bluuebunny/crossref_metadata_2025_split huggingface dataset:
Petrov‐Galerkin methods on multiply connected domains for the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations
Authors: Tezduyar T. E. , Glowinski R. , Liou J. 
Published: August 2005

AbstractIn this paper we present streamline‐upwind/Petrov‐Galerkin finite element procedures for two‐dimensional fluid dynamics computations based on the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations. We address the difficulties associated with the convection term in the vorticity transport equation, lack of boundary condition for the vorticity at no‐slip boundaries, and determination of the value of the stream function at the internal boundaries for multiply connected domains. The proposed techniques, implemented within the framework of block‐iteration methods, have successfully been applied to various problems involving simply and multiply connected domains.
Simple high‐accuracy resolution program for convective modelling of discontinuities
Authors: Leonard B. P. 
Published: August 2005

AbstractFor steady multi‐dimensional convection, the QUICK scheme has several attractive properties. However, for highly convective simulation of step profiles, QUICK produces unphysical overshoots and a few oscillations, and this may cause serious problems in non‐linear flows. Fortunately, it is possible to modify the convective flux by writing the ‘normalized’ convected control‐volume face value as a function of the normalized adjacent upstream node value, developing criteria for monotonic resolution without sacrificing formal accuracy. This results in a non‐linear functional relationship between the normalized variables, whereas standard methods are all linear in this sense. The resulting Simple High‐Accuracy Resolution Program (SHARP) can be applied to steady multi‐dimensional flows containing thin shear or mixing layers, shock waves and other frontal phenomena. This represents a significant advance in modelling highly convective flows of engineering and geophysical importance. SHARP is based on an explicit, conservative, control‐volume flux formulation, equally applicable to one‐, two‐, or three‐dimensional elliptic, parabolic, hyperbolic or mixed‐flow regimes. Results are given for the bench‐mark purely convective oblique‐step test. The monotonic SHARP solutions are compared with the diffusive first‐order results and the non‐monotonic predictions of second‐ and third‐order upwinding.
Upwind basis finite elements for convection‐dominated problems
Authors: Steffler P. M. 
Published: August 2005

AbstractFinite elements using higher‐order basis functions in the spirit of the QUICK method for convection‐dominated fluid flow and transport problems are introduced and demonstrated. Instead of introducing new internal degrees of freedom, completeness is achieved by including functions based on nodal values exterior and upwind to the element domain. Applied with linear test functions to the weak statements for convection‐dominated problems, a family of Petrov–Galerkin finite elements is developed. Quadratic and cubic versions are demonstrated for the one‐dimensional convection–diffusion test problem. Elements of up to seventh degree are used for local solution refinement. The behaviour of these elements for one‐dimensional linear and non‐linear advection is investigated. A two‐dimensional quadratic upwind element is demonstrated in a streamfunction–vorticity formulation of the Navier–Stokes equations for a driven cavity flow test problem. With some minor reservations, these elements are recommended for further study and application.
A point implicit unstructured grid solver for the euler and Navier–Stokes equations
Authors: Thareja Rajiv R. , Stewart James R. , Hassan Obey , Morgan Ken , Peraire Jaime 
Published: August 2005

AbstractAn upwind finite element technique that uses cell‐centred quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive triangular grids. The approach is an extension to unstructured grids of the LAURA algorithm due to Gnoffo. A structured grid of quadrilaterals is laid out near a solid surface. For inviscid flows the method is stable at Courant numbers of over 100000. A first‐order basic scheme and a higher‐order flux‐corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view to simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are distinctly captured with a sequence of adaptively generated grids.
A Chebyshev collocation method for the Navier–Stokes equations with application to double‐diffusive convection
Authors: Ehrenstein U. , Peyret R. 
Published: August 2005

AbstractA Chebyshev collocation method for solving the unsteady two‐dimensional Navier–Stokes equations in vorticity–streamfunction variables is presented and discussed. The discretization in time is obtained through a class of semi‐implicit finite difference schemes. Thus at each time cycle the problem reduces to a Stokes‐type problem which is solved by means of the influence matrix technique leading to the solution of Helmholtz‐type equations with Dirichlet boundary conditions. Theoretical results on the stability of the method are given. Then a matrix diagonalization procedure for solving the algebraic system resulting from the Chebyshev collocation approximation of the Helmholtz equation is developed and its accuracy is tested. Numerical results are given for the Stokes and the Navier–Stokes equations. Finally the method is applied to a double‐diffusive convection problem concerning the stability of a fluid stratified by salinity and heated from below.
A finite element method for analysis of fluid flow, heat transfer and free interfaces in Czochralski crystal growth
Authors: Sackinger P. A. , Brown R. A. , Derby J. J. 
Published: August 2005

