bluuebunny/crossref_metadata_2025_split huggingface dataset:
Non‐linear free surface flows and an application of the Orlanski boundary condition
Authors: Jagannathan Sridhar 
Published: August 2005

AbstractThe focus of this paper is the analysis of spatially two‐dimensional non‐linear free surface problems. The critical aspects of the problem concern the treatment of the non‐linear free surface, the body boundary condition for large motions and the imposition of suitable radiation conditions. To address such complexities, time domain simulation was chosen as the method of analysis. With the use of a finite domain for simulation, a major concern is with the radiation condition to be applied at the open or truncation boundary. For the two‐dimensional problem at hand, no theoretical radiation conditions are known to exist. An extension of the Orlanski open boundary condition, based on phase velocity determination at the free surface, is proposed. Three categories of problems were analysed using numerical simulation‐namely, freely moving steep waves, waves over a submerged body and forced body motion. Simulation results have been compared with linear theory and experiments.
A shock‐capturing scheme for body‐fitted meshes
Authors: Glaister P. 
Published: August 2005

AbstractA finite difference scheme based on flux difference splitting is presented for the solution of the two‐dimensional Euler equations of gas dynamics in a generalized co‐ordinate system. The scheme is based on numerical characteristic decomposition and solves locally linearized Riemann problems using upwind differencing. The decomposition is for a generalized co‐ordinate system and a convex equation of state. This ensures good shock‐capturing properties when incorporated with operator splitting and the advantage of using body‐fitted co‐ordinates. The resulting scheme is applied to supersonic flow of real air' past a circular cylinder.
A spectral multi‐domain technique for viscous compressible reacting flows
Authors: Macaraeg M. G. , Streett C. L. 
Published: August 2005

AbstractThe first application of a spectral multi‐domain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high‐order continuity of the solution is preserved. The global flux balance is imposed in terms of a spectral integral of the discrete equations across adjoining domains. Since the discretized equations interior to each domain are solved uncoupled from each other and since the interface relation has a block structure, the solution scheme can be adapted to the particular requirement in each subdomain. To illustrate these advantages a Mach 11 shock calculation is presented to study the chemical kinetics initiated as air passes through a fully resolved shock wave.
A control point form of algebraic grid generation
Authors: Eiseman Peter R. 
Published: August 2005

AbstractLocal control points are established within the context of algebraic grid generation. The method of generation is based upon a multidirectional assembly of multisurface transformations that incorporates the best features of tensor product and Boolean sum constructions. Upon assembly, the resultant capability is the capacity to conform precisely to prescribed boundaries while being able to manipulate the grid through a sparse net of control points.
Linear and non‐linear mechanisms in boundary layer turbulence
Authors: Landahl Marten T. 
Published: August 2005

AbstractThe different stages of bursting and evolution of the fluctuation field in a turbulent boundary layer are governed by mechanisms that may be identified as either predominantly linear, i.e. governed by linear interaction with the mean shear flow, or non‐linear, i.e. with interaction between the fluctuation components also being important. Wave number‐frequency spectra reveal the presence of damped wave modes that may be modelled from the Orr‐Sommerfeld equation. Conditional sampled experimental data for streamwise velocity fluctuations in the wall layer obtained using the variable interval time averaging (VITA) method scale with the threshold level in a manner consistent with linearity. High‐amplitude wall pressure peaks show an approximately linear relationship with the associated vertical velocity fluctuations. Non‐linearity acts primarily in the near‐wall region where the fluctuation velocity is relatively the highest.
Numerical simulation methods of incompressible flows and an application to the Space Shuttle main engine
Authors: Chang J. L. C. , Kwak D. , Rogers S. E. , Yang R.‐J. 
Published: August 2005

AbstractThis paper discusses incompressible Navier‐Stokes solution methods with an emphasis on the pseudocompressibility method. A steady‐state flow solver based on the pseudocompressibility approach is then described. This flow solver code has been used to analyse the internal flow in the Space Shuttle main engine hot‐gas manifold. Salient features associated with this three‐dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.
Flame computations by a Chebyshev multidomain method
Authors: Ehrenstein U. , Guillard H. , Peyret R. 
Published: August 2005

