bluuebunny/crossref_metadata_2025 huggingface dataset:
Two‐dimensional compressible Navier‐Stokes finite volume computations by means of implicit schemes
Authors: Marx Y. , Piquet J.
Published: August 2005

A finite volume method for solving the two‐dimensional compressible Navier‐Stokes equations is presented. Shortcomings of the direct extension to viscous flows of well known methods used for inviscid flows are demonstrated. Nevertheless, the method allows the computation of oscillation‐free shocks with only a few iterations. The double‐throat GAMM nozzle test case1 is considered.
Comparison of two solution strategies for use with higher‐order discretization schemes in fluid flow simulation
Authors: Gaskell P. H. , Lau A. K. C. , Wright N. G.
Published: August 2005

The paper describes and compares two different approaches to solving the equations of motion for fluid flow in a three‐dimensional lid‐driven cavity, when a higher‐order approximation to convective transport is employed. One is based on the traditional pressure correction approach in conjunction with a pentadiagonal ADI solver; the other follows a new unsegregated variable and FAS multigrid methodology. The results generated by both approaches, for laminar flow conditions, at Reynolds numbers of 100 and 1000 are compared with each other and with corresponding solutions obtained with a well known low‐order approximation to convection. Cross‐reference is also made to flow in a two‐dimensional cavity at the same Reynolds numbers.
Evaluation of Navier‐Stokes and Euler solutions for leading‐edge separation vortices
Authors: Fujii K. , Gavali S. , Holst T. L.
Published: August 2005

Extensive study on the numerical simulation of the vortical flow over a double‐delta wing is carried out using the ‘thin layer’ Navier‐Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The CL‐α characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with experiment on the CL‐α characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading‐edge separation vortex, are not consistent with experiment. Even for the fine grid Navier‐Stokes computations, further grid resolution is required to obtain good quantitative agreement with experiment.
Spatial marching techniques for approximate solutions to the hypersonic blunt body problem
Authors: Blottner Frederick G.
Published: August 2005

Two reduced forms of the Euler equations which allow spatial marching in subsonic flow regions are investigated for solving the inviscid blunt body problem. An analysis of the eignevalues to determine the properties of the steady and unsteady forms of the governing equations is performed. The steady forms of both the thin shock layer equations and the pressure gradient splitting method are appropriate for a marching solution technique. Numerical results from the thin layer equations are less accurate, and the suitability of this approach in a global iteration procedure is questioned as the analysis shows information is not transmitted upstream. The pressure gradient splitting method gives more accurate results with a single downstream march and appears better suited for use in a global iteration procedure to obtain the complete solution of the Euler equations. Further evaluation of the pressure gradient splitting method shows that it can be readily applied over a range of Mach numbers, and the accuracy of the results is only slightly dependent on the free‐stream Mach number.
Eulerian‐Lagrangian methods for the Navier‐Stokes equations at high Reynolds number
Authors: Casulli Vincenzo
Published: August 2005

In this paper an explicit Lagrangian approach to advective and diffusive term treatment has been derived to improve the stability and to reduce the artificial diffusion of a finite difference scheme for convection‐diffusion equations. This concept is then applied to discretize the convective and viscous terms in the Navier‐Stokes equations. The pressure gradient and the velocity divergence are discretized by implicit finite differences in such a way that the resulting velocity field is exactly discrete divergence‐free at all times. The stability of the method is shown to become less restrictive as the Reynolds number increases. At large time steps the artificial viscosity also reduces and higher accuracy is obtained. Moreover, the present algorithm is so devised as to take full advantage of vector computations in view of a possible implementation of it on an array computer. The performance of the method is illustrated by the numerical solution obtained for the cavity flow problem at high Reynolds numbers.
Radiative transfer to oscillatory hydromagnetic rotating flow of a rarefied gas past a horizontal flat plate
Authors: Bestman A. R.
Published: August 2005

Hydromagnetic flow past an infinite horizontal plate is considered when the flow is rarefied and the temperature of the wall is high enough for radiative heat transfer to be significant. In the undisturbed flow far away from the plate, an oscillatory velocity is superimposed on a steady mean and the whole configuration is in constant rotation. When the flow is slightly rarefied, the compressible Navier–Stokes equations and the slip boundary conditions together with the general differential approximation for radiation suffice for the analytical description of the problem. If the amplitude of oscillation is small, the problem is tackled by a perturbation scheme and numerical integration. Consequences of the effect of rotation and oscillation on the flow variables are discussed.
Mathematical derivation of a finite volume formulation for laminar flow in complex geometries
Authors: Davidson Lars , Hedberg Peter
Published: August 2005

