bluuebunny/crossref_metadata_2025_split huggingface dataset:
Comparison of several open boundary numerical treatments for laminar recirculating flows
Authors: Kobayashi M. H. , Pereira J. C. F. , Sousa J. M. M. 
Published: August 2005

AbstractSeveral open boundary conditions (OBCs) are compared and evaluated in the framework of the SIMPLE algorithm using staggered and non‐staggered grid systems. The benchmark laminar flow test cases used for the OBC evaluation are Poiseuille‐Benard flow in a channel and stratified backward‐facing step flow. The investigated OBCs are linear explicit step space extrapolation, Orlanski's monochromatic wave, and pressure extrapolation. Orlanski's and pressure extrapolation open boundary treatment for unsteady and steady flows, respectively, yield little reflection and has proved to be adequate for engineering calculations.
Some special purpose preconditioners for conjugate gradient‐like methods applied to CFD
Authors: Strigberger J. , Baruzzi G. , Habashi W. , Fortin M. 
Published: August 2005

AbstractStandard preconditioners such as incomplete LU decomposition perform well when used with conjugate gradient‐like iterative solvers such as GMRES for the solution of elliptic problems. However, efficient computation of convection‐dominated problems requires, in general, the use of preconditioners tuned to the particular class of fluid‐flow problems at hand. This paper presents three such preconditioners. The first is applied to the finite element computation of inviscid (Euler equations) transonic and supersonic flows with shocks and uses incomplete LU decomposition applied to a matrix with extra artificial dissipation. The second preconditioner is applied to the finite difference computation of unsteady incompressible viscous flow; it uses incomplete LU decomposition applied to a matrix to which a pseudo‐compressible term has been added. The third method and application are similar to the second, only the LU decomposition is replaced by Beam‐warming approximate factorization. In all cases, the results are in very good agreement with other published results and the new algorithms are found to be competitive with others; it is anticipated that the efficiency and robustness of conjugate‐gradient‐like methods will render them the method of choice as the difficulty of the problems that they are applied to is increased.
A decoupling numerical method for fluid flow
Authors: Liu Shijie , Masliyah Jacob H. 
Published: August 2005

AbstractA first‐order non‐conforming numerical methodology, Separation method, for fluid flow problems with a 3‐point exponential interpolation scheme has been developed. The flow problem is decoupled into multiple one‐dimensional subproblems and assembled to form the solutions. A fully staggered grid and a conservational domain centred at the node of interest make the decoupling scheme first‐order‐accurate. The discretization of each one‐dimensional subproblem is based on a 3‐point interpolation function and a conservational domain centred at the node of interest. The proposed scheme gives a guaranteed first‐order accuracy. It is shown that the traditional upwind (or exponentially weighted upstream) scheme is less than first‐order‐accurate. The pressure is decoupled from the velocity field using the pressure correction method of SIMPLE. Thomas algorithm (tri‐diagonal solver) is used to solve the algebraic equations iteratively. The numerical advantage of the proposed scheme is tested for laminar fluid flows in a torus and in a square‐driven cavity. The convergence rates are compared with the traditional schemes for the square‐driven cavity problem. Good behaviour of the proposed scheme is ascertained.
Numerical simulation of an isolated vortex and shear flow interaction
Authors: Antropov I. V. 
Published: August 2005

AbstractA numerical solution for the Navier‐Stokes equations in the unbounded region is considered for the interaction of an isolated vortex and shear flow. A Chebyshey collocation method in space and finite‐difference method for temporal discretization are used. The results of the numerical experiments for the interaction are discussed. It is shown that shear flow can both increase and decrease the vortex dissipation rate.
Numerical analysis of wall pressure and heat flux fluctuations in shock‐turbulent‐boundary‐layer interaction
Authors: Mehta R. C. , Sastri V. M. K. 
Published: August 2005

AbstractThe unsteady, compressible, Reynolds‐averaged Navier‐Stokes equations are solved numerically for an oblique shock‐wave‐induced turbulent boundary layer sepration. For the freestream Mach number 6 and the freestream Reynolds number 66·1 × 106 m−1, a time‐dependent computation is performed, using MacCormack's explicit‐implicit finite difference method with 82 × 42 grid points. A two‐layer eddy viscosity turbulence model is employed in conjunction with a relaxation modification. Comparisons of the mean wall pressure and the mean heat transfer coefficient with the available experimental results are made and the evaluation of unsteady data for surface pressure and heat flux fluctuations is presented. It is found that the fluctuations in heat flux have qualitatively the same features as those of wall pressure but are different quantitatively.
On the accuracy and efficiency of CFD methods in real gas hypersonics
Authors: Drikakis D. , Tsangaris S. 
Published: August 2005

