bluuebunny/crossref_metadata_2025_split huggingface dataset:
Solution of three‐dimensional viscous incompressible flows by a multi‐grid method
Authors: Fuchs L. , Zhao H.‐S. 
Published: August 2005

AbstractThe three‐dimensional Navier‐Stokes equations for viscous incompressible fluids are discretized on staggered or non‐staggered grids. The system of finite‐difference equations is solved by a multi‐grid method. The method and some possible sources of difficulties and their remedies are described. The numerical algorithm has been applied to the computations of flows in ducts for a range of Reynolds numbers up to 2000. As outflow boundary conditions, either the fully developed flow profile (Dirichlet condition) or parabolic conditions have been applied. The multi‐grid method has a fast rate of convergence (with both types of boundary conditions), and it is not sensitive to the number of mesh points and the Reynolds number. The numerical solution, using parabolic boundary conditions, is insensitive to the location of the outflow boundary, even for large Reynolds numbers, in contrast to the solution with Dirichlet boundary conditions.
Techniques of ray averaging
Authors: Southgate Howard N. 
Published: August 2005

AbstractRay methods are used in coastal and harbour wave disturbance investigations where the area to be modelled is large compared to the wavelength. The interpretation of forward‐plotted ray diagrams, once obtained, has always been a difficult problem. The technique described in this paper calculates wave amplitudes during the ray plotting process and requires only minor modifications to existing ray plotting programs. The idea is to superimpose a grid of square elements over the entire sea area under study, and to perform a spatial averaging of the rays crossing each square element. This ‘square‐averaging’ technique has a number of advantages. It smooths the rapid amplitude variations near caustics, calculates the interference of several wave trains, and generates amplitudes automatically in a square array covering the whole studied sea area. Two types of sensitivity tests are carried out. These tests are designed to determine the accuracy of the predicted wave amplitudes with respect to: (1) the square size per wavelength, and (2) the ray density. These two factors largely determine the computing storage, time and cost of a ray model. An upper limit on the square size per wavelength and a lower limit on the ray density are obtained.
Stability of viscous flow in a rotating porous medium in the form of an annulus: The small‐gap problem
Authors: Channabasappa M. N. , Ranganna G. , Rajappa B. 
Published: August 2005

AbstractThe paper deals with the linear stability analysis of laminar flow of a viscous fluid in a rotating porous medium in the form of an annulus bounded by two concentric circular impermeable cylinders. The usual no‐slip condition is imposed at both the boundaries. The resulting sixth order boundary value, eigenvalue problem has been solved numerically for the small‐gap case by the Runge‐Kutta‐Gill method, assuming that the marginal state is stationary. The results of computation reveal that the critical Taylor number increases with decreasing permeability of the medium. The problem is found to reduce to the case of ordinary viscous flow in the annulus obtained by Chandrasekhar,1 when the permeability parameter tends to zero.
Further numerical methods for the Falkner‐Skan equations: Shooting and continuation techniques
Authors: Laine Claudine , Reinhart Laure 
Published: August 2005

AbstractWe consider in this paper the numerical solution of the Falkner‐Skan differential equation, modelling under some similarity assumptions the boundary layer equation. We look for the extremal solution of this third order differential equation. The methods we use are basically the Newton method with a shooting process, which is coupled with a continuation method: they allow us to follow the solution arcs which contain regular and turning point solutions.
The stability of explicit Euler time‐integration for certain finite difference approximations of the multi‐dimensional advection–diffusion equation
Authors: Hindmarsh A. C. , Gresho P. M. , Griffiths D. F. 
Published: August 2005