AbstractA Chebyshev collocation method is proposed for the computation of laminar flame propagation in a two‐dimensional gaseous medium. The method is based on a domain decomposition technique associated with co‐ordinate transforms to map the infinite physical subdomains into finite computational ones. The influence matrix method is used to handle the patching conditions at the interfaces. This technique is particularly efficient since at each time step only matrix products have to be performed. The method is tested first on an elliptic model problem; it is then applied to laminar flame computations, including calculations of cellular instabilities of flame fronts.
An inverse finite element method with an application to extrusion with solidification
Authors: Alexandrou A. N. , Anturkar N. R. , Papanastasiou T. C. 
Published: August 2005

AbstractThe flow and solidification of planar jets are analysed by means of an efficient inverse isotherm finite element method. The method is based on a tessellation that is constructed by isotherms as characteristic co‐ordinate lines transverse to the flow direction. Thus opposite sides of finite elements lie on isotherms. The method allows the simultaneous determination of the location of the isotherms with the primary unknowns, namely, the velocity, the pressure, the temperature and the location of the free surface. Thus the determination of the location of the solidification front (which is known to pose significant computational difficulties) is automatic. This facilitates the control of the location of the solidification front by controlling macroscopic variables such as the flow rate, the cooling rate and the capillary design. The location of the solidification may then be suitably chosen to influence the frozen‐in orientation and structure in extrusion of high‐performance materials such as composites and polymers, in continuous casting of metals and in growth of crystals.
A finite element analysis of a free surface drainage problem of two immiscible fluids
Authors: Mori Masatake , Natori Makoto , Guo‐Feng Zhang 
Published: August 2005

AbstractA sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two‐dimensional model and solved numerically. This problem is a transient two‐phase free or moving boundary problem, the slag surface and the slag–metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time‐stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace is given.
Stable second‐order accurate iterative solutions for second‐order elliptic problems
Authors: Lin Avi 
Published: August 2005

AbstractThe paper describes a numerical scheme for solving a convection–diffusion elliptic system with very small diffusion coefficients. This iterative numerical procedure is unconditionally stable and converges very rapidly. Although only linear equations are considered here, this technique can be easily extended to non‐linear equations, while keeping its main features as for the linear case. The numerical experiments presented are quite general and confirm most of these features. These examples also show a good way of implementing this scheme.
Numerical perturbation method for approximate solution of poisson's equation on a moderately deforming grid
Authors: Strigberger Jack 
Published: August 2005

AbstractIn problems such as the computation of incompressible flows with moving boundaries, it may be necessary to solve Poisson's equation on a large sequence of related grids. In this paper the LU decomposition of the matrix A0 representing Poisson's equation discretized on one grid is used to efficiently obtain an approximate solution on a perturbation of that grid. Instead of doing an LU decomposition of the new matrix A, the RHS is perturbed by a Taylor expansion of A−1 about A0. Each term in the resulting series requires one ‘backsolve’ using the original LU.Tests using Laplace's equation on a square/rectangle deformation look promising; three and seven correction terms for deformations of 20% and 40% respectively yielded better than 1% accuracy.As another test, Poisson's equation was solved in an ellipse (fully developed flow in a duct) of aspect ratio 2/3 by perturbing about a circle; one correction term yielded better than 1% accuracy.Envisioned applications other than the computation of unsteady incompressible flow include: three‐dimensional parabolic problems in tubes of varying cross‐section, use of ‘elimination’ techniques other than LU decomposition, and the solution of PDEs other than Poisson's equation.
A Newton/upwind method and numerical study of shock wave/boundary layer interactions
Authors: Liou Meng‐Sing 
Published: August 2005

AbstractThe objective of the paper is twofold. First we describe an upwind/central differencing method for solving the steady Navier–Stokes equations. The symmetric line relaxation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple‐deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical and other computational results. Secondly we proceed to study numerically the shock wave/boundary layer interactions in detail, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, we find that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.
Internal wave reflections and transmissions arising from a non‐uniform mesh. Part I: An analysis for the Crank–Nicolson linear finite element scheme
Authors: Cathers B. , Bates S. , O'Connor B. A. 
Published: August 2005

