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Flow Problems (flow + problem)
Kinds of Flow Problems Selected AbstractsUpper bounds for single-source uncapacitated concave minimum-cost network flow problemsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2003Dalila B. M. M. Fontes Abstract In this paper, we describe a heuristic algorithm based on local search for the Single-Source Uncapacitated (SSU) concave Minimum-Cost Network Flow Problem (MCNFP). We present a new technique for creating different and informed initial solutions to restart the local search, thereby improving the quality of the resulting feasible solutions (upper bounds). Computational results on different classes of test problems indicate the effectiveness of the proposed method in generating basic feasible solutions for the SSU concave MCNFP very near to a global optimum. A maximum upper bound percentage error of 0.07% is reported for all problem instances for which an optimal solution has been found by a branch-and-bound method. © 2003 Wiley Periodicals, Inc. [source] Are Debt and Incentive Compensation Substitutes in Controlling the Free Cash Flow Agency Problem?FINANCIAL MANAGEMENT, Issue 3 2009Yilei Zhang This paper investigates the governance implications of a firm's capital structure and managerial incentive compensation in controlling the free cash flow agency problem. The results suggest: debt and executive stock options act as substitutes in attenuating a firm's free cash flow problem; failure to incorporate the substitutability and endogeneity leads to underestimates of the magnitude and economic implication of the disciplinary role of both mechanisms; firm characteristics differ across the prevalence of debt usage versus option usage, suggesting the heterogeneity in the costs and benefits of the monitoring devices; and all the above effects are more pronounced in firms that tend to have more severe agency problem. [source] Accelerating the convergence of coupled geomechanical-reservoir simulationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2007L. Jeannin Abstract The pressure variations during the production of petroleum reservoir induce stress changes in and around the reservoir. Such changes of the stress state can induce marked deformation of geological structures for stress sensitive reservoirs as chalk or unconsolidated sand reservoirs. The compaction of those reservoirs during depletion affects the pressure field and so the reservoir productivity. Therefore, the evaluation of the geomechanical effects requires to solve in a coupling way the geomechanical problem and the reservoir multiphase fluid flow problem. In this paper, we formulate the coupled geomechanical-reservoir problem as a non-linear fixed point problem and improve the resolution of the coupling problem by comparing in terms of robustness and convergence different algorithms. We study two accelerated algorithms which are much more robust and faster than the conventional staggered algorithm and we conclude that they should be used for the iterative resolution of coupled reservoir-geomechanical problem. Copyright © 2006 John Wiley & Sons, Ltd. [source] Parallel eigenanalysis of multiaquifer systemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005L. Bergamaschi Abstract Finite element discretizations of flow problems involving multiaquifer systems deliver large, sparse, unstructured matrices, whose partial eigenanalysis is important for both solving the flow problem and analysing its main characteristics. We studied and implemented an effective preconditioning of the Jacobi,Davidson algorithm by FSAI-type preconditioners. We developed efficient parallelization strategies in order to solve very large problems, which could not fit into the storage available to a single processor. We report our results about the solution of multiaquifer flow problems on an SP4 machine and a Linux Cluster. We analyse the sequential and parallel efficiency of our algorithm, also compared with standard packages. Questions regarding the parallel solution of finite element eigenproblems are addressed and discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] A comparative study of GLS finite elements with velocity and pressure equally interpolated for solving incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009Yongtao Wei Abstract A comparative study of the bi-linear and bi-quadratic quadrilateral elements and the quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the stabilized finite element formulation of the Galerkin/least-squares method to simulate the flows, with the pressure and velocity fields interpolated with equal orders. The tangent matrices are explicitly derived and the Newton,Raphson algorithm is employed to solve the resulting nonlinear equations. The numerical solutions of the classical lid-driven cavity flow problem are obtained for Reynolds numbers between 1000 and 20 000 and the accuracy and converging rate of the different elements are compared. The influence on the numerical solution of the least square of incompressible condition is also studied. The numerical example shows that the quadratic triangular element exhibits a better compromise between accuracy and converging rate than the other two elements. Copyright © 2008 John Wiley & Sons, Ltd. [source] Discussions on driven cavity flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009Article first published online: 9 SEP 200, Ercan Erturk Abstract The widely studied benchmark problem, two-dimensional-driven cavity flow problem is discussed in detail in terms of physical and mathematical and also numerical aspects. A very brief literature survey on studies on the driven cavity flow is given. On the basis of several numerical and experimental studies, the fact of the matter is that physically the flow in a driven cavity is not two-dimensional above moderate Reynolds numbers. However, there exist numerical solutions for two-dimensional-driven cavity flow at high Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd. [source] A numerical approximation of the thermal coupling of fluids and solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Javier Principe Abstract In this article we analyze the problem of the thermal coupling of fluids and solids through a common interface. We state the global thermal problem in the whole domain, including the fluid part and the solid part. This global thermal problem presents discontinuous physical properties that depend on the solution of auxiliary problems on each part of the domain (a fluid flow problem and a solid state problem). We present a domain decomposition strategy to iteratively solve problems posed in both subdomains and discuss some implementation aspects of the algorithm. This domain decomposition framework is also used to revisit the use of wall function approaches used in this context. Copyright © 2008 John Wiley & Sons, Ltd. [source] One-dimensional simulation of supercritical flow at a confluence by means of a nonlinear junction model applied with the RKDG2 methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008G. Kesserwani Abstract We investigate the one-dimensional computation of supercritical open-channel flows at a combining junction. In such situations, the network system is composed of channel segments arranged in a branching configuration, with individual channel segments connected at a junction. Therefore, two important issues have to be addressed: (a) the numerical solution in branches, and (b) the internal boundary conditions treatment at the junction. Going from the advantageous literature supports of RKDG methods to a particular investigation for a supercritical benchmark, the second-order Runge,Kutta discontinuous Galerkin (RKDG2) scheme is selected to compute the water flow in branches. For the internal boundary handling, we propose a new approach by incorporating the nonlinear model derived from the conservation of the momentum through the junction. The nonlinear junction model was evaluated against available experiments and then applied to compute the junction internal boundary treatment for steady and unsteady flow applications. Finally, a combining flow problem is defined and simulated by the proposed framework and results are illustrated for many choices of junction angles. Copyright © 2007 John Wiley & Sons, Ltd. [source] Time-domain BEM solution of convection,diffusion-type MHD equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008N. Bozkaya Abstract The two-dimensional convection,diffusion-type equations are solved by using the boundary element method (BEM) based on the time-dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady-state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time-domain BEM solution procedure is tested on some convection,diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time-dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright © 2007 John Wiley & Sons, Ltd. [source] Simulations of the turbulent channel flow at Re, = 180 with projection-based finite element variational multiscale methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2007Volker John Abstract Projection-based variational multiscale (VMS) methods, within the framework of an inf,sup stable second order finite element method for the Navier,Stokes equations, are studied in simulations of the turbulent channel flow problem at Re, = 180. For comparison, the Smagorinsky large eddy simulation (LES) model with van Driest damping is included into the study. The simulations are performed on very coarse grids. The VMS methods give often considerably better results. For second order statistics, however, the differences to the reference values are sometimes rather large. The dependency of the results on parameters in the eddy viscosity model is much weaker for the VMS methods than for the Smagorinsky LES model with van Driest damping. It is shown that one uniform refinement of the coarse grids allows an underresolved direct numerical simulations (DNS). Copyright © 2007 John Wiley & Sons, Ltd. [source] Application of second-order adjoint technique for conduit flow problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007T. Kurahashi Abstract This paper presents the way to obtain the Newton gradient by using a traction given by the perturbation for the Lagrange multiplier. Conventionally, the second-order adjoint model using the Hessian/vector products expressed by the product of the Hessian matrix and the perturbation of the design variables has been researched (Comput. Optim. Appl. 1995; 4:241,262). However, in case that the boundary value would like to be obtained, this model cannot be applied directly. Therefore, the conventional second-order adjoint technique is extended to the boundary value determination problem and the second-order adjoint technique is applied to the conduit flow problem in this paper. As the minimization technique, the Newton-based method is employed. The Broyden,Fletcher,Goldfarb,Shanno (BFGS) method is applied to calculate the Hessian matrix which is used in the Newton-based method and a traction given by the perturbation for the Lagrange multiplier is used in the BFGS method. Copyright © 2007 John Wiley & Sons, Ltd. [source] Two preconditioners for saddle point problems in fluid flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007A. C. de Niet Abstract In this paper two preconditioners for the saddle point problem are analysed: one based on the augmented Lagrangian approach and another involving artificial compressibility. Eigenvalue analysis shows that with these preconditioners small condition numbers can be achieved for the preconditioned saddle point matrix. The preconditioners are compared with commonly used preconditioners from literature for the Stokes and Oseen equation and an ocean flow problem. The numerical results confirm the analysis: the preconditioners are a good alternative to existing ones in fluid flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Steady filtration problems with seawater intrusion: macro-hybrid penalized finite element approximationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2005Gonzalo Alduncin Abstract Macro-hybrid penalized finite element approximations are studied for steady filtration problems with seawater intrusion. On the basis of nonoverlapping domain decompositions with vertical interfaces, sections of coastal aquifers are decomposed into subsystems with simpler geometries and small scales, interconnected via transmission conditions of pressure and flux continuity. Corresponding local penalized formulations are derived from the global penalized variational formulation of the two-free boundary flow problem, with continuity transmission conditions modelled variationally in a dual sense. Then, macro-hybrid finite element approximations are derived for the system, defined on independent subdomain grids. Parallel relaxation penalty-duality algorithms are proposed from fixed-point problem characterizations. Numerical experiments exemplify the macro-hybrid penalized theory, showing a good agreement with previous primal conforming penalized finite element approximations (Comput. Methods Appl. Mech. Engng. 2000; 190:609,624). Copyright © 2005 John Wiley & Sons, Ltd. [source] A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier,Stokes equations on all-hexahedral elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2005Mehmet Sahin Abstract A new semi-staggered finite volume method is presented for the solution of the incompressible Navier,Stokes equations on all-quadrilateral (2D)/hexahedral (3D) meshes. The velocity components are defined at element node points while the pressure term is defined at element centroids. The continuity equation is satisfied exactly within each elements. The checkerboard pressure oscillations are prevented using a special filtering matrix as a preconditioner for the saddle-point problem resulting from second-order discretization of the incompressible Navier,Stokes equations. The preconditioned saddle-point problem is solved using block preconditioners with GMRES solver. In order to achieve higher performance FORTRAN source code is based on highly efficient PETSc and HYPRE libraries. As test cases the 2D/3D lid-driven cavity flow problem and the 3D flow past array of circular cylinders are solved in order to verify the accuracy of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd. [source] A promising boundary element formulation for three-dimensional viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005Xiao-Wei Gao Abstract In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd. [source] An improved direct labeling method for the max,flow min,cut computation in large hypergraphs and applicationsINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2003Joachim Pistorius Algorithms described so far to solve the maximum flow problem on hypergraphs first necessitate the transformation of these hypergraphs into directed graphs. The resulting maximum flow problem is then solved by standard algorithms. This paper describes a new method that solves the maximum flow problem directly on hypergraphs, leading to both reduced run time and lower memory requirements. We compare our approach with a state,of,the,art algorithm that uses a transformation of the hypergraph into a directed graph and an augmenting path algorithm to compute the maximum flow on this directed graph: the run,time complexity as well as the memory space complexity are reduced by a constant factor. Experimental results on large hypergraphs from VLSI applications show that the run time is reduced, on average, by a factor approximately 2, while memory occupation is reduced, on average, by a factor of 10. This improvement is particularly interesting for very large instances, to be solved in practical applications. [source] Corporate Cash Policy and How to Manage it with Stock RepurchasesJOURNAL OF APPLIED CORPORATE FINANCE, Issue 3 2008Amy Dittmar At the end of 2004 total U.S. corporate cash holdings reached an all-time high of just under $2 trillion,an amount equal to roughly 15% of the total U.S. GDP. And during the past 25 years, average cash holdings have jumped from 10% to 23% of total corporate assets. But at the same time their levels of cash have risen, U.S. companies have paid out dramatically increasing amounts of cash to buy back shares. This article addresses the following questions: What accounts for the dramatic increase in the average level of corporate cash holdings since 1980? And why do some companies keep so much cash (with one fourth of U.S. firms holding cash amounting to at least 36% of total assets) while others have so little (with another quarter having less than 3%)? Why do companies pay out excess cash in the form of stock repurchases (rather than, say, dividends), and what explains the significant increase in repurchases (both in absolute terms and relative to dividends) over time? The author begins by arguing that cash reserves provide companies with a buffer against possible shortfalls in operating profits,one that, especially during periods of financial trouble, can be used to avoid financial distress or provide funding for promising projects that might otherwise have to be put off. Such buffers are particularly valuable in the case of smaller, riskier companies with lots of growth opportunities and limited access to capital markets. And the dramatic increase in corporate cash holdings between 1980 and the present can be attributed mainly to an increase in the risk of publicly traded companies,an increase in risk that reflects in part a general increase in competition, but also a notable change over time in the kinds of companies (smaller, newer, less profitable, non-dividend paying firms) that have chosen to go public. At the other end of the corporate spectrum are large, relatively mature companies with limited growth opportunities. Although such companies tend to produce considerable free cash flow, they also tend to retain relatively small amounts of cash (as a percentage of total assets), in part because of shareholder concern about the corporate "free cash flow problem",the well-documented tendency of such companies to destroy value through overpriced (often diversifying) acquisitions and other misguided attempts to pursue growth at the expense of profitability. For companies with highly predictable earnings and investment plans, dividends provide one means of addressing the free cash flow problem. But for companies with more variable earnings and less predictable reinvestment, open-market stock repurchases provide a more flexible means of distributing cash to shareholders. Unlike the corporate "commitment" implied by dividend payments, an open market stock repurchase program creates what amounts to an option but not an obligation to distribute funds. The value of such flexibility, which increases during periods of increased risk and uncertainty, explains much of the apparent substitution of repurchases for dividends in recent years. [source] An optimal shape design formulation for inhomogeneous dam problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2002Abdelkrim Chakib In this paper, the flow problem of incompressible liquid through an inhomogeneous porous medium (say dam), with permeability allowing parametrization of the free boundary by a graph of continuous unidimensional function, is considered. We propose a new formulation on an optimal shape design problem. We show the existence of a solution of the optimal shape design problem. The finite element method is used to obtain numerical results which show the efficiency of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd. [source] Approximation algorithms for general one-warehouse multi-retailer systemsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2009Zuo-Jun Max Shen Abstract Logistical planning problems are complicated in practice because planners have to deal with the challenges of demand planning and supply replenishment, while taking into account the issues of (i) inventory perishability and storage charges, (ii) management of backlog and/or lost sales, and (iii) cost saving opportunities due to economies of scale in order replenishment and transportation. It is therefore not surprising that many logistical planning problems are computationally difficult, and finding a good solution to these problems necessitates the development of many ad hoc algorithmic procedures to address various features of the planning problems. In this article, we identify simple conditions and structural properties associated with these logistical planning problems in which the warehouse is managed as a cross-docking facility. Despite the nonlinear cost structures in the problems, we show that a solution that is within ,-optimality can be obtained by solving a related piece-wise linear concave cost multi-commodity network flow problem. An immediate consequence of this result is that certain classes of logistical planning problems can be approximated by a factor of (1 + ,) in polynomial time. This significantly improves upon the results found in literature for these classes of problems. We also show that the piece-wise linear concave cost network flow problem can be approximated to within a logarithmic factor via a large scale linear programming relaxation. We use polymatroidal constraints to capture the piece-wise concavity feature of the cost functions. This gives rise to a unified and generic LP-based approach for a large class of complicated logistical planning problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source] k -Splittable delay constrained routing problem: A branch-and-price approachNETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2010Jérôme Truffot Abstract Routing problems, which include a QoS-based path control, play a key role in broadband communication networks. We analyze here an algorithmic procedure based on branch-and-price algorithm and on the flow deviation method to solve a nonlinear k -splittable flow problem. The model can support end-to-end delay bounds on each path and we compare the behavior of the algorithm with and without these constraints. The trade-off between QoS guarantees and CPU time is clearly established and we show that minimizing the average delay on all arcs will yield solutions close to the optimal one at a significant computational saving. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010 [source] State-space partition techniques for multiterminal flows in stochastic networksNETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2006Matthew S. Daly Abstract This article develops state-space partition methods for computing performance measures for stochastic networks with demands between multiple pairs of nodes. The chief concern is the evaluation of the probability that there exist separate, noninteracting flows that satisfy all demands. This relates to the multiterminal maximum flow problem discussed in the classic article of Gomory and Hu. The network arcs are assumed to have independent, discrete random capacities. We refer to the probability that all demands can be satisfied as the network reliability (with the understanding that its definition is application dependent). In addition, we also consider the calculation of secondary measures, such as the probability that a particular subset of demands can be met, and the probability that a particular arc lies on a minimum cut. The evaluation of each of these probabilities is shown to be NP-hard. The proposed methods are based on an iterative partition of the system state space, with each iteration tightening the bounds on the measure of interest. This last property allows the design of increasingly efficient Monte Carlo sampling plans that yield substantially more precise estimators than the standard Monte Carlo method that draws samples from the original capacity distribution. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(2), 90,111 2006 [source] The multiroute maximum flow problem revisitedNETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2006Donglei Du Abstract We are given a directed network G = (V,A,u) with vertex set V, arc set A, a source vertex s , V, a destination vertex t , V, a finite capacity vector u = {uij}(i,j),A, and a positive integer m , Z+. The multiroute maximum flow problem (m -MFP) generalizes the ordinary maximum flow problem by seeking a maximum flow from s to t subject to not only the regular flow conservation constraints at the vertices (except s and t) and the flow capacity constraints at the arcs, but also the extra constraints that any flow must be routed along m arc-disjoint s - t paths. In this article, we devise two new combinatorial algorithms for m -MFP. One is based on Newton's method and another is based on an augmenting-path technique. We also show how the Newton-based algorithm unifies two existing algorithms, and how the augmenting-path algorithm is strongly polynomial for case m = 2. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(2), 81,92 2006 [source] A branch-and-cut algorithm for the single-commodity, uncapacitated, fixed-charge network flow problem,NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2003Francisco Ortega Abstract We present a branch-and-cut algorithm to solve the single-commodity, uncapacitated, fixed-charge network flow problem, which includes the Steiner tree problem, uncapacitated lot-sizing problems, and the fixed-charge transportation problem as special cases. The cuts used are simple dicut inequalities and their variants. A crucial problem when separating these inequalities is to find the right cut set on which to generate the inequalities. The prototype branch-and-cut system, bc,nd, includes a separation heuristic for the dicut inequalities and problem-specific primal heuristics, branching, and pruning rules. Computational results show that bc,nd is competitive compared to a variety of special purpose algorithms for problems with explicit flow costs. We also examine how general purpose MIP systems perform on such problems when provided with formulations that have been tightened a priori with dicut inequalities. © 2003 Wiley Periodicals, Inc. [source] A GRASP with path-relinking for private virtual circuit routing,NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2003Mauricio G. C. Resende Abstract A frame relay service offers virtual private networks to customers by provisioning a set of long-term private virtual circuits (PVCs) between customer endpoints on a large backbone network. During the provisioning of a PVC, routing decisions are made without any knowledge of future requests. Over time, these decisions can cause inefficiencies in the network and occasional offline rerouting of the PVCs is needed. In this paper, the offline PVC routing problem is formulated as an integer multicommodity flow problem with additional constraints and with an objective function that minimizes propagation delays and/or network congestion. We propose variants of a GRASP with path-relinking heuristic for this problem. Experimental results for realistic-size problems are reported, showing that the proposed heuristics are able to improve the solutions found with standard routing techniques. Moreover, the structure of our objective function provides a useful strategy for setting the appropriate value of its weight parameter, to achieve some quality of service (QoS) level defined by a desired balance between propagation delay and delay due to network congestion. © 2003 Wiley Periodicals, Inc. [source] Maximizing residual flow under an arc destructionNETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2001Y. P. Aneja Abstract In this paper, we consider two problems related to single-commodity flows on a directed network. In the first problem, for a given s , t flow, if an arc is destroyed, all the flow that is passing through that arc is destroyed. What is left flowing from s to t is the residual flow. The objective is to determine a flow pattern such that the residual flow is maximized. We provide a strongly polynomial algorithm for this problem, called the maximum residual flow problem, and consider various extensions of this basic model. In the second problem, known as the "most vital arc" problem, the objective is to remove an arc so that the maximal flow on the residual network is as small as possible. Results are also derived which help implement an efficient scheme for solving this problem. © 2001 John Wiley & Sons, Inc. [source] Error analysis of the L2 least-squares finite element method for incompressible inviscid rotational flows,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2004Chiung-Chiou Tsai Abstract In this article we analyze the L2 least-squares finite element approximations to the incompressible inviscid rotational flow problem, which is recast into the velocity-vorticity-pressure formulation. The least-squares functional is defined in terms of the sum of the squared L2 norms of the residual equations over a suitable product function space. We first derive a coercivity type a priori estimate for the first-order system problem that will play the crucial role in the error analysis. We then show that the method exhibits an optimal rate of convergence in the H1 norm for velocity and pressure and a suboptimal rate of convergence in the L2 norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source] The Tank Drainage Problem Revisited: Do These Equations Actually Work?THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 5 2003Donald D. Joye Abstract The tank drainage problem with pipeline attached is studied in this work. Laminar and turbulent formulations of this unsteady-state flow problem are derived and evaluated by experimental data. Additional literature models are also evaluated for comparison. Several experimental configurations were used including a small tank with a vertical tube, the same with various- sized orifices, a large tank with a horizontal pipe, and a large tank including a piping system with elbows, vertical drop and horizontal extension. Not all the models performed well under all conditions. Limitations of the models are discussed. The model derived by Loiacono and the model we derived (an exact equivalent) showed the best for both laminar and turbulent flow, predicting drainage times to better than ± 8%, on average. On a étudié dans ce travail le problème du drainage des réservoirs munis de conduites. Les formulations laminaires et turbulentes de ce problème d'écoulement en régime non permanent ont été calculées et évaluées à l'aide de données expérimentales. D'autres modèles venant de la littérature scientifique ont également été évalués à des fins de comparaison. Plusieurs configurations expérimentales ont été utilisées, notamment : un petit réservoir muni d'un tube vertical, le même réservoir comprenant des orifices de tailles diverses, un grand réservoir muni d'une conduite horizontale, un grand réservoir équipé d'un système de conduites ayant des coudes, une chute verticale et une extension horizontale. Tous les modèles n'ont pas donné de bons résultats dans toutes les conditions. Les limites des modèles sont analysées. Le modèle établi par Loiacono et le modèle que nous avons calculé (un équivalent strict) montrent le meilleur potentiel autant pour l'écoulement laminaire que turbulent, prédisant des temps de drainage jusqu'à plus ± 8% en moyenne. [source] Parallel operation of CartaBlanca on shared and distributed memory computersCONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 1 2004N. T. Padial-Collins Abstract We describe the parallel performance of the pure Java CartaBlanca code on heat transfer and multiphase fluid flow problems. CartaBlanca is designed for parallel computations on partitioned unstructured meshes. It uses Java's thread facility to manage computations on each of the mesh partitions. Inter-partition communications are handled by two compact objects for node-by-node communication along partition boundaries and for global reduction calculations across the entire mesh. For distributed calculations, the JavaParty package from the University of Karlsruhe is demonstrated to work with CartaBlanca. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stability and accuracy of power-series method for one-dimensional heat conduction with non-uniform grid systemsHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 7 2005Kazuhiro Fukuyo Abstract The power-series method, a finite analytic approach to heat transfer and fluid flow problems that is based on power-series expansion, was applied to a one-dimensional heat-conduction problem to evaluate its stability and accuracy. Application to a specific heat-conduction problem with non-uniform grid systems showed that it had stability within the ranges 10,5<,t,,xE, and ,xW,a<105, and 10,5<,<105. Comparison of its solutions with those by the fully implicit and Stefanovic,Stephan methods showed that this method yielded more accurate and robust solutions. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(7): 470,480, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20085 [source] Extension of weakly compressible approximations to incompressible thermal flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Mofdi El-Amrani Abstract Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831,847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge,Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||