This paper treats the mathematical derivation of a novel formulation of the Navier–Stokes equation for general non‐orthogonal curvilinear co‐ordinates. The covariant velocity components are solved in this FVM formulation, which leads to the pressure‐velocity coupling becoming relatively easy to handle at the expense of a more complicated expression of the convective and diffusive fluxes. When a velocity component is solved at a point P, the neighbouring velocities are projected in the direction of the velocity component at the point P. Thus the base vectors are changed at the neighbouring points. This renders a simpler expression for the covariant derivatives. Neither the Cristoffel symbol nor its derivatives need be computed. This contributes to the accuracy of the formulation. The procedure of changing the base vectors affects only the convected velocity. The convecting term (dot product of velocity and area) is calculated without any change of the base vectors. The same is true for the operator on the covariant velocity in the diffusion term.

It is shown that when using upwind differencing the use of projected velocities gives better results than when curvature effects are included in the source term. The discretized equations are written in a form which enables the use of the tridiagonal matrix algorithm (TDMA). The equations can be solved using either the SIMPLEC or the PISO procedure.

Two examples of laminar flows are given.
A pressure‐smoothing scheme for incompressible flow problems
Authors: Shiojima Takeo , Shimazaki Yoji
Published: August 2005

A pressure‐smoothing scheme for Stokes and Navier–Stokes flows of Newtonian fluids and for Stokes flow of Maxwell fluids is described. The stress deviator obtained from the calculated velocity field is substituted into the governing equilibrium equation. The resulting equation is then solved to obtain a new, smoothed pressure by a least square finite element method.
A calculation procedure for steady two‐dimensional elliptic flows
Authors: Wang Y. , He J. , Zhang B. Q.
Published: August 2005

A calculation procedure is presented for predicting steady two‐dimensional elliptic flows. The method introduces a density correction concept and an algebraic equation for the velocity correction instead of the troublesome pressure correction equation in the SIMPLER procedure. Computations show that the method has the same rate of convergence as SIMPLER while saving about 20% computational effort per iteration. Although the method is described for steady two‐dimensional situations, its extension to three‐dimensional problems is very straightforward.
Suppression of irregular frequency effects in fluid–structure interaction problems using a combined boundary integral equation method
Authors: Lau Siew Ming , Hearn Grant E.
Published: August 2005

It is well known that at certain discrete frequencies the conventional boundary integral equation formulation of free surface fluid–structure interaction analyses breaks down. At such ‘irregular’ frequencies the BIE method fails to provide either an acceptable or a unique solution. Having established the existence of irregular frequencies, a review of the different approaches adopted to remedy this problem is presented.

A very simple modification of the BIE method is also presented to eliminate the irregular frequency problem. The proposed procedure, designated the combined boundary integral equation method (CBIEM), can be categorized as a modified integral domain method. A description of the CBIEM formulation is presented and its ability to provide a unique solution at all frequencies is demonstrated. Predictions of 3D hydrodynamic reactive coefficients of added mass and fluid damping for a Series 60 hull form and an ellipsoid based on the CBIEM procedure are presented. These predictions are compared with results generated using conventional integral equation methods. The numerical studies demonstrate that the CBIEM is both a practical and effective method of suppressing irregular frequencies. In particular, the procedure is easy to implement in existing BIE computer codes with minimal additional computational effort.
Internal wave reflections and transmissions arising from a non‐uniform mesh. Part II: A generalized analysis for the Crank–Nicolson linear finite element scheme
Authors: Cathers B. , Bates S. , Penoyre R. , O'Connor B. A.
Published: August 2005

Internal wave reflections and transmissions are examined for the Crank–Nicolson linear finite element scheme applied to the linear shallow water equations in a ID domain containing an abrupt change in nodal spacing. In Part I of this series the reflection/transmission analysis was verified by some ‘hot‐start’ numerical experiments. Here in Part II, however, that analysis is found wanting when it comes to providing a description of the pseudo‐steady state wave configuration which develops with some ‘cold‐start’ experiments. It is shown that the analysis of Part I can be extended to take in both the ‘hot‐’ and ‘cold‐start’ experimental results such that four essentially different wave configurations can be identified. The four configurations are discernible on the basis of group velocity. In order to be sustained, two of the configurations require one energy source whereas the other two require two energy sòurces. Numerical experiments confirmed the analysis.
Finite element technique to solve the elastic strain for Leonov fluid flow
Authors: Lin Gwo‐Geng , Tseng Hsieng‐Cheng , Ju Yi‐Shi
Published: August 2005

The finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi‐linear coupled first‐order hyperbolic differential equations together with a non‐linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not knowna prioriand an iterative procedure is needed.
Assessment of variants of the k–ϵ turbulence model for engine flow applications
Authors: Ahmadi‐Befrui B. , Gosman A. D.
Published: August 2005

This paper is concerned with simulation of the mean flow and turbulence evolution in a model engine and comparison of the behaviour of certain important turbulence parameters, namely the intensity, length scale and dissipation time scale, as predicted by three variants of the k–ϵ model developed for application to strongly compressible flows. The predictions pertain to the axisymmetric, disc‐chamber, four‐stroke, Imperial College model engine operating at 200 rpm and compression ratios of 3·5 and 6·7. The paper analyses the predicted variations of these parameters during the induction, compression and expansion strokes and identifies the versions that produce the most consistent and physically plausible variations. The significance, to the turbulence evolution, of the ratio of the turbulence dissipation time scale to the time scale of compression/expansion is also discussed. It is concluded that on these grounds the Morel–Mansour and El Tahry versions are, and the Watkins version is not, suitable for engine applications.
A velocity formulation for flow past a symmetric profile with a wake
Authors: Räsänen S. M.
Published: August 2005

A model having velocity components as basic unknowns is presented for calculation of two‐dimensional flow past a symmetric profile with a wake in a channel. A modified least squares functional is used for the finite element solution of velocities. The determination of the position of the free streamline is treated as an optimum design problem. The concepts of cost function, geometry parameter and sensitivity derivative are employed. Numerical results are compared with published results obtained with streamfunction formulations.
A fast riemann solver with constant covolume applied to the random choice method
Authors: Toro E. F.
Published: August 2005

The Riemann problem for the unsteady one‐dimensional Euler equations together with the constant‐covolume equation of state is solved exactly. The solution is then applied to the random choice method to solve the general initial‐boundary value problem for the Euler equations. The iterative procedure to find p*, the pressure between the acoustic waves, involves a single algebraic (non‐linear) equation, all other quantities follow directly throughout the x–t plane, except within rarefaction fans where an extra iterative procedure is required. The solution is validated against existing exact results both directly and in conjunction with the random choice method.
Nodal integral method solutions for Bénard natural convection
Authors: Wilson Gary L. , Rydin Roger A.
Published: August 2005

The nodal integral method is a relatively new numerical technique that has been used recently to solve both static and dynamic multidimensional problems in heat transfer, fluid flow and neutron transport. The method offers significant advantages in terms of stability, accuracy and efficiency over conventional finite elements when the problem can be adequately modelled in Cartesian co‐ordinates. This method was used to investigate bifurcation phenomena in the Bénard problem for aspect ratios in the range of one to nine. Automatic search techniques were used with a static version to find the first four critical Rayleigh values for a square cavity, to map the first two critical Rayleigh values as a function of aspect ratio, and to examine the solution types. Accuracy enhancement was obtained by factorization and extrapolation. Critical values, obtained by interpolation, were verified dynamically. Aspect ratio crossover and transition values were found for the first two critical Rayleigh numbers, with an accuracy of the order of ±3 per cent. The precision achieved in the results for Ra* and Ra** as a function of β is usually within 0.1%–0.2% except at high β (i.e. near β=9.0) and at large critical values of Ra (i.e. the first few values of Ra** near β=1). Specific results at β=1.0 are Ra*=2584±0.5, Ra**=6807, Ra3* = 19 734 and Ra4*=22 586.
Buoyancy‐driven instability in a vertical cylinder: Binary fluids with Soret effect. Part I: General theory and stationary stability results
Authors: Hardin G. R. , Sani R. L. , Henry D. , Roux B.
Published: August 2005

Buoyancy‐driven instability of a monocomponent or binary fluid which is completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and the resulting linear stability problem is solved using Galerkin's technique. The analysis considers various types of fluid mixtures, ranging from gases to liquid metals, in cylinders with a variety of radius‐to‐height ratios. The flow structure is found to depend strongly on both the cylinder aspect ratio and the magnitude of the Soret effect. Comparisons are made with experiments and other theories, and the predicted stability limits are shown to agree closely with observations.
Finite element solutions of axisymmetric Euler equations for an incompressible and inviscid fluid
Authors: Saiac Jacques‐Herve
Published: August 2005

In this paper we present a finite element method for the numerical solution of axisymmetric flows. The governing equations of the flow are the axisymmetric Euler equations. We use a streamfunction angular velocity and vorticity formulation of these equations, and we consider the non‐stationary and the stationary problems.