AbstractA study of viscous and inviscid hypersonic flows using generalized upwind methods is presented. A new family of hybrid flux‐splitting methods is examined for hypersonic flows. The hybrid method is constructed by the superposition of the flux‐vector‐splitting (FVS) method and second‐order artificial dissipation in the regions of strong shock waves. The conservative variables on the cell faces are calculated by an upwind extrapolation scheme to third‐order accuracy. A second‐order‐accurate scheme is used for the discretization of the viscous terms. The solution of the system of equations is achieved by an implicit unfactored method. In order to reduce the computational time, a local adaptive mesh solution (LAMS) method is proposed. The LAMS method combines the mesh‐sequencing technique and local solution of the equations. The local solution of either the Euler or the NAVIER‐STOKES equations is applied for the region of the flow field where numerical disturbances die out slowly. Validation of the Euler and NAVIER‐STOKES codes is obtained for hypersonic flows around blunt bodies. Real gas effects are introduced via a generalized equation of state.
Treatment of vortex sheets for the transonic full‐potential equation
Authors: Dang T. Q. 
Published: August 2005

AbstractThis paper summarizes a combined analytical‐computational technique which models vortex sheets in transonic potential‐flow methods. In this approach, the inviscid nature of discontinuities across vortex sheets is preserved by employing the step function to remove singularities at these surfaces. The location and strength of the vortex sheets are determined by satisfying the flow‐tangency boundary condition and the vorticity transport equation. The theory is formulated for the general three‐dimensional case, but its application is confined to the problem of computing slipstreams behind propellers with free‐vortex blading in axisymmetric flows.
Solution of free‐boundary problems using finite‐element/Newton methods and locally refined grids: Application to analysis of solidification microstructure
Authors: Tsiveriotis K. , Brown R. A. 
Published: August 2005

AbstractA new method is presented for the solution of free‐boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non‐conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free‐boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.
Numerical solution of axisymmetric cavity flows using the boundary element method
Authors: Wrobel L. C. 
Published: August 2005

AbstractThis paper presents a formulation of the boundary element method (BEM) for solution of axisymmetric cavity flow problems. The governing equation is written in terms of Stokes' stream function, requiring a new fundamental solution to be found. The iterative procedure for adjusting the free‐surface position is similar to that used for planar cavity flows. Numerical results are compared with finite difference and finite element solutions, showing the robustness of the BEM model.
New numerical method for partial differential equations. 1: Application to the diffusion equation
Authors: Hatzikonstantinou P. 
Published: August 2005

AbstractIn this paper a new, highly accurate method called PH is presented for the numerical integration of partial differential equations. The method is applied for the solution of the one‐dimensional diffusion equation. Upon integrating the equation within a subdomain of space and time using the prismoidal approximation, a three‐point implicit scheme is obtained with a truncation error of order O(k4, h6), where k and h represent the time and space steps respectively. The method is stable under the condition s = αk/h2 ⩽ S(δ), where the function S(δ) increases as the parameter δ decreases from 1/12 to negative values. In practice the method behaves as unconditionally stable upon choosing an appropriate value for δ. A new formula is also adopted for the implementation of a Neumann boundary condition, introducing a truncation error of order O(h4). Numerical solutions are obtained incorporating Dirichlet and Neumann boundary conditions. The results prove that our method is far more accurate than any other‐implicit or explicit method.
Optimal estimation of eddy viscosity for a quasi‐three‐dimensional numerical tidal and storm surge model
Authors: Lardner R. W. , Das S. K. 
Published: August 2005

AbstractIt is shown that the eddy viscosity profile in a quasi‐three‐dimensional numerical tidal and storm surge model can be estimated by assimilation of velocity data from one or more current meters located on the same vertical line. The computational model used is a simplified version of the so‐called vertical/horizontal splitting algorithm proposed by Lardner and Cekirge. We have estimated eddy viscosity both as a constant and as a variable parameter. The numerical scheme consists of a two‐level leapfrog method to solve the depth‐averaged equations and a generalized Crank‐Nicolson scheme to compute the vertical profile of the velocity field. The cost functional in the adjoint scheme consists of two terms. The first term is a certain norm of the difference between computed and observed velocity data and the second term measures the total variation in the eddy viscosity function. The latter term is not needed when the data are exact for the model but is necessary to smooth out the instabilities associated with ‘noisy’ data. It is shown that a satisfactory minimization can be accomplished using either the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) quasi‐Newton algorithm or Nash's truncated Newton algorithm. Very effective estimation of eddy viscosity profiles is shown to be achieved even when the amount of data is quite small.
Calculation of separated flow around multi‐element aerofoils using conformal mapping
Authors: Cao Jianfa 
Published: August 2005

