bluuebunny/crossref_metadata_2025_split huggingface dataset:
Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems
Authors: Streett C. L. 
Published: August 2005

AbstractFundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.
Adaptive finite element methods for high‐speed compressible flows
Authors: Oden J. T. , Strouboulis T. , Devloo Ph. 
Published: August 2005

AbstractWe describe an adaptive finite element algorithm for solving the unsteady Euler equations. The finite element algorithm is based on a Taylor/Galerkin formulation and uses a very fast and efficient data structure to refine and unrefine the grid in order to optimize the approximation. We give a general version of the method which can be applied to moving grids with sliding interfaces and we present the results for a transient supersonic calculation of rotor‐stator interaction.
On a finite element CFD algorithm for compressible, viscous and turbulent aerodynamic flows
Authors: Baker A. J. , Kim J. W. , Freels J. D. , Orzechowski J. A. 
Published: August 2005

AbstractThis paper develops and analyses individual construction aspects of an efficient and accurate finite element algorithm for prediction of viscous and turbulent flow fields of impact in aerodynamics. The theoretical construction employs a Taylor weak statement (TWS) for coincident embedding of stability mechanisms within a classic Galerkin finite element formulation of semi‐discrete approximation error orthogonalization. A wide variety of the stabilizing mechanisms of independently derived CFD algorithms are contained within the TWS theory. An implicit construction that meets the requirement of efficient convergence to steady state is developed. The theoretical asymptotic error estimates of the TWS finite element algorithm for supersonic and viscous boundary layer flows are verified. Application to a three‐dimensional turbulent flow is cited.
Finite element computation of a turbulent flow over a two‐dimensional backward‐facing step
Authors: Autret A. , Grandotto M. , Dekeyser I. 
Published: August 2005

AbstractThis paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a k‐ϵ turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ϵ is proposed as a numerical treatment for physically meaningless values of k and ϵ. Results obtained for a recirculating flow in a two‐dimensional channel with a sudden expansion in width are presented and compared with experimental values.
The free surface flow of Newtonian and non‐Newtonian fluids trapped by surface tension
Authors: Tidd D. M. , Thatcher R. W. , Kaye A. 
Published: August 2005

AbstractIn this paper the position of the free surface of a swirling fluid held in by surface tension is calculated by the finite element method. A new locally mass‐conserving quadratic velocity, linear pressure triangular element is used to overcome non‐physical solutions produced by the well known Taylor‐Hood element.
Dirichlet and Neumann boundary conditions for the pressure poisson equation of incompressible flow
Authors: Abdallah S. , Dreyer J. 
Published: August 2005

AbstractIn a recent paper Gresho and Sani showed that Dirichlet and Neumann boundary conditions for the pressure Poisson equation give the same solution. The purpose of this paper is to confirm this (for one case at least) by numerically solving the pressure equation with Dirichlet and Neumann boundary conditions for the inviscid stagnation point flow problem. The Dirichlet boundary condition is obtained by integrating the tangential component of the momentum equation along the boundary. The Neumann boundary condition is obtained by applying the normal component of the momentum equation at the boundary. In this work solutions for the Neumann problem exist only if a compatibility condition is satisfied. A consistent finite difference procedure which satisfies this condition on non‐staggered grids is used for the solution of the pressure equation with Neumann conditions. Two test cases are computed. In the first case the velocity field is given from the analytical solution and the pressure is recovered from the solution of the associated Poisson equation. The computed results are identical for both Dirichlet and Neumann boundary conditions. However, the Dirichlet problem converges faster than the Neumann case. In the second test case the velocity field is computed from the momentum equations, which are solved iteratively with the pressure Poisson equation. In this case the Neumann problem converges faster than the Dirichlet problem.
Wave equation hydrodynamics on deforming elements
Authors: Sidén Gunnar L. D. , Lynch Daniel R. 
Published: August 2005

AbstractThe shallow water wave equation is derived in a general deforming co‐ordinate system. A weak form is developed which displays the natural boundary condition prominently and which may be implemented on C0 elements. A time‐stepping algorithm is implemented with clastic mapping of interior node motion. Lossless test cases show agreement with analytic solutions. A simple hypothetical test case shows intuitively good behaviour at length scales approaching those required of estuarine simulations.
Generation of three‐dimensional unstructured grids by the advancing‐front method
Authors: Löhner Rainald , Parikh Paresh 
Published: August 2005

AbstractThe generation of three‐dimensional unstructured grids using the advancing‐front technique is described. This technique has been shown to be effective for the generation of unstructured grids in two dimensions.1,2 However, its extension to three‐dimensional regions required algorithms to define the surface and suitable data structures that avoid excessive CPU‐time overheads for the search operations involved. After obtaining an initial triangulation of the surfaces, tetrahedra are generated by successively deleting faces from the generation front. Details of the grid generation algorithm are given, together with examples and timings.
Two‐dimensional compressible Navier‐Stokes finite volume computations by means of implicit schemes
Authors: Marx Y. , Piquet J. 
Published: August 2005

AbstractA 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

AbstractThe 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

AbstractExtensive 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

AbstractTwo 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

AbstractIn 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

AbstractHydromagnetic 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

AbstractThis 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

AbstractA 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

AbstractA 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

AbstractIt 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

AbstractInternal 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

AbstractThe 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

AbstractThis 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

AbstractA 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

AbstractThe 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

AbstractThe 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.