For industrial applications we have developed a general model which computes the flow past an annular aerofoil and a duct propeller. It is able to take into account jumps of angular velocity and vorticiy in order to model the flow in the presence of a propeller. Moreover, we compute the complete flow around the after‐body of a ship and the interaction between a ducted propeller and the stern. In the stationary case we have developed a simple and efficient version of the characteristics/finite element method. Numerical tests have shown that this last method leads to a very fast solver for the Euler equations. The numerical results are in good agreement with experimental data.
A composite grid approach for the Euler equations
Authors: Reggio Marcelo , Trepanier Jean‐Yves , Camarero Ricardo
Published: August 2005

A zonal grid methodology has been developed for the calculation of compressible fluid flows. The domain subdivision is based on patched grid systems composed of zones or blocks within which a distinct curvilinear grid is generated. The flow simulation is then carried out with a modified scheme based on the Euler finite volume solver of Ni. This scheme uses a distribution procedure that provides an easy and accurate way for the transfer of information from one block to another. This method results in a naturally conservative computation at the interfaces. It is analysed and developed for the treatment of embedded grids with a grid point common to more than four blocks.
A design method for turbomachinery blading in three‐dimensional flow
Authors: Ghaly W. S.
Published: August 2005

A mixed spectral finite element scheme for the implementation of a design method for turbomachinery blading in three‐dimensional subcritical compressible flow is presented. The method gives the detailed blade shape that would produce a prescribed tangential mean swirl schedule, given the hub and shroud profiles, the number of blades and their stacking position. After a presentation of the mathematical formulation of the design theory, the current numerical approach is described. It is then applied to the design of blading for radial inflow turbine impellers in three‐dimensional flow.
Numerical solution of plane and axially symmetric jet flow problems based on the variational inequality formulation
Authors: Lee Han‐Yong , Kim Moon‐Uhn
Published: August 2005

The numerical analysis of plane and axially symmetric jet flows of an incompressible inviscid fluid is treated. A new formulation of the variational inequality type is developed from the variational principle associated with jet problems. A successive approximation method is formulated by the combined use of variational inequality and the finite element method. Numerical examples based on the iterative method are presented. The results obtained agree well with those by other methods.
Cascade aerodynamic gust response including steady loading effects
Authors: Chiang Hsiao‐Wei D. , Fleeter Sanford
Published: August 2005

To predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first‐order model is formulated. The flow is analysed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body‐fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analysing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.
Combined radiation and natural convection in a rectangular cavity with a transparent wall and containing a non‐participating fluid
Authors: Behnia M. , Reizes J. A. , De Vahl Davis G.
Published: August 2005

This paper describes a numerical method for the study of combined natural convection and radiation in a rectangular, two‐dimensional cavity containing a non‐participating (i.e. transparent) fluid.

One wall of the cavity is isothermal, being heated either by solar radiation or independently. The opposite wall is partially transparent, permitting radiation exchanges between the cavity and its surroundings and/or the Sun; that wall also exchanges heat by convection from its external surface to the surroundings. The other two walls are adiabatic: convection and radiation there are balanced, so that there is no heat transfer through those walls.

The equations of motion and energy are solved by finite difference methods. Coupled to these equations are the radiative flux boundary conditions which are used to determine the temperature distribution along the non‐isothermal walls. A two‐band radiation model has been employed.