AbstractThis is the first of a series of three related papers dealing with some of the consequences of non‐uniform meshes in a numerical model. In this paper the accuracy of the Crank–Nicolson linear finite element scheme, which is applied to the linear shallow water equations, is examined in the context of a single abrupt change in nodal spacing. The (in)accuracy is quantified in terms of reflection and transmission coefficients. An incident wave impinging on the interface between two regions with different nodal spacings is shown to give rise to no reflected waves and two transmitted waves. The analysis is verified using three different wavelengths (2Δx, 4Δx 8Δx) in three ‘hot‐start’ numerical experiments with a mesh expansion factor of 2 and three experiments with a mesh contraction factor of 1/2. An energy flux analysis based on the concept of group velocity shows that energy is conserved across the interface.
Internal wave reflections and transmissions arising from a non‐uniform mesh. Part III: The occurrence of evanescent waves in the Crank‐Nicolson linear finite element scheme
Authors: Cathers B. , Bates S. , O'Connor B. A. 
Published: August 2005

AbstractThe numerical scheme upon which this paper is based is the 1D Crank–Nicolson linear finite element scheme. In Part I of this series it was shown that for a certain range of incident wavelengths impinging on the interface of an expansion in nodal spacing, an evanescent (or spatially damped) wave results in the downstream region. Here in Part III an analysis is carried out to predict the wavelength and the spatial rate of damping for this wave. The results of the analysis are verified quantitatively with seven ‘hot‐start’ numerical experiments and qualitatively with seven ‘cold‐start’ experiments. Weare has shown that evanescent waves occur whenever the frequency of a disturbance at a boundary exceeds the maximum frequency given by the dispersion relation. In these circumstances the ‘extended dispersion’ relation can be used to determine the rate of spatial decay.In the context of a domain consisting of two regions with different nodal spacings, the use of the group velocity concept shows that evanescent waves have no energy flux associated with them when energy is conserved.
A total pressure correction for upstream weighted schemes
Authors: De Henau V. , Raithby G. D. , Thompson B. E. 
Published: August 2005

AbstractUpwind differencing is known to lead to a substantial loss in total pressure. The present paper illustrates the importance of this error on two problems: flow in a converging–diverging duct and flow around a cylinder. A correction is proposed that reduces the total pressure error and yields dramatically improved results for the test problems.
Three‐dimensional reduced Navier–Stokes solutions for subsonic separated and non‐separated flows, using a global pressure relaxation procedure
Authors: Cohen R. , Khosla P. K. 
Published: August 2005

AbstractThe reduced Navier–Stokes and thin layer approximations to the Navier–Stokes equations are used to obtain solutions for viscous subsonic three‐dimensional flows. A spatial marching method is combined with a direct sparse matrix solver to obtain successive solutions in a global relaxation process. Results have been obtained for flow fields with and without regions of flow reversal.
Second‐order finite difference solutions for the flow between rotating concentric spheres
Authors: Schwengels Steve , Schultz David , Shay William 
Published: August 2005

AbstractThis paper describes a second‐order method to calculate approximate solutions to flow of viscous incompressible fluid between rotating concentric spheres. The governing partial differential equations are presented in the stream–vorticity formulation and are written as a series of second‐order equations. The technique employed makes use of second‐order approximations for all terms in the governing equations and is dependent upon the direction of flow at a given point. This upwind technique has allowed us to generate approximate solutions with larger Reynolds numbers than has generally been possible for second and higher‐order techniques. Solutions have been obtained with Reynolds numbers as large as 3000 and with grids as fine as a 40 × 40 mesh. Results are displayed in the form of level curves for both the stream and vorticity functions. A dimensionless quantity related to the torque acting on both spheres has been calculated from the approximate solution and compared with other results. Results with smaller Reynolds numbers such as 100 and 1000 are in excellent agreement with other published results.
Algebraic turbulence models for the computation of two‐dimensional high‐speed flows using unstructured grids
Authors: Rostand Philippe 
Published: August 2005