AbstractA method is presented to calculate the low‐speed incompressible separated flow around multi‐element aerofoils. The geometries of multi‐element aerofoils in the physical plane are completely arbitrary and are transformed into multiple circles in the computational plane by a conformal mapping technique. Jacob's model, which distributes sources on the separated surfaces of multi‐element aerofoils to simulate the effects of separation, is adopted here. The position of the separated point and the pressure on the surfaces of multi‐element aerofoils are calculated by iteratively coupling the potential flow and boundary layer. The effects of the boundary layer are simulated by modification of the boundary condition. All iterative procedures converge rapidly as a result of using the fast Fourier transform (FFT) technique.
Aspects of the transpiration model for aerofoil design
Authors: Yiu K. F. C. , Stow P. 
Published: August 2005

AbstractTranspiration is a technique in which extra non‐physical normal flows are created on an aerofoil surface in order to form a new streamline pattern such that the surface streamlines no longer follow the aerofoil surface under inviscid flow. The transpiration model is an important technique adopted in aerofoil design either to avoid mesh regeneration when aerofoil profile co‐ordinates are adjusted or to find shape corrections in inverse design methods. A first‐order approximation (with respect to the normal streamline displacement) to the transpiration model is commonly adopted; it is shown that this can be a poor approximation especially in regions of high curvature. In this paper more accurate approximations are developed to address this problem and improve the accuracy.
On estimating pressure build‐up in severely accelerated, shocked flow
Authors: Cooke Charlie H. 
Published: August 2005

AbstractA new approach to the calculation of the high pressures characterizing the flow field in front of a piston undergoing severe acceleration over the short term is presented. In contrast with previous approaches where the computational domain is altered but which stop short of transforming velocities, here the problem is solved in an accelerating non‐Euclidean co‐ordinate system where the piston is stationary. The method is applied to a study of the problem of premature sabot separation. Through use of Harten's second‐order‐accurate TVD scheme, flow simulations are performed for both 1D and 3D axisymmetric geometries. The simple 1D model gives pressure profiles surprisingly close to those of the more physical 3D model.
A second‐order radiation boundary condition for the shallow water wave equations on two‐dimensional unstructured finite element grids
Authors: Johnsen Matthias , Lynch Daniel R. 
Published: August 2005

AbstractA second‐order radiation boundary condition (RBC) is derived for 2D shallow water problems posed in ‘wave equation’ form and is implemented within the Galerkin finite element framework. The RBC is derived by matching the dispersion relation for the interior wave equation with an approximate solution to the exterior problem for outgoing waves. The matching is correct to second order, accounting for curvature of the wave front and the geometry. Implementation is achieved by using the RBC as an evolution equation for the normal gradient on the boundary, coupled through the natural boundary integral of the Galerkin interior problem. The formulation is easily implemented on non‐straight, unstructured meshes of simple elements. Test cases show fidelity to solutions obtained on extended meshes and improvement relative to simpler first‐order RBCs.
A vertex‐centred finite volume method with shock detection
Authors: Crumpton P. I. , Shaw G. J. 
Published: August 2005

AbstractThis paper introduces a vertex‐centred finite volume method for compressible viscous flow incorporating a new shock detection procedure. The discretization is designed to be robust and accurate on the highly stretched and curved meshes necessary for resolving turbulent boundary layers around the leading edge of an aerofoil. Details of the method are described for two‐dimensional problems and the natural extension of three‐dimensional multiblock meshes is discussed. The shock detection procedure is used to limit the range of the shock‐capturing dissipation specifically to regions containing shocks. For transonic turbulent flow this is shown to improve the boundary layer representation significantly.
Analysis of periodic 3D viscous flows using a quadratic discrete Galerkin boundary element method
Authors: Chan Chiu Y. , Beris Antony N. , Advani Suresh G. 
Published: August 2005

AbstractA discrete Galerkin boundary element technique with a quadratic approximatión of the variables was developed to simulate the three‐dimensional (3D) viscous flow established in periodic assemblages of particles in suspensions and within a periodic porous medium. The Batchelor's unit‐cell approach is used. The Galerkin formulation effectively handles the discontinuity in the traction arising in flow boundaries with edges or corners, such as the unit cell in this case. For an ellipsoidal dilute suspension over the range of aspect ratio studied (1 to 54), the numerical solutions of the rotational velocity of the particles and the viscosity correction were found to agree with the analytic values within 0.2% and 2% respectively, even with coarse meshes. In a suspension of cylindrical particles the calculated period of rotation agreed with the experimental data. However, Burgers' predictions for the correction to the suspension viscosity were found to be 30% too low and therefore the concept of the equivalent ellipsoidal ratio is judged to be inadequate. For pressure‐driven flow through a fixed bed of fibres, the prediction on the permeability was shown to deviate by as much as 10% from the value calculated based on approximate permeability additivity rules using the corresponding values for planar flow past a periodic array of parallel cylinders. These applications show the versatility of the technique for studying viscous flows in complicated 3D geometries.
On the group velocity of symmetric and upwind numerical schemes
Authors: Karni Smadar 
Published: August 2005

