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Mesh Refinement (mesh + refinement)
Kinds of Mesh Refinement Selected Abstracts2-D numerical simulation of differential viscoelastic fluids in a single-screw continuous mixer: Application of viscoelastic finite element methodsADVANCES IN POLYMER TECHNOLOGY, Issue 1 2003Robin K. Connelly Abstract Viscoelastic effects on mixing flows obtained with kneading paddles in a single-screw, continuous mixer were explored using 2-D finite element method numerical simulations. The single-mode Phan,Thien Tanner nonlinear, viscoelastic fluid model was used with parameters for a dough-like material. The viscoelastic limits of the simulations were found using elastic viscous stress splitting, 4 × 4 sub-elements for stress, streamline upwind, and streamline upwind Petrov,Galerkin (SUPG). Mesh refinement and comparison between methods was also done. The single-screw mixer was modeled by taking the kneading paddle as the point of reference, fixing the mesh in time. Rigid rotation and no slip boundary conditions at the walls were used with inertia taken into account. Results include velocity, pressure, and stress profiles. The addition of viscoelasticity caused the shear and normal stresses to vary greatly from the viscous results, with a resulting loss of symmetry in the velocity and pressure profiles in the flow region. © 2003 Wiley Periodicals, Inc. Adv Polym Techn 22: 22,41, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.10038 [source] Toward anisotropic mesh construction and error estimation in the finite element methodNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2002Gerd Kunert Abstract Directional, anisotropic features like layers in the solution of partial differential equations can be resolved favorably by using anisotropic finite element meshes. An adaptive algorithm for such meshes includes the ingredients Error estimation and Information extraction/Mesh refinement. Related articles on a posteriori error estimation on anisotropic meshes revealed that reliable error estimation requires an anisotropic mesh that is aligned with the anisotropic solution. To obtain anisotropic meshes the so-called Hessian strategy is used, which provides information such as the stretching direction and stretching ratio of the anisotropic elements. This article combines the analysis of anisotropic information extraction/mesh refinement and error estimation (for several estimators). It shows that the Hessian strategy leads to well-aligned anisotropic meshes and, consequently, reliable error estimation. The underlying heuristic assumptions are given in a stringent yet general form. Numerical examples strengthen the exposition. Hence the analysis provides further insight into a particular aspect of anisotropic error estimation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 625,648, 2002; DOI 10.1002/num.10023 [source] The validation of some methods of notch fatigue analysisFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2000Taylor This paper is concerned with the testing and validation of certain methods of notch analysis which the authors have developed theoretically in earlier publications. These methods were developed for use with finite element (FE) analysis in order to predict the fatigue limits of components containing stress concentrations. In the present work we tested and compared these methods using data from standard notches taken from the literature, covering a range of notch geometries, loading types, R -ratios and materials: a total of 47 different data sets were analysed. The greatest predictive success was achieved with critical-distance methods known as the point, line and area methods: 94% of these predictions fell within 20% of the experimental fatigue limits. This was a significant improvement on previous methods of this kind, e.g. that of Klesnil and Lucas [(1980) Fatigue of Metallic Materials, Elsevier Science]. Methods based on the Smith and Miller [(1978) Int. J. Mech. Sci. 20, 201,206] concept of crack-like notches were successful in 42% of cases; they experienced difficulties dealing with very small notches, and could be improved by using an ElHaddad-type correction factor, giving 87% success. An approach known as ,crack modelling' allowed the Smith and Miller method to be used with non-standard stress concentrations, where notch geometry is ill defined; this modification, with the same short-crack correction, had 68% success. It was concluded that the critical-distance approach is more accurate and can be more easily used to analyse components of complex shape, however, the crack modelling approach is sometimes preferable because it can be used with less mesh refinement. [source] Dynamic non-planar crack rupture by a finite volume methodGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007M. Benjemaa SUMMARY Modelling dynamic rupture for complex geometrical fault structures is performed through a finite volume method. After transformations for building up the partial differential system following explicit conservative law, we design an unstructured bi-dimensional time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. On these complex surfaces, boundary conditions are set on stress fluxes and not on stress values. Prescribed rupture velocity gives accurate solutions with respect to analytical ones depending on the mesh refinement, while solutions for spontaneous propagation are analysed through numerical means. An example of non-planar spontaneous fault growth in heterogeneous media demonstrates the good behaviour of the proposed algorithm as well as specific difficulties of such numerical modelling. [source] Arbitrary Lagrangian,Eulerian method for large-strain consolidation problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2008Majidreza Nazem Abstract In this paper, an arbitrary Lagrangian,Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore-water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated-Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] The modelling of anchors using the material point methodINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2005C. J. Coetzee Abstract The ultimate capacity of anchors is determined using the material point method (MPM). MPM is a so-called meshless method capable of modelling large displacements, deformations and contact between different bodies. A short introduction to MPM is given and the derivation of the discrete governing equations. The analysis of a vertically loaded anchor and one loaded at 45° is presented. The load,displacement curves are compared to that obtained from experiments and the effect of soil stiffness and anchor roughness is investigated. The results of the vertically loaded anchor are also compared to an analytical solution. The displacement of the soil surface above the anchor was measured and compared to the numerical predictions. Convergence with mesh refinement is demonstrated and the effect of mesh size and dilatancy angle on the shear band width and orientation is indicated. The results show that MPM can model anchor pull out successfully. No special interface elements are needed to model the anchor,soil interface and the predicted ultimate capacities were within 10% of the measured values. Copyright © 2005 John Wiley & Sons, Ltd. [source] Propagation of longest-edge mesh patterns in local adaptive refinementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2008J. P. Suárez Abstract We examine the propagation of local adaptive mesh refinement (AMR) under a longest edge conformity scheme. Supporting numerical studies are included and discussed. Of specific interest is the statistical behaviour of the propagation zone in AMR of simplicial meshes. To this end three propagation metrics are used: the total number of original triangles in the propagation paths emanating from any target element, the longest individual edge path, and the extent of secondary refinement due to the conformity. Copyright © 2006 John Wiley & Sons, Ltd. [source] Efficient finite element simulation of crack propagation using adaptive iterative solversINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2006A. Meyer Abstract This paper delivers an efficient solution technique for the numerical simulation of crack propagation of 2D linear elastic formulations based on finite elements together with the conjugate gradient method in order to solve the corresponding linear equation systems. The developed iterative numerical approach using hierarchical preconditioners has the interesting feature that the hierarchical data structure will not be destroyed during crack propagation. Thus, it is possible to simulate crack advance in a very effective numerical manner, including adaptive mesh refinement and mesh coarsening. Test examples are presented to illustrate the efficiency of the given approach. Numerical simulations of crack propagation are compared with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source] A modified node-to-segment algorithm passing the contact patch testINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009Giorgio Zavarise Abstract Several investigations have shown that the classical one-pass node-to-segment (NTS) algorithms for the enforcement of contact constraints fail the contact patch test. This implies that the algorithms may introduce solution errors at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method to exactly enforce the contact geometry conditions. The situation is even worse with the penalty method, due to its inherent approximation that yields a solution affected by a non-zero penetration. The aim of this study is to analyze and improve the contact patch test behavior of the one-pass NTS algorithm used in conjunction with the penalty method for 2D frictionless contact. The paper deals with the case of linear elements. For this purpose, several sequential modifications of the basic formulation have been considered, which yield incremental improvements in results of the contact patch test. The final proposed formulation is a modified one-pass NTS algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method. In other words, this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration. Copyright © 2009 John Wiley & Sons, Ltd. [source] An extended finite element method with analytical enrichment for cohesive crack modelingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009James V. CoxArticle first published online: 28 NOV 200 Abstract A recent approach to fracture modeling has combined the extended finite element method (XFEM) with cohesive zone models. Most studies have used simplified enrichment functions to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. In this study enrichment functions based upon an existing analytical investigation of the cohesive crack problem are proposed. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation and enrichment functions are discussed. A parameter study for a simple mode I model problem is presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. The effects of mesh refinement and mesh orientation are considered. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are examined. The analysis results indicate that the analytically based enrichment functions can accurately track the cohesive crack propagation of a mode I crack independent of mesh orientation. A mixed mode example further demonstrates the potential of the formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2009Rolf Mahnken Abstract Functionally graded materials (FGMs) are advanced materials that possess continuously graded properties, such that the growth of cracks is strongly dependent on the gradation of the material. In this work a thermodynamic consistent framework for crack propagation in FGMs is presented, by applying a dissipation inequality to a time-dependent migrating control volume. The direction of crack growth is obtained in terms of material forces as a result of the principle of maximum dissipation. In the numerical implementation a staggered algorithm,deformation update for fixed geometry followed by geometry update for fixed deformation,is employed within each time increment. The geometry update is a result of the incremental crack propagation, which is driven by material forces. The corresponding mesh is generated by combining Delaunay triangulation with local mesh refinement. Furthermore a Newton algorithm is proposed, taking into account mesh transfer of displacements for crack propagation in incremental elasticity. In two numerical examples brittle crack propagation in FGMs is investigated for various directions of strength gradation within the structures. Copyright © 2008 John Wiley & Sons, Ltd. [source] Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2009Yasushi Ito Abstract An octree-based mesh generation method is proposed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy-to-implement, easy-to-understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes. A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly. Laplacian-like smoothing, angle-based smoothing and local optimization-based untangling methods are used with certain restrictions to further improve the mesh quality. Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries. Copyright © 2008 John Wiley & Sons, Ltd. [source] A posteriori error estimation for extended finite elements by an extended global recoveryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008Marc Duflot Abstract This contribution presents an extended global derivative recovery for enriched finite element methods (FEMs), such as the extended FEM along with an associated error indicator. Owing to its simplicity, the proposed scheme is ideally suited to industrial applications. The procedure is based on global minimization of the L2 norm of the difference between the raw strain field (C,1) and the recovered (C0) strain field. The methodology engineered in this paper extends the ideas of Oden and Brauchli (Int. J. Numer. Meth. Engng 1971; 3) and Hinton and Campbell (Int. J. Numer. Meth. Engng 1974; 8) by enriching the approximation used for the construction of the recovered derivatives (strains) with the gradients of the functions employed to enrich the approximation employed for the primal unknown (displacements). We show linear elastic fracture mechanics examples, both in simple two-dimensional settings, and for a three-dimensional structure. Numerically, we show that the effectivity index of the proposed indicator converges to unity upon mesh refinement. Consequently, the approximate error converges to the exact error, indicating that the error indicator is valid. Additionally, the numerical examples suggest a novel adaptive strategy for enriched approximations in which the dimensions of the enrichment zone are first increased, before standard h - and p -adaptivities are applied; we suggest to coin this methodology e-adaptivity. Copyright © 2008 John Wiley & Sons, Ltd. [source] Approximation of Cahn,Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C1 elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008Roy H. Stogner Abstract A variational formulation and C1 finite element scheme with adaptive mesh refinement and coarsening are developed for phase-separation processes described by the Cahn,Hilliard diffuse interface model of transport in a mixture or alloy. The adaptive scheme is guided by a Laplacian jump indicator based on the corresponding term arising from the weak formulation of the fourth-order non-linear problem, and is implemented in a parallel solution framework. It is then applied to resolve complex evolving interfacial solution behavior for 2D and 3D simulations of the classic spinodal decomposition problem from a random initial mixture and to other phase-transformation applications of interest. Simulation results and adaptive performance are discussed. The scheme permits efficient, robust multiscale resolution and interface characterization. Copyright © 2008 John Wiley & Sons, Ltd. [source] Parametric enrichment adaptivity by the extended finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2008Haim Waisman Abstract An adaptive method within the extended finite element method (XFEM) framework which adapts the enrichment function locally to the physics of a problem, as opposed to polynomial or mesh refinement, is presented. The method minimizes a local residual and determines the parameters of the enrichment function. We consider an energy form and a ,strong' form of the residual as error measures to drive the algorithm. Numerical examples for boundary layers and solid mechanics problems illustrate that the procedure converges. Moreover, when only the character of the solution is known, a good approximation is obtained in the area of interest. It is also shown that the method can be used to determine the order of singularities in solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Variational h -adaption in finite deformation elasticity and plasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007J. Mosler Abstract We ropose a variational h -adaption strategy in which the evolution of the mesh is driven directly by the governing minimum principle. This minimum principle is the principle of minimum potential energy in the case of elastostatics; and a minimum principle for the incremental static problem of elasto-viscoplasticity. In particular, the mesh is refined locally when the resulting energy or incremental pseudo-energy released exceeds a certain threshold value. In order to avoid global recomputes, we estimate the local energy released by mesh refinement by means of a lower bound obtained by relaxing a local patch of elements. This bound can be computed locally, which reduces the complexity of the refinement algorithm to O(N). We also demonstrate how variational h -refinement can be combined with variational r -refinement to obtain a variational hr -refinement algorithm. Because of the strict variational nature of the h -refinement algorithm, the resulting meshes are anisotropic and outperform other refinement strategies based on aspect ratio or other purely geometrical measures of mesh quality. The versatility and rate of convergence of the resulting approach are illustrated by means of selected numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] Discontinuous Galerkin framework for adaptive solution of parabolic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007Deepak V. Kulkarni Abstract Non-conforming meshes are frequently employed in adaptive analyses and simulations of multi-component systems. We develop a discontinuous Galerkin formulation for the discretization of parabolic problems that weakly enforces continuity across non-conforming mesh interfaces. A benefit of the DG scheme is that it does not introduce constraint equations and their resulting Lagrange multiplier fields as done in mixed and mortar methods. The salient features of the formulation are highlighted through an a priori analysis. When coupled with a mesh refinement scheme the DG formulation is able to accommodate multiple hanging nodes per element edge and leads to an effective adaptive framework for the analysis of interface evolution problems. We demonstrate our approach by analysing the Stefan problem of solidification. Copyright © 2006 John Wiley & Sons, Ltd. [source] A geometry projection method for shape optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004J. Norato Abstract We present a new method for shape optimization that uses an analytical description of the varying design geometry as the control in the optimization problem. A straightforward filtering technique projects the design geometry onto a fictitious analysis domain to support simplified response and sensitivity analysis. However, the analytical geometry model is referenced directly for all purely geometric calculations. The method thus combines the advantages of direct geometry representations with the simplified analysis procedures that are possible with fictitious domain analysis methods, such as the material distribution methods commonly used in topology optimization. The projected geometry measure converges to the indicator function of the analytical geometry model in the limit of numerical mesh refinement. Consequently, optimal designs obtained with the new method converge to solutions of well-defined continuum optimization problems in the limit of mesh refinement. This property is confirmed in example computations for minimum compliance design of an elastic structure subject to a volume constraint and for minimum volume design subject to a maximum stress constraint. Copyright © 2004 John Wiley & Sons, Ltd. [source] Adaptive embedded unstructured grid methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Rainald Löhner Abstract A simple embedded domain method for node-based unstructured grid solvers is presented. The key modification of the original, edge-based solver is to remove all geometry-parameters (essentially the normals) belonging to edges cut by embedded surface faces. Several techniques to improve the treatment of boundary points close to the immersed surfaces are explored. Alternatively, higher-order boundary conditions are achieved by duplicating crossed edges and their endpoints. Adaptive mesh refinement based on proximity to or the curvature of the embedded CSD surfaces is used to enhance the accuracy of the solution. User-defined or automatic deactivation for the regions inside immersed solid bodies is employed to avoid unnecessary work. Several examples are included that show the viability of this approach for inviscid and viscous, compressible and incompressible, steady and unsteady flows, as well as coupled fluid,structure problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Meshless analysis of potential problems in three dimensions with the hybrid boundary node methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2004Jianming Zhang Abstract Combining a modified functional with the moving least-squares (MLS) approximation, the hybrid boundary node method (Hybrid BNM) is a truly meshless, boundary-only method. The method may have advantages from the meshless local boundary integral equation (MLBIE) method and also the boundary node method (BNM). In fact, the Hybrid BNN requires only the discrete nodes located on the surface of the domain. The Hybrid BNM has been applied to solve 2D potential problems. In this paper, the Hybrid BNM is extended to solve potential problems in three dimensions. Formulations of the Hybrid BNM for 3D potential problems and the MLS approximation on a generic surface are developed. A general computer code of the Hybrid BNM is implemented in C++. The main drawback of the ,boundary layer effect' in the Hybrid BNM in the 2D case is circumvented by an adaptive face integration scheme. The parameters that influence the performance of this method are studied through three different geometries and known analytical fields. Numerical results for the solution of the 3D