bluuebunny/crossref_metadata_2025_split huggingface dataset:
Co‐located equal‐order control‐volume finite element method for two‐dimensional axisymmetric incompressible fluid flow
Authors: Masson C. , Saabas H. J. , Baliga B. R. 
Published: August 2005

AbstractThe formulation of a control‐volume‐based finite element method (CVFEM) for axisymmetric, two‐dimensional, incompressible fluid flow and heat transfer in irregular‐shaped domains is presented. The calculation domain is discretized into torus‐shaped elements and control volumes. In a longitudinal cross‐sectional plane, these elements are three‐node triangles, and the control volumes are polygons obtained by joining the centroids of the three‐node triangles to the mid‐points of the sides. Two different interpolation schemes are proposed for the scalar‐dependent variables in the advection terms: a flow‐oriented upwind function, and a mass‐weighted upwind function that guarantees that the discretized advection terms contribute positively to the coefficients in the discretized equations. In the discretization of diffusion transport terms, the dependent variables are interpolated linearly. An iterative sequential variable adjustment algorithm is used to solve the discretized equations for the velocity components, pressure and other scalar‐dependent variables of interest. The capabilities of the proposed CVFEM are demonstrated by its application to four different example problems. The numerical solutions are compared with the results of independent numerical and experimental investigations. These comparisons are quite encouraging.
Treatment of numerical diffusion in strong convective flows
Authors: Arampatzis G. , Assimacopoulos D. , Mitsoulis E. 
Published: August 2005

AbstractA three‐dimensional extension of the QUICK scheme adapted for the finite volume method and non‐uniform grids is presented to handle convection‐diffusion problems for high Peclet numbers and steep gradients. The algorithm is based on three‐dimensional quadratic interpolation functions in which the transverse curvature terms are maintained and the diagonal dominance of the coefficient matrix is preserved. All formulae are explicitly given in an appendix. Results obtained with the classical upwind (UDS), the simplified QUICK (transverse terms neglected) and the present full QUICK schemes are given for two benchmark problems, one two‐dimensional, steady state and the other three‐dimensional, unsteady state. Both QUICK schemes are shown to give superior solutions compared with the UDS in terms of accuracy and efficiency. The full QUICK scheme performs better than the simplified QUICK, giving even for coarse grids acceptable results closer to the analytical solutions, while the computational time is not affected much.
Investigation of flux formulae in transonic shock wave/turbulent boundary layer interaction
Authors: Drikakis D. , Durst F. 
Published: August 2005

AbstractThe aim of the present study is to examine the accuracy and improvement of various numerical methods in the solution of the transonic shock/turbulent boundary layer interaction problem and to show that a significant source of numerical inaccuracies in turbulent flows is not only the inadequacy of the turbulence model but also the numerical discretization. Comparisons between a Riemann solver and a flux‐vector‐splitting method as well as between various numerical high‐order extrapolation schemes with corresponding experimental results are presented.
Equivalence of u–p and ζ–ψ formulations of the time‐dependent Navier–Stokes equations
Authors: Guermond J.‐L. , Quartapelle L. 
Published: August 2005

AbstractThis paper deals with the non‐stationary incompressible Navier‐‐Stokes equations for two‐dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H1 for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.
Multigrid pressure correction techniques for the computation of quasi‐incompressible internal flows
Authors: Luchini P. , D'Alascio A. 
Published: August 2005

AbstractA study is reported on the possibility of improving the speed of convergence of existing numerical programmes for the simulation of flow in combustion chambers by applying the multigrid method to the pressure correction phase only. A version of the multigrid algorithm is introduced for this purpose which achieves a 1:10 residual reduction in a single V(1, 1) cycle. The overall decrease in computation time with respect to an industry‐standard SIMPLE algorithm with single‐grid pressure correction ranges from four to five times for SIMPLE itself and several other well‐known algorithms to six times for a newly developed pressure correction strategy we call difference operator triangularization (DOT).
On the Riemann problem for liquid or gas‐liquid media
Authors: Chen Tze‐Jang , Cooke Charlie H. 
Published: August 2005

AbstractSelf‐similar solutions to the Riemann problem for water with the modified Tait equation of state are presented. The methods of Smoller for gas dynamics are employed to reduce the problem to the solution of a single non‐linear equation. The same methods are used for solving the Riemann problem at a gas‐water interface. In both cases the method of interval bisections affords a solution technique free of problems with convergence.
Chebyshev collocation method and multidomain decomposition for the incompressible Navier‐Stokes equations
Authors: Pinelli A. , Vacca A. 
Published: August 2005

AbstractThe two‐dimensional incompressible Navier‐Stokes equations in primitive variables have been solved by a pseudospectral Chebyshev method using a semi‐implicit fractional step scheme. The latter has been adapted to the particular features of spectral collocation methods to develop the monodomain algorithm. In particular, pressure and velocity collocated on the same nodes are sought in a polynomial space of the same order; the cascade of scalar elliptic problems arising after the spatial collocation is solved using finite difference preconditioning. With the present procedure spurious pressure modes do not pollute the pressure field.As a natural development of the present work a multidomain extent was devised and tested. The original domain is divided into a union of patching sub‐rectangles. Each scalar problem obtained after spatial collocation is solved by iterating by subdomains. For steady problems a C1 solution is recovered at the interfaces upon convergence, ensuring a spectrally accurate solution.A number of test cases have been solved to validate the algorithm in both its single‐block and multidomain configurations.The preliminary results achieved indicate that collocation methods in multidomain configurations might become a viable alternative to the spectral element technique for accurate flow prediction.
Multigrid solution of compressible turbulent flow on unstructured meshes using a two‐equation model
Authors: Mavriplis D. J. , Martinelli L. 
Published: August 2005

AbstractThe steady state solution of the system of equations consisting of the full Navier‐Stokes equations and two turbulence equations has been obtained using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge‐Kutta time‐stepping scheme with a stability‐bound local time step, while the turbulence equations are advanced in a point‐implicit scheme with a time step which guarantees stability and positivity. Low‐Reynolds‐number modifications to the original two‐equation model are incorporated in a manner which results in well‐behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.
Boundary element method solution of MHD flow in a rectangular duct
Authors: Tezer‐Sezgin Munevver 
Published: August 2005

AbstractThe magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with an external magnetic field applied transverse to the flow has been investigated. The walls parallel to the applied magnetic field are conducting while the other two walls which are perpendicular to the field are insulators. The boundary element method (BEM) with constant elements has been used to cast the problem into the form of an integral equation over the boundary and to obtain a system of algebraic equations for the boundary unknown values only. The solution of this integral equation presents no problem as encountered in the solution of the singular integral equations for interior methods. Computations have been carried out for several values of the Hartmann number (1 ⩽ M ⩽ 10). It is found that as M increases, boundary layers are formed close to the insulated boundaries for both the velocity and the induced magnetic field and in the central part their behaviours are uniform. Selected graphs are given showing the behaviours of the velocity and the induced magnetic field.
Résumé and remarks on the open boundary condition minisymposium
Authors: Sani R. L. , Gresho P. M. 
Published: August 2005

AbstractThe incompressible Navier‐Stokes equations—and their thermal convection and stratified flow analogue, the Boussinesq equations—possess solutions in bounded domains only when appropriate/legitimate boundary conditions (BCs) are appended at all points on the domain boundary. When the boundary—or, more commonly, a portion of it—is not endowed with a Dirichlet BC, we are faced with selecting what are called open boundary conditions (OBCs), because the fluid may presumably enter or leave the domain through such boundaries. The two minisymposia on OBCs that are summarized in this paper had the objective of finding the best OBCs for a small subset of two‐dimensional test problems. This objective, which of course is not really well‐defined, was not met (we believe), but the contributions obtained probably raised many more questions/issues than were resolved—notable among them being the advent of a new class of OBCs that we call FBCs (fuzzy boundary conditions).
Finite element implementation of boundary conditions for the pressure Poisson equation of incompressible flow
Authors: Hassanzadeh Siamak , Sonnad Vijay , Foresti Stefano 
Published: August 2005

AbstractIn this paper we address the problem of the implementation of boundary conditions for the derived pressure Poisson equation of incompressible flow. It is shown that the direct Galerkin finite element formulation of the pressure Poisson equation automatically satisfies the inhomogeneous Neumann boundary conditions, thus avoiding the difficulty in specifying boundary conditions for pressure. This ensures that only physically meaningful pressure boundary conditions consistent with the Navier‐Stokes equations are imposed. Since second derivatives appear in this formulation, the conforming finite element method requires C1 continuity. However, for many problems of practical interest (i.e. high Reynolds numbers) the second derivatives need not be included, thus allowing the use of more conventional C0 elements. Numerical results using this approach for a wall‐driven contained flow within a square cavity verify the validity of the approach. Although the results were obtained for a two‐dimensional problem using the p‐version of the finite element method, the approach presented here is general and remains valid for the conventional h‐version as well as three‐dimensional problems.
The influence of normal flow boundary conditions on spurious modes in finite element solutions to the shallow water equations
Authors: Westerink J. J. , Luettich R. A. , Wu J. K. , Kolar R. L. 
Published: August 2005

AbstractFinite element solutions of the primitive equation (PE) form of the shallow water equations are notorious for the severe spurious 2Δx modes which appear. Wave equation (WE) solutions do not exhibit these numerical modes. In this paper we show that the severe spurious modes in PE solutions are strongly influenced by essential normal flow boundary conditions in the coupled continuity‐momentum system of equations. This is demonstrated through numerical examples that avoid the use of essential normal flow boundary conditions either by specifying elevation values over the entire boundary or by implementing natural flow boundary conditions in the weak weighted residual form of the continuity equation. Results from a series of convergence tests show that PE solutions are of nearly the same quality as WE solutions when spurious modes are suppressed by alternative specification of the boundary conditions. Network intercomparisons indicate that varying nodal support does not excite spurious modes in a solution, although it does enhance the spurious modes introduced when an essential normal flow boundary condition is used.Dispersion analysis of discrete equations for interior and boundary nodes offers an explanation of the observed solution behaviour. For certain PE algorithms a mixed situation can arise where the boundary nodes exhibit a monotonic (noise‐free) dispersion relationship and the interior nodes exhibit a folded (noisy) dispersion relationship. We have found that the mixed situation occurs when all boundary nodes are specified elevation nodes (which are enforced as essential conditions in the continuity equation) or when specified flow boundary nodes are treated as natural boundary conditions in the continuity equation. In either case the effect is to generate a solution that is essentially free of noise. Apparently, the monotonic dispersion behaviour at the boundaries suppresses the otherwise noisy behaviour caused by the folded dispersion relation on the interior.
Transport of radionuclides in isolated fractures in crystalline rocks
Authors: Grandi G. M. , Ferreri J. C. 
Published: August 2005

AbstractThis paper presents a generalization of a computational method for the prediction of solute dispersion in fractured porous media. This method is specially useful for the prediction of subsurface flows in crystalline rocks. The model now includes a linear kinetics mechanism to represent the effects of sorption of radionuclides in the rock matrix. The method is improved in its accuracy and provides results useful for the assessment of radionuclide migration in high‐level, radioactive waste repositories. Results including verification (analytical) and physical test simulations are given. These results provide a partial validation of the numerical model.
A semi‐implicit lagrangian scheme for 3D shallow water flow with a two‐layer turbulence model
Authors: Stansby Peter K. , Lloyd Peter M. 
Published: August 2005

AbstractA semi‐implicit Lagrangian finite difference scheme for 3D shallow water flow has been developed to include an eddy viscosity model for turbulent mixing in the vertical direction. The α‐co‐ordinate system for the vertical direction has been introduced to give accurate definition of bed and surface boundary conditions. The simple two‐layer mixing length model for rough surfaces is used with the standard assumption that the shear stress across the wall region at a given horizontal location is constant. The bed condition is thus defined only by its roughness height (avoiding the need for a friction formula relating to depth‐averaged flow, e.g. Chezy, used previously). The method is shown to be efficient and stable with an explicit Lagrangian formulation for convective terms and terms for surface elevation and vertical mixing handled implicitly. The method is applied to current flow around a circular island with gently sloping sides which produce periodic recirculation zones (vortex shedding). Comparisons are made with experimental measurements of velocity using laser Doppler anemometry (time histories at specific points) and surface particle‐tracking velocimetry.
Why you should not use ‘Hybrid’, ‘Power‐Law’ or related exponential schemes for convective modelling—there are much better alternatives
Authors: Leonard B. P. , Drummond J. E. 
Published: August 2005

AbstractIn many areas of computational fluid dynamics, especially numerical convective heat and mass transfer, the ‘Hybrid’ and ‘Power‐Law’ schemes have been widely used for many years. The popularity of these methods for steady‐state computations is based on a combination of algorithmic simplicity, fast convergence, and plausible looking results. By contrast, classical (second‐order central) methods often involve convergence problems and may lead to obviously unphysical solutions exhibiting spurious numerical oscillations. Hybrid, Power‐Law, and the exponential‐difference scheme on which they are based give reasonably accurate solutions for steady, quasi‐one‐dimensional flow (when the grid is aligned with the main flow direction). However, they are often also used, out of context, for flows oblique or skew to the grid, in which case, inherent artificial viscosity (or diffusivity) seriously degrades the solution. This is particularly trouble‐some in the case of recirculating flows, sometimes leading to qualitatively incorrect results—since the effective artificial numerical Reynolds (or Péclet) number may then be orders of magnitude less than the correct physical value. This is demonstrated in the case of thermally driven flow in tall cavities, where experimentally observed recirculation cells are not predicted by the exponential‐based schemes. Higher‐order methods correctly predict the onset of recirculation cells. In the past, higher‐order methods have not been popular because of convergence difficulties and a tendency to generate unphysical overshoots near (what should be) sharp, monotonic transitions. However, recent developments using robust deferred‐correction solution methods and simple flux‐limiter techniques have eliminated all of these difficulties. Highly accurate, physically correct solutions can now be obtained aptimum computational efficiency.
Recent advances towards an effective virtual‐pulse (VIP) explicit time integral methodology for general multidimensional thermal analysis
Authors: Tamma Kumar K. , Mei Y. , Chen X. , Sha D. 
Published: August 2005

AbstractRecent advances and progress towards the development of an effective Virtual‐Pulse (VIP) explicit time integral methodology of computation for applicability to general multidimensional non‐linear transient thermal analysis of structures and materials is overviewed. The computational methodology is derived from new and different perspectives and the theoretical basis as well as the practical applicability to multidimensional thermal analysis situations are detailed. The VIP methodology inherits improved accuracy and superior stability characteristics in comparison to the traditional approaches customarily employed by thermal analysts. With the notion of providing techniques for high‐speed computing environments and parallel architectures, the present approach is developed for such computations and also ideally suited for personal workstation computing environments. Results of the numerical test models for multidimensional problems validate the overall concepts for general applicability to thermal analysis situations.
Modelling of single shot induction heating by inverse finite element method
Authors: Maizza G. , Calì M. 
Published: August 2005

AbstractThe induction heating model described herein couples the standard heat conduction equation with electro‐magnetic proximity‐skin equations. An Inverse Finite Element procedure, which is based on prior deterministic and probabilistic concepts, has been designed to solve the inherent inverse equation model with respect to the unknown coil current parameter. Simulated experiments using different noises in the input data have been performed in order to determine their influence on the estimated parameter. The IFEM has shown its capability to predict the optimal location for the temperature sensors, together with their numbers, consistently with a pre‐specified estimate accuracy. Specifically, only one temperature sensor, located in the middle of the two turns of the coil, results to be sufficient to estimate the unknown parameter to a satisfactory accuracy degree. This, may significantly help to design optimal experiments.
Melting of a PCM inside a vertical cylindrical capsule
Authors: Wu Yong Ke , Lacroix Marcel 
Published: August 2005

AbstractA numerical study of natural convection melting of a phase change material within an isothermal vertical cylinder was conducted. The governing conservation equations are formulated in terms of a stream function, vorticity and temperature. Body‐fitted co‐ordinates are employed for tracking the irregular shape of the timewise changing solid–liquid phase front. Results show that the convective flow patterns and time evolution of the phase front, resulting from simultaneous bottom, side and top heating, are far more complicated than those for the melting from a single isothermal boundary. The heat transfer rate at the top surface is found to decrease monotonically to zero as convection is fully developed in the melt. The highest heat transfer rates are observed at the bottom surface where Bénard convective cells develop. Due to the convective motion of the melt along the vertical heated wall, the onset of Bénard convection occurs at a much earlier time than that for the case of melting within a cylinder heated from below.
Multidimensional upwinding: Its relation to finite elements
Authors: Carette J.‐C. , Deconinck H. , Paillere H. , Roe P. L. 
Published: August 2005

AbstractVertex‐based multidimensional upwind schemes for scalar advection are compared with shock‐capturing SUPG finite element methods based on linear triangular elements. Both methods share the same compact stencil and are formulated as cell‐wise residual distribution methods. The distribution for the finite element method is 1/3, supplemented with a Lax‐Wendrov‐type dissipation term, while the distribution for the upwind schemes is limited to the downstream nodes of the element. The multidimensional upwind schemes use positivity as the monotonicity criterion, while the finite element method includes a residual‐based non‐linear dissipation.For hyperbolic systems such as the compressible Euler equations the upwind method relies on a multidimensional wave model to decompose the residual into scalar contributions. From this observation a new SUPG formulation for systems is proposed in which the scalar SUPG method is applied to each of the decomposed residuals obtained from the wave model, thereby providing a better‐founded definition of the τ dissipation matrix and shock‐capturing term in the SUPG methods.
GMRES acceleration of iterative implicit finite element solvers for compressible Euler and Navier‐Stokes equations
Authors: Choquet Rémi , Leyland Pénélope , Tefy Tiana 
Published: August 2005

AbstractImplicit iterative schemes based on linearized and non‐linear Newton methods are discussed, with resolution of a matrix subsystem or a matrix‐free method by preconditioned GMRES algorithms. The defaults of convergence due to the locality of Newton algorithms can be partially overcome by using stabilizing descent techniques, restarting and global strategies such as line search backtracking procedures, or by tuning the iterations once the approximate Jacobians are closer to the exact ones. Comparison with a more conventional relaxation method and their implementation on parallel architectures are discussed.