AbstractDissipative numerical approximations to the linear advection equation are considered with respect to their behaviour in the limit of weak dissipation. The context is wave propagation under typical far‐field conditions where grids are highly stretched and waves are underresolved. Three classes of schemes are analysed: explicit two‐level (i) symmetric and (ii) upwind schemes of optimal accuracy are considered as well as (iii) (symmetric) Runge‐Kutta schemes. In the far‐field the dissipation of all schemes diminishes. Group speeds of high‐frequency modes assume the incorrect sign and may admit ‘backward’ wave propagation if waves are not damped. A fundamental difference arises between the symmetric and upwind cases owing to the different rates at which the dissipation diminishes. In the upwind case, while the amount of damping per time step diminishes, the accumulative damping remains exponential in time. In the symmetric case the accumulative damping tends to unity, yielding in practice non‐dissipative schemes. In this light, parasitic modes constitute much less of a problem in the upwind case than in the symmetric case. Numerical tests confirm these findings.
Large‐scale computational fluid dynamics by the finite element method
Authors: Habashi W. G. , Robichaud M. , Nguyen V.‐N. , Ghaly W. S. , Fortin M. , Liu J. W. H. 
Published: August 2005

AbstractSolution methods are presented for the large systems of linear equations resulting from the implicit, coupled solution of the Navier‐Stokes equations in three dimensions. Two classes of methods for such solution have been studied: direct and iterative methods.For direct methods, sparse matrix algorithms have been investigated and a Gauss elimination, optimized for vector‐parallel processing, has been developed. Sparse matrix results indicate that reordering algorithms deteriorate for rectangular, i.e. M × M × N, grids in three dimensions as N gets larger than M. A new local nested dissection reordering scheme that does not suffer from these difficulties, at least in two dimensions, is presented. The vector‐parallel Gauss elimination is very efficient for processing on today's supercomputers, achieving execution rates exceeding 2.3 Gflops the Cray YMP‐8 and 9.2 Gflops on the NEC on SX3.For iterative methods, two approaches are developed. First, conjugate‐gradient‐like methods are studied and good results are achieved with a preconditioned conjugate gradient squared algorithm. Convergence of such a method being sensitive to the preconditioning, a hybrid viscosity method is adopted whereby the preconditioner has an artificial viscosity that is gradually lowered, but frozen at a level higher than the dissipation introduced in the physical equations. The second approach is a domain decomposition one in which overlapping domain and side‐by‐side methods are tested. For the latter, a Lagrange multiplier technique achieves reasonable rates of convergence.
Numerical boundary conditions for unsteady transonic flow calculations
Authors: Jiang Hong , Lee B. H. K. , Wong Yau Shu 
Published: August 2005

AbstractIn calculations of transonic flows it is necessary to limit the domain of computation to a size that is manageable by computers. At the boundary of the computational domain, boundary conditions are required to ensure a unique solution. Since wave solutions exist in the unsteady transonic flow field, incorrect boundary conditions may result in spurious reflections from the computational boundary. This may introduce errors into the solution. To prevent the spurious reflections, absorbing boundary conditions are often used on the computational boundary. In this paper we describe a method to derive absorbing boudary conditions for transonic calculations. We demonstrate both theoretically and numerically that the use of the absorbing boundary conditions will reduce the spurious reflections in the calculation.
A multiblock Navier–Stokes algorithm using equal‐order quadratic finite elements
Authors: Hill D. L. , Baskharone E. A. 
Published: August 2005

AbstractA new multiblock pressure‐based finite element algorithm has been developed. This methodology implements quadratic interpolation for both the elemental velocity and pressure fields. A direct streamline upwinding scheme previously developedby the authors is used to model the non‐linear inertia effects. Details of the algorithm and its multiblock foundation are provided along with validating test cases. The results presented clearly demonstrate the accuracy of this new approach and the differences in the pressure field for an element using quadratic versus the traditional bi linear approximation of the pressure field.
A composite multigrid method for calculating unsteady incompressible flows in geometrically complex domains
Authors: Zang Y. , Street R. L. 
Published: August 2005

AbstractA time‐accurate, finite volume method for solving the three‐dimensional, incompressible Navier‐Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non‐orthogonal curvilinear co‐ordinate system and are discretized on a non‐staggered grid. A semi‐implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter‐grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well‐posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is secondorder‐accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency.