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Test Problems (test + problem)
Kinds of Test Problems Selected AbstractsA linearized implicit pseudo-spectral method for some model equations: the regularized long wave equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003K. Djidjeli Abstract An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. =10pt An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations (Equation (2)), with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source] Coordinated Capacitated Lot-Sizing Problem with Dynamic Demand: A Lagrangian HeuristicDECISION SCIENCES, Issue 1 2004E. Powell Robinson Jr. ABSTRACT Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedure for the single-family coordinated capacitated lot-sizing problem with dynamic demand. The problem extends both the multi-item capacitated dynamic demand lot-sizing problem and the uncapacitated coordinated dynamic demand lot-sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual-based heuristic over linear programming-based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs. [source] Using High Hydraulic Conductivity Nodes to Simulate Seepage LakesGROUND WATER, Issue 2 2002Mary P. Anderson In a typical ground water flow model, lakes are represented by specified head nodes requiring that lake levels be known a priori. To remove this limitation, previous researchers assigned high hydraulic conductivity (K) values to nodes that represent a lake, under the assumption that the simulated head at the nodes in the high-K zone accurately reflects lake level. The solution should also produce a constant water level across the lake. We developed a model of a simple hypothetical ground water/lake system to test whether solutions using high-K lake nodes are sensitive to the value of K selected to represent the lake. Results show that the larger the contrast between the K of the aquifer and the K of the lake nodes, the smaller the error tolerance required for the solution to converge. For our test problem, a contrast of three orders of magnitude produced a head difference across the lake of 0.005 m under a regional gradient of the order of 10,3 m/m, while a contrast of four orders of magnitude produced a head difference of 0.001 m. The high-K method was then used to simulate lake levels in Pretty Lake, Wisconsin. Results for both the hypothetical system and the application to Pretty Lake compared favorably with results using a lake package developed for MODFLOW (Merritt and Konikow 2000). While our results demonstrate that the high-K method accurately simulates lake levels, this method has more cumbersome postprocessing and longer run times than the same problem simulated using the lake package. [source] Numerical simulation of the forest impact on aquifersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2004A. Leontiev Abstract Here we propose a numerical method for the computer simulation of forest impact on aquifers. With this phenomenon we understand changes in the level of groundwater table beneath the areas recovered by trees. The mathematical model of the forest impact includes a boundary value problem with free and contact boundary conditions. Considering this free-contact boundary problem as a shape optimization problem we perform boundary elements discretization. Assuming the state and free boundary variables as independents, we treat the discretized problem as a non-linear mathematical program and apply interior point algorithm to solve it. Numerical results for an illustrative 2D test problem are discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source] Accelerating iterative solution methods using reduced-order models as solution predictorsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006R. Markovinovi Abstract We propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess for the iterative process based on information in the solution vectors from previous time steps. The algorithm basically consists of two projection steps: (1) projecting the governing equations onto a subspace spanned by a low number of global empirical basis functions extracted from previous time step solutions, and (2) solving the governing equations in this reduced space and projecting the solution back on the original, high dimensional one. We applied the algorithm to numerical models for simulation of two-phase flow through heterogeneous porous media. In particular we considered implicit-pressure explicit-saturation (IMPES) schemes and investigated the scope to accelerate the iterative solution of the pressure equation, which is by far the most time-consuming part of any IMPES scheme. We achieved a substantial reduction in the number of iterations and an associated acceleration of the solution. Our largest test problem involved 93 500 variables, in which case we obtained a maximum reduction in computing time of 67%. The method is particularly attractive for problems with time-varying parameters or source terms. Copyright © 2006 John Wiley & Sons, Ltd. [source] Solving time-dependent PDEs using the material point method, a case study from gas dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010L. T. Tran Abstract The material point method (MPM) developed by Sulsky and colleagues is currently being used to solve many challenging problems involving large deformations and/or fragementations with some success. In order to understand the properties of this method, an analysis of the considerable computational properties of MPM is undertaken in the context of model problems from gas dynamics. The MPM method in the form used here is shown both theoretically and computationally to have first-order accuracy for a standard gas dynamics test problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] A finite-volume particle method for conservation laws on moving domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008D. Teleaga Abstract The paper deals with the finite-volume particle method (FVPM), a relatively new method for solving hyperbolic systems of conservation laws. A general formulation of the method for bounded and moving domains is presented. Furthermore, an approximation property of the reconstruction formula is proved. Then, based on a two-dimensional test problem posed on a moving domain, a special Ansatz for the movement of the particles is proposed. The obtained numerical results indicate that this method is well suited for such problems, and thus a first step to apply the FVPM to real industrial problems involving free boundaries or fluid,structure interaction is taken. Finally, we perform a numerical convergence study for a shock tube problem and a simple linear advection equation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical computation of three-dimensional incompressible Navier,Stokes equations in primitive variable form by DQ methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2003C. Shu Abstract In this paper, the global method of differential quadrature (DQ) is applied to solve three-dimensional Navier,Stokes equations in primitive variable form on a non-staggered grid. Two numerical approaches were proposed in this work, which are based on the pressure correction process with DQ discretization. The essence in these approaches is the requirement that the continuity equation must be satisfied on the boundary. Meanwhile, suitable boundary condition for pressure correction equation was recommended. Through a test problem of three-dimensional driven cavity flow, the performance of two approaches was comparatively studied in terms of the accuracy. The numerical results were obtained for Reynolds numbers of 100, 200, 400 and 1000. The present results were compared well with available data in the literature. In this work, the grid-dependence study was done, and the benchmark solutions for the velocity profiles along the vertical and horizontal centrelines were given. Copyright © 2003 John Wiley & Sons, Ltd. [source] Coupled lubrication and Stokes flow finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003Matthew S. Stay Abstract A method is developed for performing a local reduction of the governing physics for fluid problems with domains that contain a combination of narrow and non-narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the fluid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two-dimensional Navier,Stokes equations to the one-dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non-narrow region with boundary conditions on the mass and momentum flux. The localized reduction technique, termed ,stitching,' is demonstrated on Stokes flow for various geometries of the hydrodynamic journal bearing,a non-trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes,Reynolds method is illustrated on an industrially applicable fully-flooded deformable-roll coating example. The examples in this paper are limited to two-dimensional Stokes flow, but extension to three-dimensional and Navier,Stokes flow is possible. Copyright © 2003 John Wiley & Sons, Ltd. [source] Dispersion analysis of the least-squares finite-element shallow-water systemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003D. Y. Le Roux Abstract The frequency or dispersion relation for the least-squares mixed formulation of the shallow-water equations is analysed. We consider the use of different approximation spaces corresponding to co-located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd. [source] Branch-and-Price Methods for Prescribing Profitable Upgrades of High-Technology Products with Stochastic Demands*DECISION SCIENCES, Issue 1 2004Purushothaman Damodaran ABSTRACT This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high-technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch-and-price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer "what if" questions. [source] A Stable and Efficient Numerical Algorithm for Unconfined Aquifer AnalysisGROUND WATER, Issue 4 2009Elizabeth Keating The nonlinearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to the solution of Richard's equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table, does not require "dry" cells to convert to inactive cells, and allows recharge to flow through relatively dry cells to the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem as well. [source] Development of a technique for modelling clay liner desiccationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2003Y. Zhou Abstract This paper presents a model for the analysis of clay liner desiccation in a landfill barrier system due to temperature effects. The model incorporates consideration of fully coupled heat-moisture-air flow, a non-linear constitutive relationship, the dependence of void ratio and volumetric water content on stress, capillary pressure and temperature, and the effect of mechanical deformation on all governing equations. Mass conservative numerical schemes are proposed to improve the accuracy of the finite element solution to the governing equations. The application of the model is then demonstrated by examining three test problems, including isothermal infiltration, heat conduction and non-isothermal water and heat transport. Comparisons are made with results from literature, and good agreement is observed. Copyright © 2003 John Wiley & Sons, Ltd. [source] A new approach to avoid excessive numerical diffusion in Eulerian,Lagrangian methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008A. Younes Abstract Lumping is often used to avoid non-physical oscillations for advection,dispersion equations but is known to add numerical diffusion. A new approach is detailed in order to avoid excessive numerical diffusion in Eulerian,Lagrangian methods when several time steps are used. The basic idea of this approach is to keep the same characteristics during all time steps and to interpolate only the concentration variations due to the dispersion process. In this way, numerical diffusion due to the lumping is removed at the end of each time step. The method is combined with the Eulerian,Lagrangian localized adjoint method (ELLAM) which is a mass conservative characteristic method for solving the advection,dispersion equation. Two test problems are modelled to compare the proposed method to the consistent, the full and the selective lumping approaches for linear and non-linear transport equations. Copyright © 2007 John Wiley & Sons, Ltd. [source] An integral-collocation-based fictitious-domain technique for solving elliptic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008N. Mai-Duy Abstract This paper presents a new fictitious-domain technique for numerically solving elliptic second-order partial differential equations (PDEs) in complex geometries. The proposed technique is based on the use of integral-collocation schemes and Chebyshev polynomials. The boundary conditions on the actual boundary are implemented by means of integration constants. The method works for both Dirichlet and Neumann boundary conditions. Several test problems are considered to verify the technique. Numerical results show that the present method yields spectral accuracy for smooth (analytic) problems. Copyright © 2007 John Wiley & Sons, Ltd. [source] An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2008N. Mai-Duy Abstract In this paper, a new numerical scheme based on non-overlapping domain decompositions and integrated Chebyshev approximations for solving elliptic differential equations (DEs) is presented. The distinguishing feature of the present scheme is that it achieves a Cp continuous solution across the interfaces (p is the order of the DE). Several test problems are employed to verify the method. The obtained results indicate that the achievement of higher-order smoothness leads to a significant improvement in accuracy. Copyright © 2007 John Wiley & Sons, Ltd. [source] A second order discontinuous Galerkin method for advection on unstructured triangular meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2003H. J. M. Geijselaers Abstract In this paper the advection of element data which are linearly distributed inside the elements is addressed. Across element boundaries the data are assumed discontinuous. The equations are discretized by the Discontinuous Galerkin method. For stability and accuracy at large step sizes (large values of the Courant number), the method is extended to second order. Furthermore the equations are enriched with selective implicit terms. This results in an explicit and local advection scheme, which is stable and accurate for Courant numbers less than .95 on unstructured triangle meshes. Results are shown of some pure advection test problems. Copyright © 2003 John Wiley & Sons, Ltd. [source] A new 3-node triangular flat shell elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2002J. G. Kim Abstract The purpose of this work is to propose a new 3-node triangular flat shell element with 18 degrees of freedom. The element is constructed by superimposing the local membrane formulation due to Bergan and Felippa with the well-known DKT bending formulation due to Batoz. The numerical performance of the present element has been compared with several reported 18 degrees-of-freedom triangular shell elements in a number of benchmark test problems. Copyright © 2002 John Wiley & Sons, Ltd. [source] A mixed finite element for plate bending with eight enhanced strain modesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2001Reinhard Piltner Abstract A low-order thick and thin plate bending element is derived using bilinear approximations for the transverse deflection, the two rotations and the thickness change. The stress,strain relationships from three-dimensional elasticity are used without any modifications. In order to avoid locking and to improve the accuracy of the results eight enhanced strain modes are used. For an efficient implementation of the mixed element, orthogonal stress and strain functions are utilized. Although the element is a low-order finite element the numerical results for a series of standard test problems are excellent. Copyright © 2001 John Wiley & Sons, Ltd. [source] Hybrid finite element/volume method for shallow water equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Shahrouz Aliabadi Abstract A hybrid numerical scheme based on finite element and finite volume methods is developed to solve shallow water equations. In the recent past, we introduced a series of hybrid methods to solve incompressible low and high Reynolds number flows for single and two-fluid flow problems. The present work extends the application of hybrid method to shallow water equations. In our hybrid shallow water flow solver, we write the governing equations in non-conservation form and solve the non-linear wave equation using finite element method with linear interpolation functions in space. On the other hand, the momentum equation is solved with highly accurate cell-center finite volume method. Our hybrid numerical scheme is truly a segregated method with primitive variables stored and solved at both node and element centers. To enhance the stability of the hybrid method around discontinuities, we introduce a new shock capturing which will act only around sharp interfaces without sacrificing the accuracy elsewhere. Matrix-free GMRES iterative solvers are used to solve both the wave and momentum equations in finite element and finite volume schemes. Several test problems are presented to demonstrate the robustness and applicability of the numerical method. Copyright © 2010 John Wiley & Sons, Ltd. [source] Axial symmetric elasticity analysis in non-homogeneous bodies under gravitational load by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009Yoshihiro Ochiai Abstract In general, internal cells are required to solve elasticity problems by involving a gravitational load in non-homogeneous bodies with variable mass density when using a conventional boundary element method (BEM). Then, the effect of mesh reduction is not achieved and one of the main merits of the BEM, which is the simplicity of data preparation, is lost. In this study, it is shown that the domain cells can be avoided by using the triple-reciprocity BEM formulation, where the density of domain integral is expressed in terms of other fields that are represented by boundary densities and/or source densities at isolated interior points. Utilizing the rotational symmetry, the triple-reciprocity BEM formulation is developed for axially symmetric elasticity problems in non-homogeneous bodies under gravitational force. A new computer program was developed and applied to solve several test problems. Copyright © 2008 John Wiley & Sons, Ltd. [source] An adaptive multiresolution method for parabolic PDEs with time-step controlINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009M. O. Domingues Abstract We present an efficient adaptive numerical scheme for parabolic partial differential equations based on a finite volume (FV) discretization with explicit time discretization using embedded Runge,Kutta (RK) schemes. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. Compact RK methods of second and third order are then used to choose automatically the new time step while controlling the approximation error in time. Non-admissible choices of the time step are avoided by limiting its variation. The implementation of the multiresolution representation uses a dynamic tree data structure, which allows memory compression and CPU time reduction. This new numerical scheme is validated using different classical test problems in one, two and three space dimensions. The gain in memory and CPU time with respect to the FV scheme on a regular grid is reported, which demonstrates the efficiency of the new method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Higher-resolution convection schemes for flow in porous media on highly distorted unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008Sadok Lamine Abstract Higher-resolution schemes are presented for convective flow approximation on highly distorted unstructured grids. The schemes are coupled with continuous full-tensor Darcy-flux approximations. A sequence of non-uniform and distorted grid formulations are developed and compared for a range of unstructured meshes with variable grid spacing. The higher-order schemes are constructed using non-uniform grid slope limiters such that they are stable with a local maximum principle, ensuring that solutions are free of spurious oscillations. Benefits of the resulting schemes are demonstrated for classical test problems in reservoir simulation including cases with full-tensor permeability fields. The test cases involve a range of unstructured grids with variations in grid spacing, orientation and permeability that lead to flow fields that are poorly resolved by standard simulation methods. The higher-order formulations are shown to effectively reduce numerical diffusion, leading to improved resolution of concentration and saturation fronts. Copyright © 2008 John Wiley & Sons, Ltd. [source] Discrete element method for modelling solid and particulate materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2007Federico A. Tavarez Abstract The discrete element method (DEM) is developed in this study as a general and robust technique for unified two-dimensional modelling of the mechanical behaviour of solid and particulate materials, including the transition from solid phase to particulate phase. Inter-element parameters (contact stiffnesses and failure criteria) are theoretically established as functions of element size and commonly accepted material parameters including Young's modulus, Poisson's ratio, ultimate tensile strength, and fracture toughness. A main feature of such an approach is that it promises to provide convergence with refinement of a DEM discretization. Regarding contact failure, an energy criterion based on the material's ultimate tensile strength and fracture toughness is developed to limit the maximum contact forces and inter-element relative displacement. This paper also addresses the issue of numerical stability in DEM computations and provides a theoretical method for the determination of a stable time-step. The method developed herein is validated by modelling several test problems having analytic solutions and results show that indeed convergence is obtained. Moreover, a very good agreement with the theoretical results is obtained in both elastic behaviour and fracture. An example application of the method to high-speed penetration of a concrete beam is also given. Copyright © 2006 John Wiley & Sons, Ltd. [source] A structural damage identification method based on genetic algorithm and vibrational dataINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2007Carlos C. H. Borges Abstract The problem of damage identification in framed structures using vibrational data is considered. The identification problem is modelled as an optimization task and the use of measured natural frequencies as well as modeshape information in the construction of objective functions is discussed. In a first attempt, a standard genetic algorithm is shown to be ineffective in obtaining the correct damage distribution in test problems. Using domain knowledge, modifications are introduced in the coding process, in the initial population generation, in the fitness function, and in the genetic operators, leading to a promising tool to solve this class of problems. Synthetic problems, with the addition of noise in the simulated measured data associated with the damaged structure, are analysed in order to assess the capability of the proposed technique. Copyright © 2006 John Wiley & Sons, Ltd. [source] Topology optimization by a neighbourhood search method based on efficient sensitivity calculationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006K. Svanberg Abstract This paper deals with topology optimization of discretized load-carrying continuum structures, where the design of the structure is represented by binary design variables indicating material or void in the various finite elements. Efficient exact methods for discrete sensitivity calculations are developed. They utilize the fact that if just one or two binary variables are changed to their opposite binary values then the new stiffness matrix is essentially just a low-rank modification of the old stiffness matrix, even if some nodes in the structure may disappear or re-enter. As an application of these efficient sensitivity calculations, a new neighbourhood search method is presented, implemented, and applied on some test problems, one of them with 6912 nine-node finite elements where the von Mises stress in each non-void element is considered. Copyright © 2006 John Wiley & Sons, Ltd. [source] Insight into the flow-condition-based interpolation finite element approach: solution of steady-state advection,diffusion problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005Haruhiko Kohno Abstract The flow-condition-based interpolation (FCBI) finite element approach is studied in the solution of advection,diffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advection,diffusion equation is embedded into the interpolation, and in the second scheme, the link-cutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Péclet number flows. The procedures have been implemented for two-dimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI solution approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Reduced modified quadratures for quadratic membrane finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2004Craig S. Long Abstract Reduced integration is frequently used in evaluating the element stiffness matrix of quadratically interpolated finite elements. Typical examples are the serendipity (Q8) and Lagrangian (Q9) membrane finite elements, for which a reduced 2 × 2 Gauss,Legendre integration rule is frequently used, as opposed to full 3 × 3 Gauss,Legendre integration. This ,softens' these element, thereby increasing accuracy, albeit at the introduction of spurious zero energy modes on the element level. This is in general not considered problematic for the ,hourglass' mode common to Q8 and Q9 elements, since this spurious mode is non-communicable. The remaining two zero energy modes occurring in the Q9 element are indeed communicable. However, in topology optimization for instance, conditions may arise where the non-communicable spurious mode associated with the elements becomes activated. To effectively suppress these modes altogether in elements employing quadratic interpolation fields, two modified quadratures are employed herein. For the Q8 and Q9 membrane elements, the respective rules are a five and an eight point rule. As compared to fully integrated elements, the new rules enhance element accuracy due to the introduction of soft, higher-order deformation modes. A number of standard test problems reveal that element accuracy remains comparable to that of the under-integrated counterparts. Copyright © 2004 John Wiley & Sons, Ltd. [source] A spline strip kernel particle method and its application to two-dimensional elasticity problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003K. M. Liew Abstract In this paper we present a novel spline strip kernel particle method (SSKPM) that has been developed for solving a class of two-dimensional (2D) elasticity problems. This new approach combines the concepts of the mesh-free methods and the spline strip method. For the interpolation of the assumed displacement field, we employed the kernel particle shape functions in the transverse direction, and the B3 -spline function in the longitudinal direction. The formulation is validated on several beam and semi-infinite plate problems. The numerical results of these test problems are then compared with the existing solutions obtained by the exact or numerical methods. From this study we conclude that the SSKPM is a potential alternative to the classical finite strip method (FSM). Copyright © 2003 John Wiley & Sons, Ltd. [source] A Galerkin/least-squares finite element formulation for consolidationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2001A. Truty Abstract A Galerkin/least-squares (GLS) finite element formulation for problem of consolidation of fully saturated two-phase media is presented. The elimination of spurious pressure oscillations appearing at the early stage of consolidation for standard Galerkin finite elements with equal interpolation order for both displacements and pressures is the goal of the approach. It will be shown that the least-squares term, based exclusively on the residuum of the fluid flow continuity equation, added to the standard Galerkin formulation enhances its stability and can fully eliminate pressure oscillations. A reasonably simple framework designed for derivation of one-dimensional as well as multi-dimensional estimates of the stabilization factor is proposed and then verified. The formulation is validated on one-dimensional and then on two-dimensional, linear and non-linear test problems. The effect of the fluid incompressibility as well as compressibility will be taken into account and investigated. Copyright © 2001 John Wiley & Sons Ltd. [source] | ||||||||||||||||