Results are presented for a square cavity with a vertical hot wall at 150 °C, the ambient at 20 °C and 104 ⩽ Ra ⩽ 3 × 105, in the absence of direct insolation. The effects on the flow and heat transfer in the cavity of radiation and external convection have been examined. More extensive results will be presented in subsequent papers.
A proper orthogonal decomposition of a simulated supersonic shear layer
Authors: Kirby M. , Boris J. P. , Sirovich L.
Published: August 2005

The Karhunen–Loève procedure is applied to the analysis of an ensemble of snapshots obtained from a conditionally sampled localized shear layer simulation. The computed set of optimal basis functions is used to economically characterize sampled flow realizations. Pictorially it is seen that the essential features (and roughly 80% of the energy) of typical flows are captured by retaining roughly 10–20 parameters in the expansion. Smaller‐scale features are resolved by retaining more terms in the series.
An iterative implementation of the Uzawa algorithm for 3‐D fluid flow problems
Authors: Robichaud Michel P. , Tanguy Philippe A. , Fortin M.
Published: August 2005

A new iterative algorithm for the solution of the three‐dimensional Navier–Stokes equations by the finite element method is presented. This algorithm is based on a combination of the Uzawa and the Arrow–Hurwicz algorithms and uses a preconditioning technique to enhance convergence. Numerical tests are presented for the cubic cavity problem with two elements, namely the linear brick Q1−P0 and the enriched linear brick Q1+ − P1. It is shown that the proposed methodology is optimal with the enriched element and that the CPU time varies as NEQ1·44, where NEQ is the number of equations.
Finite element solution of the Navier–Stokes equations by a velocity–vorticity method
Authors: Guevremont G. , Habashi W. G. , Hafez M. M.
Published: August 2005

A velocity–vorticity formulation of the Navier–Stokes equations is presented as an alternative to the primitive variables approach. The velocity components and the vorticity are solved for in a fully coupled manner using a Newton method. No artificial viscosity is required in this formulation. The pressure is updated by a method allowing natural imposition of boundary conditions. Incompressible and subsonic results are presented for two‐dimensional laminar internal flows up to high Reynolds numbers.
Solution of viscous fluid flows on a distributed memory concurrent computer
Authors: Braaten Mark E.
Published: August 2005

A concurrent algorithm for the solution óf the Navier–Stokes equations expressed in curvilinear co‐ordinates has been developed for execution on a distributed memory parallel computer. This algorithm offers the ultimate promise of near‐supercomputer performance on relatively low‐cost parallel computers. The new algorithm is based on an existing serial pressure‐correction‐based algorithm, and uses domain decomposition to partition the problem onto the processors. The algorithm is demonstrated on an Intel iPSC for a complicated two‐dimensional laminar flow problem, for various grid sizes and numbers of processors. Initial results based on straightforward domain decomposition showed that the speed‐up per iteration approached 100% parallel efficiency as the grid size was increased, but that the convergence rate of the algorithm deteriorated relative to the original serial algorithm as the number of processors was increased, limiting the speed‐up achieved. This degradation in convergence rate was traced to a poorer solution of the pressure correction equation in the concurrent procedure. The addition of a global block correction procedure, implemented via efficient global communications routines, remedied this problem, making the convergence rate of the concurrent procedure equivalent to the serial algorithm. The maximum speed‐up achieved with the revised concurrent algorithm was a factor of 12·3 with 16 processors, representing a parallel efficiency of 77%.
Adaptive grid computation of three‐dimensional natural convection in horizontal high‐pressure mercury lamps
Authors: Chang P. Y. , Shyy W.
Published: August 2005

A three‐dimensional model has been developed to compute the thermofluid transport within a discharge arctube. The model has proved very useful for guiding the choice of design parameters to optimize the lamp performance. However, uncertainties exist with respect to quantitative aspects of the physical model, especially those related to radiation heat transfer. In the present work a grid refinement procedure and an adaptive grid method are used to improve the quantitative accuracy of the model and to help improve the physical modelling. The adaptive grid method, based on the multiple one‐dimensional equidistribution concept, can responsively redistribute the grids to optimize the grid resolutions. Adaptive grid solutions modify the predicted maximum gas temperature, the buoyancy‐induced convection strength, the location of the high‐temperature core, and the wall temperature profiles. The adaptive grid solutions show more consistent trends when compared to the measurements. On the basis of the quantitatively more definite information, adjustments can be made with regard to the uncertainties of the physical model.
An implicit characteristic‐flux‐averaging method for the euler equations for real gases
Authors: Drikakis D. , Tsangaris S.
Published: August 2005

A formulation of an implicit characteristic‐flux‐averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux‐split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh‐sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.
A general numerical method for the solution of gravity wave problems. Part 1: 2D steep gravity waves in shallow water
Authors: Liao S. J.
Published: August 2005

In this paper, 2D steep gravity waves in shallow water are used to introduce and examine a new kind of numerical method for the solution of non‐linear problems called the finite process method (FPM). On the basis of the velocity potential function and the FPM, a numerical method for 2D non‐linear gravity waves in shallow water is described which can be applied to solve 3D problems, e.g. the wave resistance of a ship moving in deep or shallow water. The convergence is examined and a comparison with the results of other authors is made.