AbstractThe incorporation of algebraic turbulence models in a solver for the 2D compressible Navier–Stokes equations using triangular grids is described. A practical way to use the Cebeci–Smith model and to modify it in separated regions is proposed. The ability of the model to predict high‐speed perfect‐gas boundary layers is investigated from a numerical point of view.
Laminar flow and heat transfer over a two‐dimensional triangular step
Authors: Kumar S. G. Ravi , Narayana P. A. Aswatha , Seetharamu K. N. , Ramaswamy B. 
Published: August 2005

AbstractThe velocity correction algorithm is used in the finite element method to solve forced convection problems between parallel plates with a triangular step, for Reynolds numbers up to 1000. Equal‐order interpolation functions for velocity, pressure and temperature are used. The solutions show a smooth variation of pressure. The streamfunction, isotherms, isobars and velocity profiles are presented for a typical Reynolds number of 500. The skin friction and heat transfer results are presented for Reynolds numbers up to 1000.
Fundamental solutions of the streamfunction–vorticity formulation of the Navier–Stokes equations
Authors: Rodriguez‐Prada H. A. , Pironti F. F. , Sáez A. E. 
Published: August 2005

AbstractA new boundary element procedure is developed for the solution of the streamfunction–vorticity formulation of the Navier–Stokes equations in two dimensions. The differential equations are stated in their transient version and then discretized via finite differences with respect to time. In this discretization, the non‐linear inertial terms are evaluated in a previous time step, thus making the scheme explicit with respect to them. In the resulting discretized equations, fundamental solutions that take into account the coupling between the equations are developed by treating the non‐linear terms as in homogeneities. The resulting boundary integral equations are solved by the regular boundary element method, in which the singular points are placed outside the solution domain.
A finite element solution of unsteady two‐dimensional flow in cascades
Authors: Whitehead D. S. 
Published: August 2005

AbstractA theory is presented for unsteady two‐dimensional potential transonic flow in cascades of compressor and turbine blades using a mesh of triangular finite elements. The theory leads to a computer program, FINSUP, which is fast and has moderate storage requirements, so that it can be run on a personal computer. Comparisons with other theories in special cases show that the program is accurate in subsonic flow, and that in supersonic flow, although the wave effects are smeared by the numerical process, the results for overall blade force and moment have acceptable accuracy. The program is useful for engineering assessment of unstalled flutter of actual compressor and turbine blades.
A Taylor–Galerkin‐based algorithm for viscous incompressible flow
Authors: Hawken D. M. , Tamaddon‐Jahromi H. R. , Townsend P. , Webster M. F. 
Published: August 2005

AbstractIn this paper the development and behaviour of a new finite element algorithm for viscous incompressible flow is presented. The stability and background theory are discussed and the numerical performance is considered for some benchmark problems. The Taylor–Galerkin approach naturally leads to a time‐stepping algorithm which is shown to perform well for a wide range of Reynolds numbers (1 ⩽Re⩽ 400).A conventional definition forReis assumed.Various modifications to the algorithm are investigated, particularly with respect to their effects on stability and accuracy.
Singular finite elements for the sudden‐expansion and the die‐swell problems
Authors: Georgiou Georgios C. , Schultz William W. , Olson Lorraine G. 
Published: August 2005

AbstractThe singular finite element method is used to solve the sudden‐expansion and the die‐swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The method requires minor modifications to standard finite element schemes, and even coarse meshes give more accurate results than refined ordinary finite element meshes. Improved normal stress results for the sudden‐expansion problem have been obtained for various Reynolds numbers up to 100 using the singular elements constructed for the creeping flow problem. In addition, the normal stresses at the walls appear to be insensitive to the singularity powers used in the construction of the singular basis functions. The die‐swell problem is solved using the singular elements constructed for the stick–slip problem. The singular elements accelerate the convergence of the free surface dramatically.