Laplace's equation show that high convergence rates with mesh refinement and high accuracy are achievable. Copyright © 2004 John Wiley & Sons, Ltd. [source] Natural hierarchical refinement for finite element methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003Petr Krysl Abstract Current formulations of adaptive finite element mesh refinement seem simple enough, but their implementations prove to be a formidable task. We offer an alternative point of departure which yields equivalent adapted approximation spaces wherever the traditional mesh refinement is applicable, but our method proves to be significantly simpler to implement. At the same time it is much more powerful in that it is general (no special tricks are required for different types of finite elements), and applicable for some newer approximations where traditional mesh refinement concepts are not of much help, for instance on subdivision surfaces. Copyright © 2003 John Wiley & Sons, Ltd. [source] Voxel-based meshing and unit-cell analysis of textile compositesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2003Hyung Joo Kim Abstract Unit-cell homogenization techniques are frequently used together with the finite element method to compute effective mechanical properties for a wide range of different composites and heterogeneous materials systems. For systems with very complicated material arrangements, mesh generation can be a considerable obstacle to usage of these techniques. In this work, pixel-based (2D) and voxel-based (3D) meshing concepts borrowed from image processing are thus developed and employed to construct the finite element models used in computing the micro-scale stress and strain fields in the composite. The potential advantage of these techniques is that generation of unit-cell models can be automated, thus requiring far less human time than traditional finite element models. Essential ideas and algorithms for implementation of proposed techniques are presented. In addition, a new error estimator based on sensitivity of virtual strain energy to mesh refinement is presented and applied. The computational costs and rate of convergence for the proposed methods are presented for three different mesh-refinement algorithms: uniform refinement; selective refinement based on material boundary resolution; and adaptive refinement based on error estimation. Copyright © 2003 John Wiley & Sons, Ltd. [source] A plasticity based model and an adaptive algorithm for finite element analysis of reinforced concrete panelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002J. Pravida Abstract This paper deals with an adaptive finite element procedure for the analysis of plain and reinforced concrete panels in a state of plane stress. Therefore, we will present a plasticity based model for plain concrete which captures the two failure modes of concrete within one formulation. In spite of a simple formulation the model is capable to describe the different mechanisms for tensile failure as well as for compression fracture. To restrict the time discretization error and the spatial discretization error to certain tolerances, the constitutive model is embedded in an adaptive algorithm which controls the size of the incremental load steps and leads to a hierarchical mesh refinement if necessary. The application of the model will be shown by various numerical examples. Copyright © 2002 John Wiley & Sons, Ltd. [source] A hybrid boundary node methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002Jianming Zhang Abstract A new variational formulation for boundary node method (BNM) using a hybrid displacement functional is presented here. The formulation is expressed in terms of domain and boundary variables, and the domain variables are interpolated by classical fundamental solution; while the boundary variables are interpolated by moving least squares (MLS). The main idea is to retain the dimensionality advantages of the BNM, and get a truly meshless method, which does not require a ,boundary element mesh', either for the purpose of interpolation of the solution variables, or for the integration of the ,energy'. All integrals can be easily evaluated over regular shaped domains (in general, semi-sphere in the 3-D problem) and their boundaries. Numerical examples presented in this paper for the solution of Laplace's equation in 2-D show that high rates of convergence with mesh refinement are achievable, and the computational results for unknown variables are most accurate. No further integrations are required to compute the unknown variables inside the domain as in the conventional BEM and BNM. Copyright © 2001 John Wiley & Sons, Ltd. [source] Development of an optimal hybrid finite volume/element method for viscoelastic flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003M. Aboubacar Abstract A cell-vertex hybrid finite volume/element method is investigated that is implemented on triangles and applied to the numerical solution of Oldroyd model fluids in contraction flows. Particular attention is paid to establishing high-order accuracy, whilst retaining favourable stability properties. Elevated levels of elasticity are sought. The main impact of this study reveals that switching from quadratic to linear finite volume stress representation with discontinuous stress gradients, and incorporating local reduced quadrature at the re-entrant corner, provide enhance stability properties. Solution smoothness is achieved by adopting the non-conservative flux form with area integration, by appealing to quadratic recovered velocity-gradients, and through consistency considerations in the treatment of the time term in the constitutive equation. In this manner, high-order accuracy is maintained, stability is ensured, and the finer features of the flow are confirmed via mesh refinement. Lip vortices are observed for We>1, and a trailing-edge vortex is also apparent. Loss of evolution and solution asymptotic behaviour towards the re-entrant corner are also discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Three-dimensional transient free-surface flow of viscous fluids inside cavities of arbitrary shapeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2003Kyu-Tae Kim Abstract The three-dimensional transient free-surface flow inside cavities of arbitrary shape is examined in this study. An adaptive (Lagrangian) boundary-element approach is proposed for the general three-dimensional simulation of confined free-surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free-surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free-surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. The method is used to determine the flow field and free-surface evolution inside cubic, rectangular and cylindrical containers. These problems illustrate the transient nature of the flow during the mixing process. Surface tension effects are also explored. Copyright © 2003 John Wiley & Sons, Ltd. [source] Patched grid and adaptive mesh refinement strategies for the calculation of the transport of vorticesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2002A. Benkenida Abstract This paper presents two techniques allowing local grid refinement to calculate the transport of vortices. one is the patched grid (PG) method which allows non-coincident interfaces between blocks. Treatment of the non-coincident interfaces is given in detail. The second one is the adaptive mesh refinement (AMR) method which has been developed in order to create embedded sub-grids. The efficiency of these two methods is demonstrated by some validating tests. Then the PG and AMR strategies are applied in the computation of the transport of vortices. We start with a simple vortex flow in a cubic box. Then, the flowfield around a complex aircraft configuration is calculated using the two refinement techniques. Results are compared with a fine, referenced grid calculation. Copyright © 2002 John Wiley & Sons, Ltd. [source] An adaptive remeshing technique based on hierarchical error estimates for simulation of semiconductor devicesINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1 2004Geng Yang Abstract We discuss first hierarchical error estimates and a criterion for mesh refinement. Then we describe briefly the hydrodynamic model of semiconductor model. Based on artificial viscosity technique about electron velocity, we propose to solve a Poisson equation to obtain a correction about mesh optimization. Finally, we simulate a GaAs MESFET's device with a gate of 0.3 µm length and give some discussions about numerical results. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical simulations of type III planetary migration , I. Disc model and convergence testsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2008A. Pepli ABSTRACT We investigate the fast (type III) migration regime of high-mass protoplanets orbiting in protoplanetary discs. This type of migration is dominated by corotational torques. We study the details of flow structure in the planet's vicinity, the dependence of migration rate on the adopted disc model and the numerical convergence of models (independence of certain numerical parameters such as gravitational softening). We use two-dimensional hydrodynamical simulations with adaptive mesh refinement, based on the flash code with improved time-stepping scheme. We perform global disc simulations with sufficient resolution close to the planet, which is allowed to freely move throughout the grid. We employ a new type of equation of state in which the gas temperature depends on both the distance to the star and planet, and a simplified correction for self-gravity of the circumplanetary gas. We find that the migration rate in the type III migration regime depends strongly on the gas dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is sensitive to the aspect ratio of the circumplanetary disc. Furthermore, corrections due to the gas self-gravity are necessary to reduce numerical artefacts that act against rapid planet migration. Reliable numerical studies of type III migration thus require consideration of both the thermal and the self-gravity corrections, as well as a sufficient spatial resolution and the calculation of disc,planet attraction both inside and outside the Hill sphere. With this proviso, we find type III migration to be a robust mode of migration, astrophysically promising because of a speed much faster than in the previously studied modes of migration. [source] Static reanalysis of structures with added degrees of freedomINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2006Baisheng Wu Abstract This paper deals with static reanalysis of a structure with added degrees of freedom where the nodes of the original structure form a subset of the nodes of the modified structure. A preconditioned conjugate-gradient approach is developed. The preconditioner is constructed, and the implementation of the approach involves only decomposition of the stiffness matrix corresponding to the newly added degrees of freedom. In particular, the approach can adaptively monitor the accuracy of approximate solutions. The approach is applicable to the reanalysis of the structural layout modifications for the case of addition of some nodes, deletion and addition of elements and further changes in the geometry as well as to the local mesh refinements. Numerical examples show that the condition number of the selected preconditioned matrix is largely reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] | |||||||||||||