bluuebunny/crossref_metadata_2025_split huggingface dataset:
Spectral element‐FCT method for scalar hyperbolic conservation laws
Authors: Giannakouros John , Karniadakis George Em 
Published: August 2005

AbstractA new algorithm based on spectral element discretizations and flux‐corrected transport (FCT) ideas is developed for the solution of discontinuous hyperbolic problems. A conservative formulation is proposed, based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss–Chebyshev and Gauss–Lobatto–Chebyshev discretizations. In addition, high‐order time‐differencing schemes, a flux limiter and a general spectral filter are employed to improve the quality of the solution. It is demonstrated through model problems of linear advection and examples of one‐dimensional shock formation that the proposed algorithm leads to stable, non‐oscillatory solutions of high accuracy away from discontinuities. Typically, spectral or spectral element methods perform very poorly in the presence of even weak discontinuities, although they produce only exponentialy small errors for smooth solutions. Spectral element–FCT methods can provide spectral properties (i.e. minimum dispersion and diffusion errors) as well as great flexibility in the discretization, since a variable number of macroelements or collocation points per element can be employed to accommodate both accuracy and geometric requirements.
A hybrid method for computing the flow of viscoelastic fluids
Authors: Ariel P. D. 
Published: August 2005

AbstractA hybrid method for computing the flow of viscoelastic and second‐order fluids is presented. It combines the features of the finite difference technique and the shooting method. The method is accurate because it uses central differences. Its convergence is at least superlinear.The method is applied to obtain the solutions to three problems of flow of Walters' B' fluid: (a) flow near a stagnation point, (b) flow over a stretching sheet and (c) flow near a rotating disk. Numerical results reveal some new characteristics of flows which are not easy to demonstrate using the perturbation technique.
Energy flux equalization: An open boundary condition for non‐linear free surface flows
Authors: Jagannathan Sridhar 
Published: August 2005

AbstractIn the simulation of non‐linear free surface flows in a finite domain a major concern is with the radiation condition to be applied at the ‘open’ boundary. No general theoretical radiation conditions are known to exist. In this paper a new open boundary condition is formulated based on energy flux equalization between the non‐linear inner domain and a linear outer domain. The non‐linear flow in the inner domain is solved numerically using a semi‐Lagrangian procedure. The energy flux arriving at the open boundary is removed using a new open boundary condition which acts as a linear wave absorber. For the cases studied the performance of this boundary condition is found to be quite good.
A structured tri‐tree search method for generation of optimal unstructured finite element grids in two and three dimensions
Authors: Wille S. Ø. 
Published: August 2005

AbstractA new method for generating finite element grids in two and three dimensions is developed. The method is based on a new search tree structure. The search tree is built upon triangles in two dimensions and tetrahedra in three dimensions. The density of elements can be varied throughout the computational domain. Efficient search algorithms for finding points in space and for finding the boundary of the domain have been developed. The speed of the grid algorithm will permit adaptive gridding during computation. The grid algorithm is generally applicable to both hydrodynamic as well as aerodynamic finite element computations. The technique has been used with success for gridding the North Sea‐Skagerrak area.
Simulating two‐dimensional turbulent flow by using the κ–ϵ model and the vorticity–streamfunction formulation
Authors: Elkaim D. , Reggio M. , Camarero R. 
Published: August 2005

AbstractA numerical procedure to solve turbulent flow which makes use of the κ–ϵ model has been developed. The method is based on a control volume finite element method and an unstructured triangular domain discretization. The velocity‐pressure coupling is addressed via the vorticity‐streamfunction and special attention is given to the boundary conditions for the vorticity. Wall effects are taken into account via wail functions or a low‐Reynolds‐number model. The latter was found to perform better in recirculation regions. Source terms of the κ and ε transport equations have been linearized in a particular way to avoid non‐realistic solutions. The vorticity and streamfunction discretized equations are solved in a coupled way to produce a faster and more stable computational procedure. Comparison between the numerical predictions and experimental data shows that the physics of the flow is correctly simulated.
Boundary‐conforming mapping applied to computations of highly deformed solidification interfaces
Authors: Tsiveriotis K. , Brown R. A. 
Published: August 2005

AbstractA new boundary‐conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational fomulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.
River and reservoir flow modelling using the transformed shallow water equations
Authors: Borthwick A. G. L. , Barber R. W. 
Published: August 2005