AbstractA comprehensive study is presented regarding the numerical stability of the simple and common forward Euler explicit integration technique combined with some common finite difference spatial discretizations applied to the advection‐diffusion equation. One‐dimensional results are obtained using both the matrix method (for several boundary conditions) and the classical von Neumann method of stability analysis and arguments presented showing that the latter is generally to be preferred, regardless of the type of boundary conditions. The less‐well‐known Godunov‐Ryabenkii theory is also applied for a particular (Robin) boundary condition. After verifying portions of the one‐dimensional theory with some numerical results, the stabilities of the two‐ and three‐dimensional equations are addressed using the von Neumann method and results presented in the form of a new stability theorem. Extension of a useful scheme from one dimension, where the pure advection limit is known variously as Leith's method or a Lax‐Wendroff method, to many dimensions via finite elements is also addressed and some stability results presented.
Three‐dimensional free‐surface suspended particles transport in the South Biscayne Bay, Florida
Authors: Miller Harvey P. 
Published: August 2005

AbstractA three‐dimensional, time‐dependent free surface model has been developed which takes account of topographical and meterological parameters for application to suspended particles transport. This investigation of suspended particles transport is the most realistic in regard to treating the moving free‐surface in computing the hydrodynamic field. A unique mass‐conserving numerical model is used for solving the concentration equation by an explicit finite difference scheme. The paper presents a mathematical model which can be applied to surface water dispersion of particulates associated with dredging operations and land‐fill. The effects of settling velocity and bottom bed deposition rate are compared and discussed.
Finite element solution of the shallow water equations by a quasi‐direct decomposition procedure
Authors: Goussebaile J. , Hecht F. , Labadie G. , Reinhart L. 
Published: August 2005

AbstractWe describe in this paper some new methods for solving the shallow water flow problem; this problem is composed of two coupled non‐linear equations. First a fractional step method is used to decouple the difficulties due to the convection and the propagation. The diffusion propagation step amounts to solving two coupled linear equations on the water depth and the fluxes. We used then some quasi‐direct decomposition techniques to decouple the unknowns, leading to symmetric systems only. In addition some non‐trivial boundary conditions on the flux are examined. Particularly we are interested to get decoupled systems on the two components of the flux. Numerical tests are presented to enlighten the behaviour and the capabilities of the method. Finally an industrial example is treated on the Dunkirk harbour.
A Kantorovich computational method for free surface gravity flows
Authors: Toro E. F. , O'Carroll M. J. 
Published: August 2005

AbstractComputing free surface gravity flows involves basically two coupled problems, namely, the location of the free surface position and the determination of the internal flow field (for assumed values H0 and Q of the total head and discharge, respectively).Solution techniques are invariably based on iterative procedures, but those that iterate between the two coupled problems may become unstable.In this paper we present a computational method in which the coupling is kept throughout the process of iteration. This is achieved by converting the coupled problems (by means of the Kantorovich method) into the single problem of finding a set of streamlines, including that of the free surface. These streamlines are moved (iteratively) to satisfy the stationary conditions of the governing variational principle.The algorithm is very stable and converges rapidly. It is also easy to implement to solve various types of steady flows with a free surface under gravity.
Numerical study of thermal convection in rotating channel flow
Authors: Thangam Sivagnanam , Speziale Charles G. 
Published: August 2005

AbstractA numerical study is conducted on the effect of sidewall heating in the pressure‐driven laminar flow of an incompressible viscous fluid through a rectangular channel that is subjected to a spanwise rotation. The time‐dependent Navier‐Stokes equations are solved along with the conservation equations for energy and mass by a finite‐difference technique. The effect of weak to moderate sidewall heating on the overall flow structure at different rotation rates is studied. It is observed that for weak sidewall heating, the secondary flow structure is quite similar to the corresponding isothermal case. However, when the sidewall heating is moderate, various types of secondary flow fields are found to occur depending on the magnitude of the rotation. The influence of rotational speed on the net heat transport for different levels of sidewall heating is also studied. It is found that when the sidewall heating is weak, the basic secondary flow structure for the non‐rotating case is of a unicellular form and an increase in the rotation speed leads to an increase in the net heat transfer due mainly to the rotationally driven transport of fluid from the high temperature to the low temperature region. On the other hand, when the sidewall heating is moderate so that the basic secondary flow structure for the non‐rotating case has a multicellular configuration, an increase in the rotation speed leads to a decrease in the heat transport due to the weakening of the shear layer near the hot wall.
On the solution for steady state and time dependent flows in certain channels with small wall curvature
Authors: Georgiou G. A. , Ellinas C. P. 
Published: August 2005

