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Fine Mesh (fine + mesh)
Selected AbstractsNonlinear transient dynamic analysis by explicit finite element with iterative consistent mass matrixINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2009Shen Rong Wu Abstract Various mass matrices in the explicit finite element analyses of nonlinear transient dynamic problems are investigated. The matrices are obtained as a linear combination of lumped and consistent mass matrices. An iterative procedure to calculate the inverse of the consistent and the mixed mass matrices in the framework of explicit finite element method is presented. The convergence of the iterative procedure is proved. The inverse of the consistent and mixed mass matrices is approximated by the iteration and is used to compare the results from the lumped mass matrix. For the impact of a structural component and a vehicle, some difference in the results by using coarse mesh is observed. For the component using fine mesh, no significant difference is found. Copyright © 2008 John Wiley & Sons, Ltd. [source] FLEXMG: A new library of multigrid preconditioners for a spectral/finite element incompressible flow solverINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010M. Rasquin Abstract A new library called FLEXMG has been developed for a spectral/finite element incompressible flow solver called SFELES. FLEXMG allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods. Two families of algebraic multigrid preconditioners have been implemented, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least-square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics, their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in the study. Copyright © 2010 John Wiley & Sons, Ltd. [source] Multi-scale domain decomposition method for large-scale structural analysis with a zooming technique: Application to plate assemblyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009A. Mobasher Amini Abstract This article is concerned with a multi-scale domain decomposition method (DDM), based on the FETI-DP solver, for large-scale structural elastic analysis and suited to problems that exhibit structural heterogeneities, such as plate assemblies in the presence of structural details. In this approach once a partition of the global fine mesh into subdomains has been performed (all subdomains possess a fine mesh) and to optimize the computational time, the fine mesh is preserved only in the zones of interest (with local phenomena due to discontinuity, hole, etc.) while the remaining subdomains are replaced by numerical homogenized coarse elements. Indeed, the multi-scale aspect is introduced by the description of subdomains with either a fine or a coarse scale mesh. As a result, an extension of the FETI-DP DDM is proposed in this article (called herein FETI-DP micro,macro) that allows the simultaneous usage of different discretizations: fine (microscopic) mesh for subdomains in zones of interest and coarse (macroscopic or homogenized) mesh for the complementary part of the structure. Using this strategy raises the problem of the determination of the stiffness of coarse subdomains, and of the incompatible finite element connection between fine and coarse subdomains. Two approaches (collocation and Mortar) are presented and compared. The article ends with patch tests and some numerical examples in 2D and 3D. The obtained numerical results exemplify the efficiency and capability of the FETI-DP micro,macro approach and reveal that the Mortar approach is more accurate, at constant cost, than the collocation approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] On algebraic multigrid methods derived from partition of unity nodal prolongatorsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2006Tim Boonen Abstract This paper is concerned with algebraic multigrid for finite element discretizations of the divgrad, curlcurl and graddiv equations on tetrahedral meshes with piecewise linear shape functions. First, an edge, face and volume prolongator are derived from an arbitrary partition of unity nodal prolongator for a tetrahedral fine mesh, using the formulas for edge, face and volume elements. This procedure can be repeated recursively. The implied coarse topology and the normalization of the prolongators are analysed. It is proved that the range spaces of the nodal prolongator and of the derived edge, face and volume prolongators form a discrete de Rham complex if these prolongators have full rank. It is shown that on simplicial meshes, the constructed edge prolongator is a generalization of the Reitzinger,Schöberl prolongator. The derived edge and face prolongators are applied in an algebraic multigrid method for the curlcurl and graddiv equations, and numerical results are presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Parallel simulation of unsteady hovering rotor wakesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2006C. B. Allen Abstract Numerical simulation using low diffusion schemes, for example free-vortex or vorticity transport methods, and theoretical stability analyses have shown the wakes of rotors in hover to be unsteady. This has also been observed in experiments, although the instabilities are not always repeatable. Hovering rotor wake stability is considered here using a finite-volume compressible CFD code. An implicit unsteady, multiblock, multigrid, upwind solver, and structured multiblock grid generator are presented, and applied to lifting rotors in hover. To allow the use of very fine meshes and, hence, better representation of the flow physics, a parallel version of the code has been developed, and parallel performance using upto 1024 CPUs is presented. A four-bladed rotor is considered, and it is demonstrated that once the grid density is sufficient to capture enough turns of the tip vortices, hover exhibits oscillatory behaviour of the wake, even using a steady formulation. An unsteady simulation is then performed, and also shows an unsteady wake. Detailed analysis of the time-accurate wake history shows that three dominant unsteady modes are captured, for this four-bladed case, with frequencies of one, four, and eight times the rotational frequency. A comparison with theoretical stability analysis is also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Parallel solution of lifting rotors in hover and forward flightINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007C. B. Allen Abstract An implicit unsteady, multiblock, multigrid, upwind solver including mesh deformation capability, and structured multiblock grid generator, are presented and applied to lifting rotors in both hover and forward flight. To allow the use of very fine meshes and, hence, better representation of the flow physics, a parallel version of the code has been developed. It is demonstrated that once the grid density is sufficient to capture enough turns of the tip vortices, hover exhibits oscillatory behaviour of the wake, even using a steady formulation. An unsteady simulation is then presented, and detailed analysis of the time-accurate wake history is performed and compared to theoretical predictions. Forward flight simulations are also presented and, again, grid density effects on the wake formation investigated. Parallel performance of the code using up to 1024 CPU's is also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical aspects of an algorithm for the Eulerian simulation of two-phase flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2003Paulo J. Oliveira Abstract It is often the case that the numerical simulation of two phase flows leads to a number of difficulties associated with the solution algorithms utilized. Those difficulties manifest themselves as an impossibility to converge the iterative solution process, typical of the finite-volume pressure-correction methods, and are particularly persistent in cases with phase segregation (complete, or almost complete, separation of one phase from the other) and with fine meshes. A number of effective measures to overcome such problems are here proposed and tested, encompassing: (1) modification of the momentum equations formulation in a way that avoids singularity as volume fractions (,) tend to zero; (2) bounding of the volume fractions during the iterative algorithm in a way that enforces the physical limits, ,0 and 1; (3) symmetric treatment of some terms in the equations, and consistent formulation of cell-face fluxes in order to prevent numerical-induced oscillations. Copyright © 2003 John Wiley & Sons, Ltd. [source] Modelling electrospinning of nanofibresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Tomasz A. Kowalewski Electrospinning is based on so-called bending instability which results in an erratic spiralling motion of the liquid jet as it proceeds towards a collecting electrode, where it is eventually deposited as a mat of micro/nanosized fibres. Most electrospinning models formulated within the slender approximation rely, however, on an inconsistent description of electrostatic interactions which renders them grossly inappropriate whenever the discretization is either too coarse or too fine. The present work aims at proposing a discrete slender model which is numerically consistent (allowing use of arbitrary fine meshes) and remains accurate even for coarse meshes. At the same time, efficient numerical techniques based on hierarchical charge clustering are introduced that drastically decrease computational times. Finally, a versatile boundary value method is implemented to enforce fixed-potential boundary conditions, allowing realistic electrode configurations to be investigated. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||