AbstractThis paper describes a versatile finite difference scheme for the solution of the two‐dimensional shallow water equations on boundary‐fitted non‐orthogonal curvilinear meshes. It is believed that this is the first non‐orthogonal shallow water equation model incorporating the advective acceleration terms to have been developed in the United Kingdom.The numerical scheme has been validated against the severe condition of jet‐forced flow in a circular reservoir with vertical side walls, where reflections of the initial free surface waves pose major problems in achieving a stable solution. Furthermore, the validation exercises are designed to test the computer model for artificial diffusion, which may be a consequence of the numerical scheme adopted to stabilize the shallow water equations. The model is shown to be capable of simulating the flow conditions in an irregularly shaped domain typical of the geometries frequently encountered in civil engineering river basin management.
A coding error elimination procedure for validating isotropic turbulent convection numerical calculations in axisymmetric flows with Eulerian and Lagrangian descriptions
Authors: Blank David A. 
Published: August 2005

AbstractA procedure which ensures the elimination of discretization and coding errors in the numerical solution of a set of governing equations describing internal turbulent convection flows is given and illustrated. The governing equations investigated in the validation analysis are of general form. The equations for the turbulence model (k‐8) assume the turbulence to be isotropic. In the analysis a portion of the solution region uses a Lagrangian description while a Eulerian description is used elsewhere. The work was originally motivated by the need to validate numerical calculations performed in the modelling of cornbusting fluid flow within symmetric piston engines. Thus the procedure is demonstrated for an axisymmetric formulation. The same methodology can be even more easily applied to Cartesian‐based problems using the guidelines given in this work. Details of the procedure are presented in a very practical format, making it possible to consider both simpler and more complex governing equation sets with little additional effort. Thus the implementation of this procedure by researchers to a variety of both turbulent and laminar internal flow problems should prove to be easy.
An inviscid/viscous coupling approach for vortex flow field calculations
Authors: Lee K. D. , Brandt S. A. 
Published: August 2005

AbstractA new computational approach is developed for the analysis of vortex‐dominated flow fields around highly swept wings at high angles of attack. In this approach an inviscid Euler technology is coupled with viscous models, similar to inviscid/boundary layer coupling. The viscous nature of the vortex core is represented by an algebraic model derived from the Navier–Stokes equations. The approach also accounts for the effects of the viscous shear layer near a wing surface through a modified surface boundary condition. The inviscid/viscous coupling consistently provides improved predictions of leading edge separation, vortex bursting and secondary vortex formation at relatively low computational cost. Results for several cases are compared with wind tunnel tests and other Euler and Navier‐Stokes solutions.
Numerical simulation of jet‐forced flow in a circular reservoir using discrete and random vortex methods
Authors: Borthwick A. G. L. , Barber R. W. 
Published: August 2005

AbstractThis paper describes a Biot–Savart discrete vortex model for simulating the flow patterns which occur when a single high‐velocity inflow jet is used to stir the fluid within a circular container. The first stage of the model consists of conformally mapping the circular perimeter of the container onto a rectangle by means of a Schwarz–Christoffel transformation. A potential flow solution is then obtained for the flow inside the rectangle and this is transformed to give the potential flow inside the circle. In the second stage of the simulation, discrete vortices are added at the inlet of the physical system in order to model the inflow shear layers. Velocity components resulting from the discrete vortices and their images in the walls of the cylinder are superimposed on the uniform potential flow solution. The positions of the vortices are updated using a Lagrangian tracking procedure. Viscous effects are incorporated through the use of random walks. From the results it is shown that the discrete vortex method does predict qualitatively the important features of jet‐forced reservoir flow.
Numerical investigation of confined wakes behind a square cylinder in a channel
Authors: Mukhopadhyay A. , Biswas G. , Sundararajan T. 
Published: August 2005

AbstractThe structure of confined wakes behind a square cylinder in a channel is investigated via the numerical solution of the unsteady Navier–Stokes equations. Vortex shedding behind the cylinder induces periodicity in the flow field. Details of the phenomenon are simulated through numerical flow visualization. The unsteady periodic wake can be characterized by the Strouhal number, which varies with the Reynolds number and the blockage ratio of the channel. The periodicity of the flow is, however, damped in the downstream region of a long duct. This damping may be attributed to the influence of side walls on the flow structure.
A study of laminar air flow through cracks by numerical solution of the differential equations
Authors: Mokhtarzadeh‐Dehghan M. R. , Ward‐Smith A. J. , Walker R. N. 
Published: August 2005

AbstractThis paper describes a numerical study of laminar flow through building cracks such as those found around doors or windows. The mathematical model is based on the solution of the two‐dimensional conservation equations of mass and momentum by a finite volume method. The results are presented for two crack geometries, namely double‐bend and four‐bend cracks. The variation in local pressure coefficient along the crack walls and the velocity and pressure distributions within the cracks are described. The overall predicted pressure coefficient for the double‐bend crack for the double‐bend crack is compared with the results obtained using a correlation given by Baker et al.5.
Computing brine transport in porous media with an adaptive‐grid method
Authors: Trompert R. A. , Verwer J. G. , Blom J. G. 
Published: August 2005

