bluuebunny/crossref_metadata_2025_split huggingface dataset:
An efficient shock‐capturing algorithm for compressible flows in a duct of variable cross‐section
Authors: Glaister P. 
Published: August 2005

AbstractA numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co‐ordinate. This includes flow in a duct of variable cross‐section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two‐dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two‐dimensional problem with no sources.
Modelling the non‐linear interaction of wind and tide: Its influence on current profiles
Authors: Davies A. M. , Lawrence J. 
Published: August 2005

AbstractA single‐point model in the vertical is used to examine the coupling between tidal currents and wind‐driven flows in shallow near‐coastal regions. Calculations using both a linear slip and a no‐slip condition at the sea bed clearly show that coupling between tidal and wind‐driven currents cannot occur in a linear model with a time‐independent eddy viscosity. However with a physically more realistic time‐varying viscosity related to the flow field, coupling does occur, the magnitude of this non‐linear interaction depending upon the change in eddy viscosity over a tidal cycle and the intensity of shear in the vertical. A point model in the vertical with flow induced by an oscillatory pressure gradient and an additional constant wind stress is used to examine the influence of viscosity parametrization and water depth upon this coupling.The solution in the vertical is accomplished using both a functional approach and a finite difference method. Some conclusions as to the relative merits of these approaches, particularly the use of a transformed grid in the case of high‐shear surface and bed boundary layers, are made in the paper.
A new general‐purpose least‐squares finite element model for steady incompressible low‐viscosity laminar flow using isoparametric C1‐continuous Hermite elements
Authors: Nassehi V. , Petera J. 
Published: August 2005

AbstractThis paper deals with a critical evaluation of various finite element models for low‐viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least‐squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low‐viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least‐squares method in conjunction with C1‐continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping of C1 Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least‐squares method in combination with isoparmetric Hermite elements offers a new general‐purpose modelling technique which can accurately simulate all types of low‐viscosity incompressible laminar flow in complex domains.
Numerical investigations of radial jet reattachment flows
Authors: Laschefski H. , Braess D. , Haneke H. , Mitra N. K. 
Published: August 2005

AbstractA finite volume computational scheme to solve the Navier‐Stokes equations for the laminar flow fields of partially enclosed axial and radial jets impinging on a flat plate has been devised and tested. This scheme is based on the SIMPLEC technique. However, because of the backflow at the ‘outflow’ boundary, the SIMPLEC pressure correction technique has to be modified. The need for this modification, necessitated by the convergence failure, showed the ‘hidden’ pressure boundary condition of SIMPLE‐type techniques. Test computations with the present scheme for flows in a channel with a built‐in cylinder show that the location of the exit boundary affects very slightly the separated flow behind the cylinder. Computed Squire jet flows compare quite well with the available analytical solution. Finally, impinging radial jets have been computed for different Reynolds numbers. The results show the critical Reynolds number below which a steady solution is obtained and above which periodic and eventually chaotic flows result.
Implicit schemes for unsteady Euler equations on triangular meshes
Authors: Sens A. S. , Mortchelewicz G. D. 
Published: August 2005

AbstractAn implicit finite element method is presented for the solution of steady and unsteady inviscid compressible flows on triangular meshes under transonic conditions. The method involves a first‐order time‐stepping scheme with a finite element discretization that reduces to central differencing on a rectangular mesh. On a solid wall the slip condition is prescribed and the pressure is obtained from an approximation of the normal momentum equation. With this solver no artificial viscosity is added to ensure the success of the calculation. Numerical examples are given for steady and unsteady cases.
A net inflow method for incompressible viscous flow with moving free surface
Authors: Wang S. P. , Wang K. K. 
Published: August 2005

AbstractA new finite element procedure called the net inflow method has been developed to simulate time‐dependent incompressible viscous flow including moving free surfaces and inertial effects. As a fixed mesh approach with triangular element, the net inflow method can be used to analyse the free surface flow in both regular and irregular domains. Most of the empty elements are excluded from the computational domain, which is adjusted successively to cover the entire region occupied by the liquid. The volume of liquid in a control volume is updated by integrating the net inflow of liquid during each iteration. No additional kinetic equation or material marker needs to be considered. The pressure on the free surface and in the liquid region can be solved explicitly with the continuity equation or implicitly by using the penalty function method. The radial planar free surface flow near a 2D point source and the dam‐breaking problem on either a dry bed or a still liquid have been analysed and presented in this paper. The predictions agree very well with available analytical solutions, experimental measurements and/or other numerical results.
Finite volume methods for laminar and turbulent flows using a penalty function approach
Authors: Simoneau J. , Pollard A. 
Published: August 2005

AbstractA penalty function, finite volume method is described for two‐dimensional laminar and turbulent flows. Turbulence is modelled using the k‐ϵ model. The governing equations are discretized and the resulting algebraic equations are solved using both sequential and coupled methods. The performance of these methods is gauged with reference to a tuned SIMPLE‐C algorithm. Flows considered are a square cavity with a sliding top, a plane channel flow, a plane jet impingement and a plane channel with a sudden expansion. A sequential method is employed, which uses a variety of dicretization practices, but is found to be extremely slow to converge; a coupled method, evaluated using a variety of matrix solvers, converges rapidly but, relative to the sequential approach, requires larger memory.
A multigrid method for predicting periodically fully developed flow
Authors: Bai L. , Mitra N. K. , Fiebig M. , Kost A. 
Published: August 2005

AbstractThe use of multigrid methods in complex fluid flow problems is still under development. In this paper a full multigrid procedure has been incorporated in a finite volume solution for predicting fully developed fluid flow in a streamwise periodic geometry. Steady computations in two‐dimensional body fitted co‐ordinates have shown considerable savings in computation time by this multigrid method.
Taylor‐Galerkin‐based spectral element methods for convection‐diffusion problems
Authors: Timmermans L. J. P. , Van De Vosse F. N. , Minev P. D. 
Published: August 2005

AbstractSeveral explicit Taylor‐Galerkin‐based time integration schemes are proposed for the solution of both linear and non‐linear convection problems with divergence‐free velocity. These schemes are based on second‐order Taylor series of the time derivative. The spatial discretization is performed by a high‐order Galerkin spectral element method. For convection‐diffusion problems an operator‐splitting technique is given that decouples the treatment of the convective and diffusive terms. Both problems are then solved using a suitable time scheme. The Taylor‐Galerkin methods and the operator‐splitting scheme are tested numerically for both convection and convection‐diffusion problems.
The effects of flow split ratio and flow rate in manifolds
Authors: Fu H. , Watkins A. P. , Yianneskis M. 
Published: August 2005

AbstractThis paper reports a combined experimental and numerical investigation of three‐dimensional steady turbulent flows in inlet manifolds of square cross‐section. Predictions and measurements of the flows were carried out using computational fluid dynamics and laser Doppler anemometry techniques respectively. The flow structure was characterized in detail and the effects of flow split ratio and inlet flow rate were studied. These were found to cause significant variations in the size and shape of recirculation regions in the branches, and in the turbulence levels. It was then found that there is a significant difference between the flow rates through different branches.The performance of the code was assessed through a comparison between predictions and measurements. The comparison demonstrates that all important features of the flow are well represented by the predictions.
A preconditioned alternating inner‐outer iterative solution method for the mixed finite element formulation of the Navier‐Stokes equations
Authors: Wille S. Ø. 
Published: August 2005

AbstractIn the present work a new iterative method for solving the Navier‐Stokes equations is designed. In a previous paper a coupled node fill‐in preconditioner for iterative solution of the Navier‐Stokes equations proved to increase the convergence rate considerably compared with traditional preconditioners. The further development of the present iterative method is based on the same storage scheme for the equation matrix as for the coupled node fill‐in preconditioner. This storage scheme separates the velocity, the pressure and the coupling of pressure and velocity coefficients in the equation matrix. The separation storage scheme allows for an ILU factorization of both the velocity and pressure unknowns. With the inner‐outer solution scheme the velocity unknowns are eliminated before the resulting equation system for the pressures is solved iteratively. After the pressure unknown has been found, the pressures are substituted into the original equation system and the velocities are also found iteratively. The behaviour of the inner‐outer iterative solution algorithm is investigated in order to find optimal convergence criteria for the inner iterations and compared with the solution algorithm for the original equation system. The results show that the coupled node fill‐in preconditioner of the original equation system is more efficient than the coupled node fill‐in preconditioner of the reduced equation system. However, the solution technique of the reduced equation system revals properties which may be advantageous in future solution algorithms.
Parallel computation of the flow of integral viscoelastic fluids on a heterogeneous network of workstations
Authors: Henriksen P. , Keunings R. 
Published: August 2005

AbstractWe consider the parallel computation of flows of integral viscoelastic fluids on a heterogeneous network of workstations. The proposed methodology is relevant to computational mechanics problems which involve a compute‐intensive treatment of internal variables (e.g. fibre suspension flow and deformation of viscoplastic solids). The main parallel computing issue in such applications is that of load balancing. Both static and dynamic allocation of work to processors are considered in the present paper. The proposed parallel algorithms have been implemented in an experimental, parallel version of the commercial POLYFLOW package developed in Louvain‐la‐Neuve. The implementation uses the public domain PVM software library (Parallel Virtual Machine), which we have extended in order to ease porting to heterogeneous networks. We describe parallel efficiency results obtained with three PVM configurations, involving up to seven workstations with maximum relative processing speeds of five. The physical problems are the stick/slip and abrupt contraction flows of a K.B.K.Z. integral fluid. Using static allocation, parallel efficiencies in the range 67%–85% were obtained on a PVM network with four workstations having relative speeds of 2:1:1:1. Parallel efficiencies higher than 90% were obtained on the three PVM configurations using the dynamic load‐balancing schemes.
Finite element formulations for large‐scale, coupled flows in adjacent porous and open fluid domains
Authors: Salinger A. G. , Aris R. , Derby J. J. 
Published: August 2005

AbstractTwo approaches which employ the finite element method to solve for large‐scale, coupled, incompressible flows through adjacent porous and open domains are developed and evaluated in a model for the spontaneous ignition of coal stockpiles. Both formulations employ the Navier‐Stokes equations do describe flow in the open region; two different descriptions, Darcy's law and the Brinkman equation, are employed to model flows within the porous region. The formulation which uses Darcy's law employs the Beavers‐Joseph slip condition and a novel implementation of the interfacial conditions. The other approach invokes the Brinkman equation: this considerably simplifies the implementation of matching conditions at the interface between the porous and open fluid domains, but also results in velocity boundary layers in the porous region adjacent to this interface which can be difficult to resolve numerically. A direct comparison of model results shows that the Darcy‐slip formulation produces solutions which are more accurate and more economical to compute than those obtained using the Brinkman formulation.
An Euler solver for three‐dimensional turbomachinery flows
Authors: Soulis Johannes Vassiliou 
Published: August 2005

AbstractA time‐marching finite volume numerical procedure is presented for three‐dimensional Euler analysis of turbomachinery flows. The proposed scheme is applied to the conservative form of the Euler equations written in general curvilinear co‐ordinates. A simple but computationally efficient grid is constructed. Numerical solution results for three 3D turbine cascade flows have been presented and compared with available measurements as well as with another state‐of‐the‐art 3D Euler analysis numerical solution in order to demonstrate the accuracy and computational efficiency of the analysis method. Also, the predicted results are compared with a 3D potential flow solver and comparison is made with the analytical solution. The proposed method is an accurate and reliable technique for solving the compressible flow equations in turbomachinery geometries.
An ILU smoother for the incompressible Navier‐Stokes equations in general co‐ordinates
Authors: Zeng S. , Wesseling P. 
Published: August 2005

AbstractThe solution of the incompressible Navier‐Stokes equations in general two‐ and three‐dimensional domains using a multigrid method is considered. Because a great variety of boundary‐fitted grids may occur, robustness is at a premium. Therefore a new ILU smoother called CILU (collective ILU) is described, based on r‐transformations. In CILU the matrix that is factorized is block‐structured, with blocks corresponding to the set of physical variables. A multigrid algorithm using CILU as smoother is investigated. The performance of the algorithm in two and three dimensions is assessed by numerical experments. The results show that CILU is a good smoother for the incompressible Navier‐Stokes equations discretized on general non‐orthogonal curvilinear grids.
A weighted least squares method for first‐order hyperbolic systems
Authors: Zeitoun D. G. , Laible J. P. , Pinder G. F. 
Published: August 2005