The FPM can successfully avoid the use of iterative methods and therefore can overcome the disadvantages and limitations of such methods. In contrast to iterative methods, the FPM is insensitive to the selection of the initial solution and the number of unknowns. The basic idea of the FPM can be used to solve other non‐linear problems. Its disadvantage is that much more CPU time is needed to obtain a sufficiently accurate result.
Numerical computation of fluid pressure transients in pumping installations with air entrainment
Authors: Lee T. S.
Published: August 2005

In pumping installations such as sewage pumping stations, where gas content and air entrainment exist, the computation of fluid pressure transients in the pipelines becomes grossly inaccurate when constant wave speed and constant friction are assumed. A numerical model and computational procedure have been developed here to better compute the fluid pressure transient in a pipeline by including the effects of air entrainment and gas evolution characteristics of the transported fluid. Free and dissolved gases in the fluid and cavitation at the fluid vapour pressure are modelled. Numerical experiments show that entrained, entrapped or released gases amplify the pressure peak, increase surge damping and produce asymmetric pressure surges. The transient pressure shows a longer period for down‐surge and a shorter period for up‐surge. The up‐surge is considerably amplified and the down‐surge marginally reduced when compared with the gas‐free case. These observations are consistent with the experimental observations of other investigators. Numerical experiments also show that the use of a variable loss factor in the pressure transient analysis produces marginally higher maximum and lower minimum pressure transients when compared with the constant‐loss‐factor model for pipelines where the pressures are above the fluid vapour pressure.
Three‐dimensional desingularized boundary integral methods for potential problems
Authors: Cao Yusong , Schultz William W. , Beck Robert F.
Published: August 2005

The concept of desingularization in three‐dimensional boundary integral computations is re‐examined. The boundary integral equation is desingularized by moving the singular points away from the boundary and outside the problem domain. We show that the desingularization gives better solutions to several problems. As a result of desingularization, the surface integrals can be evaluated by simpler techniques, speeding up the computation. The effects of the desingularization distance on the solution and the condition of the resulting system of algebraic equations are studied for both direct and indirect versions of the boundary integral method. Computations show that a broad range of desingularization distances gives accurate solutions with significant savings in the computation time. The desingularization distance must be carefully linked to the mesh size to avoid problems with uniqueness and ill‐conditioning. As an example, the desingularized indirect approach is tested on unsteady non‐linear three‐dimensional gravity waves generated by a moving submerged disturbance; minimal computational difficulties are encountered at the truncated boundary.
Dynamics of liquid membranes. I: Non‐adaptive finite difference methods
Authors: Ramos J. I. , Pitchumani R.
Published: August 2005

A non‐adaptive method and a Lagrangian‐Eulerian finite difference technique are used to analyse the dynamic response of liquid membrancs to imposed pressure variations. The non‐adaptive method employs a fixed grid and upwind differences for the convection terms, whereas the Lagrangian‐Eulerian technique uses operator splitting and decomposes the mixed convection‐diffusion system of equations into a sequence of convection and diffusion operators. The convection operator is solved exactly by means of the method of characteristics, and its results are interpolated onto the fixed (Eulerian) grid used to solve the diffusion operator. It is shown that although the method of characteristics eliminates the numerical diffusion associated with upwinding the convection terms in a fixed Eulerian grid, the Lagrangian‐Eulerian method may yield overshoots and undershoots near steep flow gradients or when rapid pressure gradients are imposed, owing to the interpolation of the results of the convection operator onto the fixed grid used to solve the diffusion operator. This interpolation should be monotonic and positivity‐preserving and should satisfy conservation of mass and linear momentum. It is also shown that both the non‐adaptive and Lagrangian‐Eulerian finite difference methods produce almost identical (within 1%) results when liquid membranes are subjected to positive and negative step and ramp changes in the pressure coefficient. However, because of their non‐adaptive character, these techniques require an estimate of the (unknown) length of the membrane and do not use all the grid points in the calculations. The liquid membrane dynamic response is also analysed as a function of the Froude number, convergence parameter and nozzle exit angle for positive and negative step and ramp changes in the pressure coefficient.
Dynamics of liquid membranes. II: Adaptive finite difference methods
Authors: Ramos J. I.
Published: August 2005

Two domain‐adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time‐dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time‐dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non‐linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non‐conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non‐adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.
A solution for the vertical variation of stress, rather than velocity, in a three‐dimensional circulation model
Authors: Luettich Richard A. , Westerink Joannes J.
Published: August 2005

A simple technique is presented that allows a numerical solution to be sought for the vertical variation of shear stress as a substitute for the vertical variation of velocity in a three‐dimensional hydrodynamic model. In its most general form the direct stress solution (DSS) method depends only upon the validity of an eddy viscosity relation between the shear stress and the vertical gradient of velocity. The rationale for preferring a numerical solution for shear stress to one for velocity is that shear stress tends to vary more slowly over the vertical than velocity, particularly near boundaries. Consequently, a numerical solution can be obtained much more efficiently for shear stress than for velocity. When needed, the velocity profile can be recovered from the stress profile by solving a one‐dimensional integral equation over the vertical. For most practical problems this equation can be solved in closed form.

Comparisons are presented between the DSS technique, the standard velocity solution technique and analytical solutions for wind‐driven circulation in an unstratified, closed, rectangular channel governed by the linear equations of motion. In no case was the computational effort required by the velocity solution competitive with the DSS when a physically realistic boundary layer was included.

The DSS technique should be particularly beneficial in numerical models of relatively shallow water bodies in which the bottom and surface boundary layers occupy a significant portion of the water column.
An algorithm that accelerates convergence rates for incompressible Navier‐Stokes problems
Authors: Shih T. M. , Hwang B. C.
Published: August 2005

An algorithm, called the Algebraic Continuity Equations Solver (ACES), is developed based on the concept that two algebraic equations (three for 3D problems) can be generated from rearranging the discretized continuity equations. These rearranged equations are used to re‐compute the two velocity components (three for 3D problems), whose values are already obtained from solving the momentum equations. When written in a Navier‐Stokes computer code, this algorithm is equivalent to a fairly concise set of statements and can be implemented immediately after the computation of the continuity equation. In our analysis, ACES is used in conjunction with a grid having nodal velocity components at the vertices and the nodal pressure at the centre of each computational cell.

With the aid of ACES, correction of velocity components during the iteration can be inexpensively made, leading to faster convergence rates or rendering otherwise divergent computations convergent.

Test problems include benchmark problems such as lid‐driven cavity flows and buoyancy‐driven cavity flows of various parametric values and grid sizes. A 3D time‐dependent flow in an irregular geometry is also investigated. Discussions are presented to clarify some relevant issues. A possible reason why we think ACES is capable of improving the convergence rates is also given.
Computation of waves generated by submarine landslides
Authors: Verriere M. , Lenoir M.
Published: August 2005

Waves generated by submarine landslides are treated as three‐dimensional flows of a perfect incompressible fluid. For the solution of the Cauchy‐Poisson problem a time‐discretization is applied which leads at each time step to a non‐homogeneous free surface condition; the solution is then divided into two parts. The first part, subject to the true free surface condition, is computed in a simplified domain with constant depth. The second part involves a homogeneous free surface condition, a corrected bottom condition and the true bathymetry. In the case of constant depth, unconditional stability of the time discretization is derived. In the case of variable depth, mass and energy conservation is derived. Numerical results are presented. Comparison is made with other methods for the generation of axisymmetric waves. The transient propagation along a rectilinear coast is studied, including a comparison between two different bathymetries; trapping of energy is observed.
Finite volume computation of the turbulent flow over a hill employing 2D or 3D non‐orthogonal collocated grid systems
Authors: Coelho P. J. , Pereira J. C. F.
Published: August 2005

A general numerical method for the solution of the complete Reynolds‐averaged Navier‐Stokes equations for 2D or 3D flows is described. The method uses non‐orthogonal co‐ordinates, Cartesian velocity components and a pressure‐velocity‐coupling algorithm adequate for non‐staggered grid systems. The capability of the method and the overall performance of the κ–ϵ eddy viscosity model are demonstrated by calculations of 2D and 3D flow over a hill. Solution error estimations based on fine grids, e.g. 320 × 192 control volumes, together with comparisons with standard turbulence model modifications, low‐Reynoldsnumber or streamline curvature effects, have allowed the investigation of model drawbacks in predicting turbulent flows over surface‐mounted hills.
Periodic solution of turbulent oscillating channel flows
Authors: Zhong Qin , Olson M. D.
Published: August 2005