AbstractAn asymptotic scheme is presented for the solution of the steady state and time dependent stream functions for flows in symmetric curved walled channels. In this scheme a class of non‐linear Jeffery‐Hamel solutions appear at O(1), and thus provide the first approximation to the steady state stream function. This class of Jeffery‐Hamel solutions are evaluated by using a simple perturbation about Poiseuille flow.The classic Orr‐Sommerfeld eigenproblem appears at O(1) in the asymptotic development of the time dependent stream function, but here there is a slow streamwise dependence. This eigenvalue problem, for a complex wave number, is solved using an algorithm which automatically provides an initial guess which is then used to iterate to the correct eigenvalue.Higher order terms in the asymptotic development, for both the steady state and time dependent stream functions, are evaluated to provide a solution for the total stream function.
Finite element analysis of the steady Navier‐Stokes equations by a multiplier method
Authors: Mizukami Akira 
Published: August 2005

AbstractIn this paper a fully explicit finite element method (FEFEM) is presented for solving steady incompressible viscous flow problems. This full explicitness is achieved by combining the multiplier (or augmented Lagrangian) method with a pseudo‐time‐iteration method. FEFEM needs no global matrix at all and is of great advantage to large‐scale problems because they can be solved within the limit of core memory.The optimum choice of a time increment and a penalty parameter is discussed and the driven cavity flow at a Reynolds number of 1000 is computed with a refined mesh (60 × 60 elements).
A three‐level generalized‐co‐ordinate group finite‐element method for compressible viscous flow
Authors: Srinivas K. , Fletcher C. A. J. 
Published: August 2005

AbstractA consistent three‐level time‐split group finite‐element method, suitable for the computation of viscous compressible flows in irregular geometric domains, is described. Exploitation of the group12 formulation permits an accurate and economical algorithm to be developed in a generalized‐co‐ordinate (ζ,η) space. A variable sweep cycle is used to accelerate convergence to the steady state. The method is demonstrated by computing laminar and turbulent flow past a trailing edge. The method uses an algebraic eddy viscosity model to represent turbulence and produces results in close agreement with the experiments and computations of Viswanath et al8.
Computation of three‐dimensional flow using the Euler equations and a multiple‐grid scheme
Authors: Koeck Charles 
Published: August 2005

AbstractThe unsteady Euler equations are numerically solved using the finite volume one‐step scheme recently developed by Ron‐Ho Ni. The multiple‐grid procedure of Ni is also implemented. The flows are assumed to be homo‐enthalpic; the energy equation is eliminated and the static pressure is determined by the steady Bernoulli equation; a local time‐step technique is used. Inflow and outflow boundaries are treated with the compatibility relations method of ONERA. The efficiency of the multiple‐grid scheme is demonstrated by a two‐dimensional calculation (transonic flow past the NACA 12 aerofoil) and also by a three‐dimensional one (transonic lifting flow past the M6 wing). The third application presented shows the ability of the method to compute the vortical flow around a delta wing with leading‐edge separation. No condition is applied at the leading‐edge; the vortex sheets are captured in the same sense as shock waves. Results indicate that the Euler equations method is well suited for the prediction of flows with shock waves and contact discontinuities, the multiple‐grid procedure allowing a substantial reduction of the computational time.
Solution of shallow water equations for complex flow domains via boundary‐fitted co‐ordinates
Authors: Haeuser J. , Paap H.‐G. , Eppel D. , Mueller A. 
Published: August 2005