AbstractThe paper presents a generalization of the classical L2‐norm weighted least squares method for the numerical solution of a first‐order hyperbolic system. This alternative least squares method consists of the minimization of the weighted sum of the L2 residuals for each equation of the system. The order of accuracy of global conservation of each equation of the system is shown to be inversely proportional to the weight associated with the equation. The optimal relative weights between the equations are then determined in order to satisfy global conservation of the energy of the physical system.As an application of the algorithm, the shallow water equations on an irregular domain are first discretized in time and then solved using Laplace modification and the proposed least squares method.
Numerical calculations of three‐dimensional turbulent vortex breakdown
Authors: Spall Robert E. , Gatski Thomas B. 
Published: August 2005

AbstractNumerical solutions to the three‐dimensional, unsteady, incompressible Reynolds‐averaged Navier‐Stokes equations have been obtained for bubble‐type vortex breakdown. Two different turbulence models were employed: (1) standard K‐ε and (2) an explicit, regularized algebraic Reynolds stress model. Results are computed at a Reynolds number of 10,000. The algebraic Reynolds stress model produced a breakdown bubble with a larger length‐to‐diameter ratio than did the K‐ε model. Breakdown also occurred at lower levels of adverse pressure gradient for the algebraic stress model than for the K‐ε model. In each case single‐cell breakdown structures resulted. This is contrasted with numerical calculations for laminar breakdown which reveal the existence of complex multicell bubble breakdown structures.
Finite element modelling of the flow of chemically reactive polymeric liquids
Authors: Lefebvre L. , Keunings R. 
Published: August 2005

AbstractWe consider steady state and time‐dependent flows of chemically reactive polymeric systems in two‐dimensional geometries. A numerical simulation tool is proposed for predicting the evolution of the macroscopic velocity, temperature, stress and species concentration fields in such flows. We formulate a general mathematical model on the basis of the first principles of continuum mechanics, which includes a description of the non‐liner coupling between kinematics, heat transfer and chemical kinetics. The resulting set of non‐linear partial differential equations is solved numerically by means of appropriate finite element techniques. We have implemented the resulting numerical model in the general‐purpose POLYFLOWR software developed in Louvain‐la‐Neuve, Belgium. Simulation results for various steady state and time‐dependent reactive flows are reported.
A second order finite element method for the solution of the transonic Euler and Navier‐Stokes equations
Authors: Baruzzi G. S. , Habashi W. G. , Guevremont J. G. , Hafez M. M. 
Published: August 2005

AbstractThe numerical solution of the compressible Euler and Navier‐Stokes equations in primitive variables form requires the use of artificial viscosity or upwinding. Methods that are first‐order‐accurate are too dissipative and reduce the effective Reynolds number substantially unless a very fine grid is used. A first‐order finite element method for the solution of the Euler and Navier‐Stokes equations can be constructed by adding Laplacians of the primitive variables to the governing equations. Second‐order schemes may require a fourth‐order dissipation and higher‐order elements. A finite element approach is proposed in which the fourth‐order dissipation is recast as the difference of two Laplacian operators, allowing the use of bilinear elements. The Laplacians of the primitive variables of the first‐order scheme are thus balanced by additional terms obtained from the governing equations themselves, tensor identities or other forms of nodal averaging. To demonstrate formally the accuracy of this scheme, an exact solution is introduced which satisfies the continuity equation identically and the momentum equations through forcing functions. The solutions of several transonic and supersonic inviscid and laminar viscous test cases are also presented and compared to other available numerical data.
Numerical simulation and optimal shape for viscous flow by a fictitious domain method
Authors: Glowinski Roland , Pan Tsorng‐Whay , Kearsley Anthony J. , Periaux Jacques 
Published: August 2005

AbstractIn this article we discuss the fictitious domain solution of the Navier‐Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no‐slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regriding. The resulting methodology is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier‐Stokes equations and then to an optimal shape problem for Stokes and Navier‐Stokes flow.
Positive schemes and shock modelling for compressible flows
Authors: Jameson Antony 
Published: August 2005

AbstractA unified theory of non‐oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presented which confirm the properties of these schemes.