The time‐dependent turbulent Navier–Stokes equations are solved numerically by a finite element method with an algebraic eddy viscosity model (Baldwin–Lomax formulation) for oscillating turbulent channel flows. The method of averaging is used to analyse the resulting periodic motion of the fluid. Numerical results are obtained for various Strouhal numbers and relative amplitudes. A comparison is made between the numerical and published experimental results. It appears that for low relative amplitudes in a certain range of frequencies the agreement is satisfactory.
Numerical simulation of twin‐jet impingement on a flat plate coupled with cross‐flow
Authors: Chuang Shu‐Hao , Chen Ming‐Hua , Lii Shen‐Wu , Tai Fang‐Mei
Published: August 2005

Theoretical research to simulate twin‐jet impingement with cross‐flow has been undertaken. An impinging twin jet coupled with cross‐flow in closed ground effect has been studied by using the compressible Navier‐Stokes equation with a Jones–Launder κ–ϵ two‐equation turbulence model. The velocity results without cross‐flow were compared with the data of Saripalli et al. and found to show good agreement. The calculated results show that several recirculating zones are distributed around the flow field. Their size and location are closely related to the jet exit height above the ground, the nozzle space and the strength of cross‐flow. In addition, a fountain upwash flow occurs between the nozzles, and two low‐pressure recirculating zones are induced by the interaction between the nozzle mainstream and the fountain upwash flow. This induce a loss of lift force of the aircraft. The effects of the cross‐flow induce the sudden decrease in the lift force of the aircraft; the stronger the cross‐flow, the lower is the lift force of the flow field.
Cell vertex finite volume discretizations in three dimensions
Authors: Crumpton P. I. , Shaw G. J.
Published: August 2005

The cell vertex method is generalized to three dimensions. It is proved that there exists a one‐parameter family of eight‐point three‐dimensional methods with second‐order truncation error on parallelepipeds. Using different triangulations of control volume faces, various finite volume methods are derived. Some of these are identified as members of the aforementioned one‐parameter family and may be regarded as second‐order upwind schemes. A Fourier analysis is used to investigate the spectral properties of these discretizations.

Numerical experiments illustrate that second‐order global accuracy is achieved on parallelepiped grids, as suggested by the theory. Randomly perturbed, stretched, sheared meshes are used to test these methods to destruction. It is found that upwinding improves both the accuracy on distorted meshes and the spectrum of the discretization.
The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a vertical cylindrical jet
Authors: Hunt Roland
Published: August 2005

The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a single vertical cylindrical jet is obtained. This is effected by transforming the domain of the flow, which contains a free surface, onto a rectangular parallelepiped and using a marching strategy to solve the ensuing parabolic equations. The flow terminates at a finite distance along the cylinder, its position depending on the velocity and mass flux of the jet. A comparison with the usual two‐dimensional model in which the jet is replaced by a vertical sheet shows that such a representation is valid provided the overall width of the flow is not too large. In particular, the differences in heat transfer characteristics amount to a few per cent, thus validating the use of the two‐dimensional model when applied to heat exchanger tubes. A comparison with the more usual multicolumn case is also considered.
Multivariant finite elements for three‐dimensional simulation of viscous incompressible flows
Authors: Gupta Mahesh , Kwon Tai H. , Jaluria Yogesh
Published: August 2005

Within multivariant elements, which have restricted degrees of freedom at some nodes, different velocity components have different variations. Shape functions for the multivariant elements Q Po and R Po are developed. With such shape functions the value of a velocity component within a multivariant element is shown to depend upon all the independent components of velocity at the nodes of the element.

The use of the Q1 P0 element to simulate flows with discontinuous boundary conditions generated disturbance throughout the flow domain, giving erroneous pressure and velocity distributions. The Q Po element restricted the disturbance due to such discontinuities to a small region near the singular points, whereas the P Po element completely eliminated the fluctuations. Flows with discontinuous boundary conditions were simulated with reasonable accuracy by partially relaxing the no‐slip condition on the Q1 Po elements near the singular points.