AbstractAn adaptive‐grid finite‐difference method is applied to a model for non‐isothermal, coupled flow and transport of brine in porous media. In the vicinity of rock salt formations the salt concentration in the fluid becomes large, giving rise to disparate scales in the salt concentrations profiles. A typical situation one encounters is that of a sharp freshwater‐saltwater interface that moves in time. In such situations adaptive‐grid methods are more effective than standard fixed‐grid methods, since they refine the space grid locally and, hence, provide for substantial reduction in the number of grid points, memory use and CPU time. The adaptive‐grid method of this paper is a static, local uniform grid refinement method. Its main feature is that it integrates on nested sequences of locally uniformly refined Cartesian space grids, which are automatically adjusted in time to follow rapid spatial transitions. Variable time steps are used to cope with rapid temporal transitions, including a fast march to possible steady‐state solutions. For time stepping, the implicit, second‐order BDF scheme is used. Two specific example problems are numerically illustrated. The main physical properties involved here are advection and dispersion and in case of dominant advection sharp freshwater‐saltwater interfaces arise.
A complete boundary integral formulation for steady compressible inviscid flows governed by non‐linear equations
Authors: Zuosheng Yang 
Published: August 2005

AbstractA complete boundary integral formulation for steady compressible inviscid flows governed by non‐linear equations is established by using the specific mass flux as a dependent variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain. It is shown that the boundary integral formulation developed in this paper is equivalent of the results of distributions of the fundamental solutions of the Laplacian operator equation with a different order along the boundaries of the domain. Hence, we have succeeded in establishing the fundamental‐solution method for compressible inviscid flows governed by non‐linear equations.
Influence of particle diameter distribution on the downstream particle turbulence in a two‐phase, turbulent, round jet
Authors: Sargianos N. P. , Anagnostopoulos J. S. , Bergeles G. 
Published: August 2005

AbstractA numerical algorithm is used to study the ‘fan‐spreading’ mechanism of axial particle turbulence acquisition and the effects on it of the inlet particle diameter distribution, downstream of a particle‐laden, turbulent, round jet. The algorithm is based on the particle‐source‐in‐cell numerical technique for two‐phase flows. Eulerian equations are used for the description of the gas‐phase dynamics, whilst the solid particles are treated within the Lagrangian framework. The turbulent particle dispersion is simulated with the aid of the stochastic separated flow model. It was found that the ‘fan‐spreading’ turbulence is very much affected by the mean and standard deviation of the particle size distribution; in particular, it was found that the ‘fan‐spreading’ mechanism becomes weaker when the standard deviation of the particle diameter distribution is higher and the mean particle diameter smaller. An analytical expression describing the axial particle turbulence due to ‘fan‐spreading’ is proposed and tested, along with a similarity profile valid for the particles of bigger size.
Use of characteristics method with cubic interpolation for unsteady‐flow computation
Authors: Yang Jinn‐Chuang , Chiu Kuang‐Ping 
Published: August 2005

AbstractThe specified‐time‐interval (STI) scheme has been used commonly in applying the method of characteristics (MOC) to unsteady open‐channel flow problems. However, with the use of STI scheme, the numerical error for the simulation results can always be induced due to the interpolation used to approximate the characteristics trajectory. Hence, in order to remedy the numerical errors caused by the interpolation, one needs to seek some kind of interpolation technique with higher‐order accuracy. Instead of the linear interpolation technique, which has been used very commonly and can induce serious numerical diffusion, the Holly‐‐Preissmann two‐point, method, which is a cubic interpolation technique with fourth‐order of accuracy, is proposed here to integrate with the method of characteristics for the computation of one‐dimensional unsteady flow in open channel. The concept of reachback and reachout in space and time directions for the characteristics is also introduced to assure the model stability. The computed results from this new model are compared with those computed by using the Preissmann four‐point scheme and the multimode method of characteristics with linear interpolation.
A high‐resolution Godunov‐type scheme in finite volumes for the 2D shallow‐water equations
Authors: Alcrudo Francisco , Garcia‐Navarro Pilar 
Published: August 2005