AbstractA finite element algorithm is presented for simultaneous calculation of the steady state, axisymmetric flows and the crystal, melt/crystal and melt/ambient interface shapes in the Czochralski technique for crystal growth from the melt. The analysis is based on mixed Lagrangian finite element approximations to the velocity, temperature and pressure fields and isoparametric approximations to the interface shape. Galerkin's method is used to reduce the problem to a non‐linear algebraic set, which is solved by Newton's method. Sample solutions are reported for the thermophysical properties appropriate for silicon, a low‐Prandtl‐number semiconductor, and for GGG, a high–Prandtl–number oxide material. The algorithm is capable of computing solutions for both materials at realistic values of the Grashof number, and the calculations are convergent with mesh refinement. Flow transitions and interface shapes are calculated as a function of increasing flow intensity and compared for the two material systems. The flow pattern near the melt/gas/crystal tri‐junction has the asymptotic form predicted by an inertialess analysis assuming the meniscus and solidification interfaces are fixed.
An efficient upwind/relaxation algorithm for the Euler and Navier–Stokes equations
Authors: Zha Ge‐Cheng , Liu Dao‐Zhi , Ma Tie‐You 
Published: August 2005

AbstractAn efficient Euler and full Navier–Stokes solver based on a flux splitting scheme is presented. The original Van Leer flux vector splitting form is extended to arbitrary body‐fitted co‐ordinates in the physical domain so that it can be used with a finite volume scheme. The block matrix is inverted by Gauss–Seidel iteration. It is verified that the often used reflection boundary condition will produce incorrect flux crossing the wall and cause too large numerical dissipation if flux vector splitting is used. To remove such errors, an appropriate treatment of wall boundary conditions is suggested. Inviscid and viscous steady transonic internal flows are analysed, including the case of shock‐induced boundary layer separation.
Galerkin finite element simulation of convection driven by rotation and gravitation
Authors: Ladeinde Foluso , Torrance K. E. 
Published: August 2005

AbstractThe performance of the Galerkin finite element method when applied to time‐dependent convection involving rotation, self‐gravitation and the normal gravity field in a horizontal cylinder is discussed in this paper. The governing equations, the parameters of the problem and our implementation of the numerical schemes are presented. The accuracy, spatial scale of resolution, flexibility and robustness of the resulting code show the element method as a valuable tool for research in this area or in related problems in astrophysical fluid dynamics. The numerical difficulties in large‐amplitude flows are associated with an error‐control scheme for time integration and the ‘short‐time’ wiggles in transient Dirichlet problems. Coarse grids give the correct qualitative picture in most simulations, but the type of solution at short time (and hence grid refinement) presumably resolves the degeneracy in the azimuthal orientation of convection cells in flows driven by self‐gravitation and (perhaps) centrifugal buoyancy. The final state in transient flows is a motionless isothermal fluid. However, residual motions can be nullified only in the limit of zero grid size in flows driven by centrifugal buoyancy (self‐gravitation), while a fairly coarse grid is sufficient for this purpose in normal gravity‐driven flows.
Iterative stabilization of the bilinear velocity–constant pressure element
Authors: Fortin M. , Boivin S. 
Published: August 2005

AbstractSome finite element approximations of incompressible flows, such as those obtained with the bilinear velocity–constant pressure element (Q1−P0), are well known to be unstable in pressure while providing reasonable results for the velocity.We shall see that there exists a subspace of piecewise constant pressures that leads to a stable approximation. The main drawback associated with this subspace is the necessity of assembling groups of elements, the so‐called ‘macro‐elements’, which increases dramatically the bandwidth of the system.We study a variant of Uzawa's method which enables us to work in the desired subspace without increasing the bandwidth of the system. Numerical results show that this method is efficient and can be made to work at a low extra cost. The method can easily be generalized to other problems and is very attractive in three‐dimensional cases.
A control volume finite difference method for buoyant flow in three‐dimensional curvilinear non‐orthogonal co‐ordinates
Authors: Yang H. Q. , Yang K. T. , Lloyd J. R. 
Published: August 2005