AbstractMany problems of applied oceanography and environmental science demand the solution of the momentum, mass and energy equations on physical domains having curving coastlines. Finite‐difference calculations representing the boundary as a step function may give inaccurate results near the coastline where simulation results are of greatest interest for numerous applications. This suggests the use of methods which are capable of handling the problem of boundary curvature.This paper presents computational results for the shallow water equations on a circular ring of constant depth, employing the concept of boundary fitted grids (BFG) for an accurate representation of the boundary. All calculations are performed on a rectangle in the transformed plane using a mesh with square grid spacing. Comparisons of the simulations of transient normal mode oscillations and analytic solutions are shown, demonstrating that this technique yields accurate results in situations (provided that there is a reasonable choice of grid) involving a curved boundary. The software developed allows application to any two‐dimensional area, regardless of the complexity of the geometry.Simulation runs were made with two co‐ordinate systems. For the first system, the grid point distribution was obtained from polar co‐ordinates. For the second one, grid point positions were calculated numerically, solving Poisson's equation. It was found that small variations in the metric coefficients do not deteriorate the accuracy of the simulation results.Moreover, comparisons of surface elevation and velocity components at grid points near the inner and outer radii obtained from an x−y Cartesian grid model with the BFG simulation were made. The former model produced inacccuracies at grid points near boundaries, and, owing to the large number of mesh points used to yield the necessary fine resolution, the computation time was found to be a factor of three higher.
The calculation of Green's functions in three dimensional hydrodynamic gravity wave problems
Authors: Pidcock M. K. 
Published: August 2005

AbstractWe have studied the problem of calculating Green's functions in three dimensional hydrodynamic gravity wave problems. A number of new expressions for these functions are presented for both finite and infinite depths. Various techniques for accelerating the convergence of some infinite series in these expressions are investigated and compared with the normal methods of evaluation. A significant improvement in the efficiency of the calculation is found using the results described in this paper.
Finite element analysis of density flow using the velocity correction method
Authors: Kawahara Mutsuto , Ohmiya Kiyotaka 
Published: August 2005

AbstractA finite element method is proposed for the analysis of density flow which is induced by a difference of density. The method employs the idea that density variation can be pursued by using markers distributed in the flow field. For the numerical integration scheme, the velocity correction method is successfully used, introducing a potential for the correction of velocity. This method is useful because one can use linear interpolation functions for velocity, pressure and potential based on the triangular finite element. The final equations can be formulated using the quasi‐explicit finite element method. A flume in a tank with sloping bottom has been analysed by the present method. The computed results show extremely good agreement with the experimental observations.
Inverse laminar boundary‐layer problems with assigned shear. The mechul function revisited
Authors: Kaufman K. C. , Hoffman G. H. 
Published: August 2005

AbstractAn inverse method is presented which accurately determines the pressure distribution for assigned wall shear in a two‐dimensional, laminar, incompressible boundary layer. The method reformulates the mechul function scheme of Cebeci and Keller to produce a stable solution in the marching direction and to increase accuracy in the normal direction. In the reformulation a modified pressure gradient parameter variation in the normal direction is used in conjunction with three‐point backward differences for streamwise derivatives and fourth‐order accurate splines for normal derivatives. The resulting spline‐finite difference equations are solved by Newton‐Raphson iteration together with partial pivoting. Numerical solutions are presented for self‐similar and non self‐similar flows and compared with published results.
Asymptotic finite element method for boundary value problems
Authors: Bar‐Yoseph Pinchas , Israeli Moshe 
Published: August 2005

AbstractThe Asymptotic Finite Element method for improvement of standard finite element solutions of perturbation equations by the addition of asymptotic corrections to the right hand side terms is presented. It is applied here to 1‐D and 2‐D diffusion–convection equations and to non‐linear similarity equations. Excellent results were obtained without the a priori use of special trial and test functions. Theoretical expectations were confirmed.
Improved averaging method for turbulent flow simulation. Part I: Theoretical development and application to Burgers' transport equation
Authors: Dakhoul Youssef M. , Bedford Keith W. 
Published: August 2005