AbstractA high‐order Godunov‐type scheme based on MUSCL variable extrapolation and slope limiters is presented for the resolution of 2D free‐surface flow equations. In order to apply a finite volume technique of integration over body‐fitted grids, the construction of an approximate Jacobian (Roe type) of the normal flux function is proposed. This procedure allows conservative upwind discretization of the equations for arbitrary cell shapes. The main advantage of the model stems from the adaptability of the grid to the geometry of the problem and the subsequent ability to produce correct results near the boundaries. Verification of the technique is made by comparison with analytical solutions and very good agreement is found. Three cases of rapidly varying two‐dimensional flows are presented to show the efficiency and stability of this method, which contains no terms depending on adjustable parameters. It can be considered well suited for computation of rather complex free‐surface two‐dimensional problems.
Employment of second‐moment closure for calculation of turbulent recirculating flows in complex geometries with collocated variable arrangement
Authors: Farhanieh Bijan , Davidson Lars , Sundén Bengt 
Published: August 2005

AbstractThis paper addresses the implementation of second‐moment closure into a collocated variable arrangement body‐fitted‐finite‐volume scheme in which Cartesian velocity components are used. The methods for avoiding instability in the solution procedure are described. A new method for the treatment of the near‐wall regions for the momentum equations, as well as the prescription of the stresses at the wall, is described in detail. The performance of the methodology is assessed by applying it to two flow situations, where experimental data are available: the flow over a backward step, and the flow through a sinusoidal pipe constriction. The results are very promising.
Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake
Authors: Sun J. , Li J. , Roux B. 
Published: August 2005

AbstractThis paper describes flow around a pair of cylinders in tandem arrangement with a downstream cylinder being fixed or forced to oscillate transversely. A sinusoidal parietal velocity is applied to simulate cylinder oscillation. Time‐dependent Navier‐Stokes equations are solved using finite element method. It is shown that there exist two distinct flow regimes: ‘vortex suppression regime’ and ‘vortex formation regime’. Averaged vortex lengths between the two cylinders, pressure variations at back and front stagnant points as well as circumferential pressure profiles of the downstream cylinder are found completely different in the two regimes and, thus, can be used to identify the flow regimes. It is shown that frequency selection in the wake of the oscillating cylinder is a result of non‐linear interaction among vortex wakes upstream and downstream of the second cylinder and its forced oscillation. Increasing cylinder spacing results in a stronger oscillatory incident flow upstream of the second cylinder and, thus, a smaller synchronization zone.
Evaluation of various high‐order‐accuracy schemes with and without flux limiters
Authors: Tamamidis Panos , Assanis Dennis N. 
Published: August 2005

AbstractConventional high‐order schemes with reduced levels of numerical diffusion produce results with spurious oscillations in areas where steep velocity gradients exist. To prevent the development of non‐physical oscillations in the solution, several monotonic schemes have been proposed. In this work, three monotonic schemes, namely Van Leer's scheme, Roe's flux limiter and the third‐order SHARP scheme, are compared and evaluated against schemes without flux limiters. The latter schemes include the standard first‐order upwind scheme, the second‐order upwind scheme and the QUICK scheme. All the above schemes are applied to four two‐dimensional problems: (i) rotation of a scalar ‘cone’ field, (ii) transport of a scalar ‘square’ field, (iii) mixing of a cold with a hot front and (iv) deformation of a scalar ‘cone’ field. These problems test the ability of the selected schemes to produce oscillation‐free and accurate results in critical convective situations. The evaluation of the schemes is based on several aspects, such as accuracy, economy and complexity. The tests performed in this work reveal the merits and demerits of each scheme. It is concluded that high‐order schemes with flux limiters can significantly improve the accuracy of the results.
Unstructured volume‐agglomeration MG: Solution of the Poisson equation
Authors: Koobus Bruno , Lallemand Marie‐Hélène , Dervieux Alain 
Published: August 2005

AbstractWe are interested in solving second‐order PDEs with multigrid and unstructured meshes. The multigrid strategy we present here is adapted from the generalized finite volume agglomeration multigrid algorithm we have developed recently for the solution of the Euler equations. We now focus on Poisson's equation. A strategy is defined by introducing a correction factor for the diffusive terms, and some illustrating results are given.
Tools for simulating non‐stationary incompressible flow via discretely divergence‐free finite element models
Authors: Turek Stefan 
Published: August 2005

AbstractWe develop simulation tools for the non‐stationary incompressible 2D Navier‐‐Stokes equations. The most important components of the finite element code are: the fractional step ϑ‐scheme, which is of second‐order accuracy and strongly A‐stable, for the time discretization; a fixed point defect correction method with adaptive step length control for the non‐linear problems (stationary Navier‐Stokes equations); a modified upwind discretization of higher‐order accuracy for the convective terms. Finally, the resulting nonsymmetric linear subproblems are treated by a special multigrid algorithm which is adapted to the quadrilateral non‐conforming discretely divergence‐free finite elements. For the graphical postprocess we use a fully non‐stationary and interactive particle‐tracing method. With extensive test calculations we show that our method is a candidate for a ‘black box’ solver.