituted into the original equation system and the velocities are also found iteratively. The behaviour of the inner‐outer iterative solution algorithm is investigated in order to find optimal convergence criteria for the inner iterations and compared with the solution algorithm for the original equation system. The results show that the coupled node fill‐in preconditioner of the original equation system is more efficient than the coupled node fill‐in preconditioner of the reduced equation system. However, the solution technique of the reduced equation system revals properties which may be advantageous in future solution algorithms.
Parallel computation of the flow of integral viscoelastic fluids on a heterogeneous network of workstations
Authors: Henriksen P. , Keunings R.
Published: August 2005

We consider the parallel computation of flows of integral viscoelastic fluids on a heterogeneous network of workstations. The proposed methodology is relevant to computational mechanics problems which involve a compute‐intensive treatment of internal variables (e.g. fibre suspension flow and deformation of viscoplastic solids). The main parallel computing issue in such applications is that of load balancing. Both static and dynamic allocation of work to processors are considered in the present paper. The proposed parallel algorithms have been implemented in an experimental, parallel version of the commercial POLYFLOW package developed in Louvain‐la‐Neuve. The implementation uses the public domain PVM software library (Parallel Virtual Machine), which we have extended in order to ease porting to heterogeneous networks. We describe parallel efficiency results obtained with three PVM configurations, involving up to seven workstations with maximum relative processing speeds of five. The physical problems are the stick/slip and abrupt contraction flows of a K.B.K.Z. integral fluid. Using static allocation, parallel efficiencies in the range 67%–85% were obtained on a PVM network with four workstations having relative speeds of 2:1:1:1. Parallel efficiencies higher than 90% were obtained on the three PVM configurations using the dynamic load‐balancing schemes.
Finite element formulations for large‐scale, coupled flows in adjacent porous and open fluid domains
Authors: Salinger A. G. , Aris R. , Derby J. J.
Published: August 2005

Two approaches which employ the finite element method to solve for large‐scale, coupled, incompressible flows through adjacent porous and open domains are developed and evaluated in a model for the spontaneous ignition of coal stockpiles. Both formulations employ the Navier‐Stokes equations do describe flow in the open region; two different descriptions, Darcy's law and the Brinkman equation, are employed to model flows within the porous region. The formulation which uses Darcy's law employs the Beavers‐Joseph slip condition and a novel implementation of the interfacial conditions. The other approach invokes the Brinkman equation: this considerably simplifies the implementation of matching conditions at the interface between the porous and open fluid domains, but also results in velocity boundary layers in the porous region adjacent to this interface which can be difficult to resolve numerically. A direct comparison of model results shows that the Darcy‐slip formulation produces solutions which are more accurate and more economical to compute than those obtained using the Brinkman formulation.
An Euler solver for three‐dimensional turbomachinery flows
Authors: Soulis Johannes Vassiliou
Published: August 2005

A time‐marching finite volume numerical procedure is presented for three‐dimensional Euler analysis of turbomachinery flows. The proposed scheme is applied to the conservative form of the Euler equations written in general curvilinear co‐ordinates. A simple but computationally efficient grid is constructed. Numerical solution results for three 3D turbine cascade flows have been presented and compared with available measurements as well as with another state‐of‐the‐art 3D Euler analysis numerical solution in order to demonstrate the accuracy and computational efficiency of the analysis method. Also, the predicted results are compared with a 3D potential flow solver and comparison is made with the analytical solution. The proposed method is an accurate and reliable technique for solving the compressible flow equations in turbomachinery geometries.
An ILU smoother for the incompressible Navier‐Stokes equations in general co‐ordinates
Authors: Zeng S. , Wesseling P.
Published: August 2005

The solution of the incompressible Navier‐Stokes equations in general two‐ and three‐dimensional domains using a multigrid method is considered. Because a great variety of boundary‐fitted grids may occur, robustness is at a premium. Therefore a new ILU smoother called CILU (collective ILU) is described, based on r‐transformations. In CILU the matrix that is factorized is block‐structured, with blocks corresponding to the set of physical variables. A multigrid algorithm using CILU as smoother is investigated. The performance of the algorithm in two and three dimensions is assessed by numerical experments. The results show that CILU is a good smoother for the incompressible Navier‐Stokes equations discretized on general non‐orthogonal curvilinear grids.
A weighted least squares method for first‐order hyperbolic systems
Authors: Zeitoun D. G. , Laible J. P. , Pinder G. F.
Published: August 2005

The paper presents a generalization of the classical L2‐norm weighted least squares method for the numerical solution of a first‐order hyperbolic system. This alternative least squares method consists of the minimization of the weighted sum of the L2 residuals for each equation of the system. The order of accuracy of global conservation of each equation of the system is shown to be inversely proportional to the weight associated with the equation. The optimal relative weights between the equations are then determined in order to satisfy global conservation of the energy of the physical system.

As an application of the algorithm, the shallow water equations on an irregular domain are first discretized in time and then solved using Laplace modification and the proposed least squares method.