AbstractThis paper presents a control‐volume‐based finite difference method in non‐orthogonal curvilinear coordinates on a local basis in which the vectors and tensors are all based on the general curvilinear coordinates for buoyant flow calculations in arbitrary three‐dimensional geometries. The governing equations are transformed from Cartesian co‐ordinates into generalized curvilinear co‐ordinates. After integrating the set of equations for the control volumes, the finite difference equations are then formulated by a proper treatment of the heat flux and stress tensors and by incorporating the QUICK scheme for the convective terms. The solution procedure then follows the one for three‐dimensional Cartesian co‐ordinates.Examples are given in problems of natural convection in such three‐dimensional enclosures as parallelepiped enclosures and horizontal closed cylinders with differentially heated ends. In the latter case, important applications have been found in crystal growth by means of chemical vapour deposition in a cylindrical ampoule, in which uniform heat fluxes along the two ends are required in order to produce high‐quality crystals. Special attention is given to the insertion of baffles in the cylinder to improve the recirculating flow patterns near the two ends.
Self‐adaptive hierarchic finite element solution of the one‐dimensional unsaturated flow equation
Authors: Abriola Linda M. , Lang John R. 
Published: August 2005

AbstractThe advantages associated with the use of self‐adaptive methods for the solution of problems which require the prediction of a frontal position in time are well known. In this paper a self‐adaptive finite element solution for the non‐linear unsaturated flow equation is developed using hierarchic p‐version enrichment of the interpolating space. Additional computational advantages are demonstrated for an iteration scheme in which iterations after enrichment are performed only over a subdomain. Numerical solutions are presented for a one‐dimensional infiltration scenario.
High‐order methods for differential equations with large first‐derivative terms
Authors: Dekema Sandra Kay , Schultz David H. 
Published: August 2005

AbstractA method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non‐linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one‐dimensional case an approximating equation is developed using just three points. The method first presented is a fourth‐order approximation but is extended to become a higher‐order method. Results are included for the fourth‐, sixth‐, eighth‐ and tenth‐order methods.The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie.The method of this paper was also tested on the solution of some non‐linear diffusion equations with concentration‐dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two‐dimensional problems.The method developed in this paper is accurate, easy to use and can be generalized to other problems.
On the reversed flow and oscillating wake in an asymmetrically heated channel
Authors: Chang T. S. , Lin T. F. 
Published: August 2005

AbstractThe detailed processes of flow reversal in a buoyancy‐induced flow through a one‐side‐heated vertical channel of finite height were simulated numerically. It is of interest to note that the wake above the heated plate is oscillatory at high Rayleigh number and there exists a minimum in the transient variation of the average Nusselt number. Additionally, the predicted steady average Nusselt number and induced flow rate are correlated by empirical equations.
Numerical simulation of three‐dimensional transonic flows
Authors: Sahu Jubaraj , Steger Joseph L. 
Published: August 2005

AbstractThe three‐dimensional flow over a projectile has been computed using an implicit, approximately factored, partially flux‐split algorithm. A simple composite grid scheme has been developed in which a single grid is partitioned into a series of smaller grids for applications which require an external large memory device such as the SSD of the CRAY X‐MP/48 or multi‐tasking. The accuracy and stability of the composite grid scheme have been tested by numerically simulating the flow over an ellipsoid at an angle of attack and comparing the solution with a single‐grid solution. The flow field over a projectile at M = 0·96, 1·1 and 4° angle of attack has been computed using a fine grid and compared with experiment.
An application of the vorticity–vector potential method to laminar cube flow
Authors: Raul Robin , Bernard Peter S. , Buckley Frank T. 
Published: August 2005

AbstractThree‐dimensional incompressible laminar flow around a cube is investigated using the vorticity–vector potential formulation of the equations of motion. Numerical solutions to á semi‐implicit finite difference approximation to the vorticity transport equation coupled to discrete Poisson equations for the scalar and vector potentials are obtained using an eight‐colour SOR algorithm. Calculations are done at a range of Reynolds numbers from 10 to 100. The predicted drag and other flow characteristics are found to agree well with experimental results, including those from a cube drop experiment performed for the present study.
Solving numerically the Navier–Stokes equations on parallel systems
Authors: Lin Avi 
Published: August 2005

AbstractA new general approach for numerically computing flow fields on parallel computing environments is presented, discussed and analysed. The hierarchy presented here is based on a parallel split of operators. A portion of the theory is presented together with its application to two‐ and three‐dimensional flows. This strategy is applied to a two‐dimensional problem for which a specific parallel split, called a parabolized split, is given. The parallel algorithm that results from this split is analysed, leading to reasonably good parallel efficiency, which is close to 50%. Actual experiments lead to similar conclusions. This parallel strategy can also be used together with other parallel computing algorithms, such as domain decomposition, to give an optimal‐type parallel algorithm for the Navier–Stokes equations.
Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulation
Authors: Howard D. , Connolley W. M. , Rollett J. S. 
Published: August 2005