AbstractThis is the first of two articles intended to develop, apply and verify a new method for averaging the momentum and mass transport equations for turbulence. The new method is based on Gaussian filtering in both the spatial and temporal domains. Application is made to the problem of momentum and scalar transport in a one‐dimensional transient Burgers' flow field. No actual calculations, with the averaged equations, are presented in this paper. However, an ‘exact’ solution of the one‐dimensional flow situation is presented as an economical tool for verifying the performance of the different turbulence models. In the second paper calculations are performed with the averaged one‐dimensional equations on coarse grids, and the results are compared to the exact or fully simulated data with a statistical verification procedure.
Unsteady compressible flow in long pipelines following a rupture
Authors: Flatt René 
Published: August 2005

AbstractThe unsteady frictional flow of a compressible fluid generated in a long pipeline after an accidental rupture is of considerable interest to the offshore gas industry. It answers several important questions concerning safety and pollution, e.g. the flow rate at the broken pipe end.Laboratory tests cannot simulate the rather complex phenomenon satisfactorily. The problem is highly non‐linear and no general analytical solution is yet known.In this study, based on computational fluid dynamics, the simplifying assumptions of isothermal and low Mach number flow often applied in the case of unsteady compressible flows in pipelines, have not been used.Owing to the choking condition (Ma=1) which prevails for some time at the broken end. and the cumulative effect of friction over the 145 km long pipeline, we obtain (∂p/∂x)t→−∞. This analytically established singularity leads to numerical difficulties which seriously affect the accuracy. For short tubes (such as shock tubes) this negative feature is much less severe. Special procedures were necessary to keep the accuracy within the chosen limit of 1 per cent.
A discussion and comparison of numerical techniques used to solve the Navier–Stokes and Euler equations
Authors: Connell S. D. , Stow P. 
Published: August 2005

AbstractThis paper is intended to provide some background to a number of widely used methods for solving the Navier–Stokes and Euler equations. The difference between coupled and uncoupled iterative schemes is discussed together with methods for solving the equations. Methods covered include time marching (both explicit and implicit), pressure correction and a Newton–Raphson technique. The relationship between the methods is illustrated.
Comparison between two finite‐difference schemes for computing the flow around a cylinder
Authors: Borthwick A. 
Published: August 2005

AbstractSeparated flow past a circular cylinder is computed from two finite‐difference Navier–Stokes models. Stream functions are calculated using a successive‐over‐relaxation (SOR) procedure. Alternating‐direction‐implicil (ADI) and ‘upwind’ directional difference explicit (DDE) numerical schemes for solving the vorticity‐transport equation are compared. The ‘upwind’ differencing technique produces artificial viscosity which damps the wake and suppresses vortex shedding. It is shown to be unreliable and so the ADI approach is recommended.
Treatment of non‐linearities in the numerical solution of the incompressible Navier–Stokes equations
Authors: Galpin P. F. , Raithby G. D. 
Published: August 2005

AbstractThe solution of the full non‐linear set of discrete fluid flow equations is usually obtained by solving a sequence of linear equations. The type of linearization used can significantly affect the rate of convergence of the sequence to the final solution. The first objective of the present study was to determine the extent to which a full Newton–Raphson linearization of all non‐linear terms enhances convergence relative to that obtained using the ‘standard’ incompressible flow linearization. A direct solution procedure was employed in this evaluation. It was found that the full linearization enhances convergence, especially when grid curvature effects are important.The direct solution of the linear set is uneconomical. The second objective of the paper was to show how the equations can be effectively solved by an iterative scheme, based on a coupled‐equation line solver, which implicitly retains all the inter‐equation couplings. This solution method was found to be competitive with the highly refined segregated solution methods that represent the current state‐of‐the‐art.