AbstractA series of numerical experiments on the Cray XMP/48 and on the Cray 2 investigate the robustness and economy of direct and unsymmetric conjugate gradient (CG) type methods for the solution of matrix systems arising from a 3D FEM discretization of fluid flow problems. Computations on a Boussinesq flow model problem with either ILU preconditioned or unpreconditioned unsymmetric CG methods are presented. Such experiments seem to indicate that the unpreconditioned BICG method is robust for moderately non‐linear incompressible Navier–Stokes FEM discretizations and that the ILU preconditioned BICG method is very robust and more economic than an unsymmetric frontal solver when the generous memory of the Cray 2 is exploited to store both the matrix and its preconditioner. We cover some of the programming aspects of direct and iterative methods on a supercomputer and find that direct methods have advantages: the crucial CPU‐consuming area of code is compact but overwhelming, and its percentage of total CPU usage is independent of the spectral properties of the matrix involved. An optimal implementation of the unsymmetric CG method is more difficult because its work is related to the spectral distribution of the matrix considered and because there is no single portion of the code that overwhelmingly dominates the CPU usuage.
On the accuracy of finite difference and modal methods for computing tidal and wind wave current profiles
Authors: Davies A. M. 
Published: August 2005

AbstractThis paper deals with the comparative accuracy of using finite difference grids or a modal representation through the vertical in modelling tidally or wind wave induced current profiles.A point model is used in the vertical, with a no‐slip condition at the sea bed. In the finite difference approach the high‐shear bottom layer is resolved using either a regular grid on a logarithmic or log‐linear transformed co‐ordinate or an irregular grid, varying in such a manner as to retain second‐order accuracy. The accuracy of these various grid schemes is considered in detail.The relative merits of using either the Crank‐Nicolson or Dufort‐Frankel time integration methods are considered; in the case of a fine grid in a high‐viscosity region, some numerical problems are found with the Dufort‐Frankel method.An alternative approach to using a finite difference grid in the vertical, namely a modal (spectral) method, is described. The form of the modes is such that they can accurately resolve the high‐shear bottom boundary layer.Calculations show that the thickness of the bottom boundary layer in relation to the total water depth is important in determining the choice of grid transform and rates of convergence of solutions using finite difference or modal methods. However, for the majority of problems the modal solution is numerically attractive owing to its computational efficiency and the ease with which solution algorithms based upon it can be coded in vectorizable form suitable for the new generation of vector computers.The influence of viscosity profile, its time variation and water depth upon tidally induced or wave induced currents is considered. Calculations suggest that near‐bed measurements of tidal flow in shallow water together with associated modelling would enable appropriate formulations of eddy viscosity to be determined. Similar measurements, though using a laboratory flume, would be appropriate for wind wave problems.
Finite difference solution of a Newtonian jet swell problem
Authors: Liu Ta‐Jo , Yu Tsai‐An , Cheng Shu‐Hue 
Published: August 2005

AbstractA finite difference technique has been developed to study the Newtonian jet swell problem. The streamfunction and vorticity were used as dependent variables to describe the jet flow. The boundary‐fitted co‐ordinate transformation method was adopted to map the flow geometry into a rectangular domain. The standard finite difference method was then applied for solving the flow equations. The location of the jet free surface was updated by the kinematic boundary condition, and an adjustable parameter was included in the free‐surface iteration. We could obtain numerical solutions for the Reynolds number as high as 100, and the differences between the present study and previous finite element simulations on the jet swell ratio are less than 5%.
Assessment of TVD schemes for inviscid and turbulent flow computation
Authors: Chen Ming‐Hsiung , Hsu Chen‐Chi , Shyy Wei 
Published: August 2005

AbstractA systematic study has been conducted to assess the performance of the TVD schemes for practical flow computation. The viewpoint adopted here is to treat the TVD schemes as a combination of the standard central difference scheme with numerical dissipation terms. The controlled amount of numerical dissipation modifies the computed fluxes to ensure that the solution is oscillation‐free. Four variants of TVD schemes, two with upwind dissipation terms and two with symmetric dissipation terms, have been studied and compared with the conventional Beam‐Warming scheme for inviscid and turbulent axisymmetric flow computations. The results obtained show that all four variants can accurately resolve the shock and flow profiles with fewer grid points than the Beam‐Warming scheme. The convergence rates of the TVD schemes are also substantially superior to that of the Beam‐Warming scheme. The combination of high accuracy, good robustness and improved computational efficiency offered by the TVD schemes makes them attractive for computing high‐speed flow with shocks. In terms of the relative performances it is found that the symmetric schemes converge slightly faster but that the upwind schemes are less sensitive to the number of grid points being employed.