共查询到20条相似文献，搜索用时 0 毫秒
1.
Isaac Harari Kirill Gosteev 《International journal for numerical methods in engineering》2007,70(10):1241-1260
A comparison of two bubble‐enriched methods, derived by different considerations, indicates that the methods are identical in some cases. Thus, series representations of auxiliary functions, derived independently for the two methods, turn out to be equivalent prior to truncation. Three such series for time‐harmonic acoustics are considered. Dispersion analysis points to the more efficient series representation and provides guidelines for the number of terms to be retained. Numerical tests confirm the validity of these practical guidelines. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
2.
Santiago Badia Ramon Planas Juan Vicente Gutiérrez‐Santacreu 《International journal for numerical methods in engineering》2013,93(3):302-328
In this article, we propose different splitting procedures for the transient incompressible magnetohydrodynamics (MHD) system that are unconditionally stable. We consider two levels of splitting, on one side we perform the segregation of the fluid pressure and magnetic pseudo‐pressure from the vectorial fields computation. At the second level, the fluid velocity and induction fields are also decoupled. This way, we transform a fully coupled indefinite multi‐physics system into a set of smaller definite ones, clearly reducing the CPU cost. With regard to the finite element approximation, we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization, allows to circumvent inf‐sup conditions (clearly simplifying implementation issues), and is able to capture non‐smooth solutions of the magnetic subproblem. However, residual‐based finite element formulations are not suitable for segregation, because they lose the skew‐symmetry of the off‐diagonal blocks. Therefore, in this work, we have proposed a novel term‐by‐term stabilization of the MHD system based on projections that is still unconditionally convergent. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
3.
Marco Lucio Cerquaglia Geoffrey Deliége Romain Boman Vincent Terrapon Jean‐Philippe Ponthot 《International journal for numerical methods in engineering》2017,110(10):921-946
The possibility of using free‐slip conditions within the context of the particle finite element method (PFEM) is investigated. For high Reynolds number engineering applications in which tangential effects at the fluid–solid boundaries are not of primary interest, the use of free‐slip conditions can alleviate the need for very fine boundary layer meshes. Two novel ways for the imposition of free‐slip conditions in the framework of the PFEM are presented. The proposed approach emphasizes robustness and simplicity, while retaining a sufficient level of generality. These two methods are then tested in the case of dam break and sloshing problems, and their respective advantages and drawbacks are discussed. It is also shown how the use of free‐slip conditions can indirectly improve mass conservation properties of the PFEM, even when coarse meshes are employed. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
Minjie Zhu Michael H. Scott 《International journal for numerical methods in engineering》2014,99(12):925-944
Numerical difficulties are present in the particle finite element method even though it has been shown to be a powerful and effective approach to simulating fluid‐structure interaction. To overcome problems of mass loss on the free surface and the added‐mass effect, an improved fractional step method (FSM) that handles added‐mass terms in a mathematically exact way is developed. A further benefit is that no assumptions regarding the structural response are made in handling added‐mass terms, thus it is straightforward to incorporate material nonlinearity in fluid‐structure interaction (FSI) under this approach. Patch tests and comparisons with experimental data are presented in order to verify and validate the improved FSM for FSI applications. The computational cost of this approach is shown to be negligible compared with the other aspects of the FSM, particularly when the size of the structure and the fluid‐structure interface is small relative to the volume of fluid. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
5.
Bahareh Banijamali Klaus‐Jürgen Bathe 《International journal for numerical methods in engineering》2007,71(1):66-80
Quite effective low‐order finite element and finite volume methods for incompressible fluid flows have been established and are widely used. However, higher‐order finite element methods that are stable, have high accuracy and are computationally efficient are still sought. Such discretization schemes could be particularly useful to establish error estimates in numerical solutions of fluid flows. The objective of this paper is to report on a study in which the cubic interpolated polynomial (CIP) method is embedded into 4‐node and 9‐node finite element discretizations of 2D flows in order to stabilize the convective terms. To illustrate the capabilities of the formulations, the results obtained in the solution of the driven flow square cavity problem are given. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
6.
Arif Masud Timothy J. Truster Lawrence A. Bergman 《International journal for numerical methods in engineering》2012,92(2):141-177
We present a derivation of a new interface formulation via a merger of continuous Galerkin and discontinuous Galerkin concepts, enhanced by the variational multiscale method. Developments herein provide treatment for the pure‐displacement form and mixed form of small deformation elasticity as applied to the solution of two problem classes: domain decomposition and contact mechanics with friction. The proposed framework seamlessly accommodates merger of different element types within subregions of the computational domain and nonmatching element faces along embedded interfaces. These features are retained in the treatment of multibody small deformation contact problems as well, where an unbiased treatment of the contact interface stands in contrast to classical master/slave constructs. Numerical results for problems in two and three spatial dimensions illustrate the robustness and versatility of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
Lucia Catabriga Alvaro L. G. A. Coutinho Leopoldo P. Franca 《International journal for numerical methods in engineering》2004,60(9):1513-1534
In this work we evaluate the performance of the left conjugate direction method recently introduced by Yuan, Golub, Plemmons and Cecílio for the solution of non‐symmetric systems of linear equations arising from the implicit semi‐discrete SUPG finite element formulation of advective–diffusive and inviscid compressible flows. We extend the original algorithm to accommodate restarts and typical element‐by‐element preconditioners. We also show how to select the first left conjugate vector to start LCD. Several problems are solved, accessing performance parameters such as number of iterations, memory requirements and CPU times, and results are compared with other algorithms, such as GMRES, TFQMR and Bi‐CGSTAB. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
8.
Rainald Lhner Carlos Sacco Eugenio Oate Sergio Idelsohn 《International journal for numerical methods in engineering》2002,53(8):1765-1779
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge‐based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh‐based finite volume or finite element techniques, making the present finite point method competitive. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
9.
Kenn K. Q. Zhang 《International journal for numerical methods in engineering》2005,64(3):285-303
The presence of the pressure and the convection terms in incompressible Navier–Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill‐conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non‐linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
10.
Guglielmo Scovazzi Brian Carnes Xianyi Zeng Simone Rossi 《International journal for numerical methods in engineering》2016,106(10):799-839
We propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piecewise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
Xianyi Zeng Guglielmo Scovazzi Nabil Abboud Oriol Colomés Simone Rossi 《International journal for numerical methods in engineering》2017,112(13):1951-2003
In this article, we develop a dynamic version of the variational multiscale (D‐VMS) stabilization for nearly/fully incompressible solid dynamics simulations of viscoelastic materials. The constitutive models considered here are based on Prony series expansions, which are rather common in the practice of finite element simulations, especially in industrial/commercial applications. Our method is based on a mixed formulation, in which the momentum equation is complemented by a pressure equation in rate form. The unknown pressure, displacement, and velocity are approximated with piecewise linear, continuous finite element functions. To prevent spurious oscillations, the pressure equation is augmented with a stabilization operator specifically designed for viscoelastic problems, in that it depends on the viscoelastic dissipation. We demonstrate the robustness, stability, and accuracy properties of the proposed method with extensive numerical tests in the case of linear and finite deformations. 相似文献
12.
Peter Arbenz G. Harry van Lenthe Uche Mennel Ralph Müller Marzio Sala 《International journal for numerical methods in engineering》2008,73(7):927-947
The recent advances in microarchitectural bone imaging disclose the possibility to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. Coupling these imaging possibilities with microstructural finite element (µFE) analysis offers a powerful tool to improve bone stiffness and strength assessment for individual fracture risk prediction. Many elements are needed to accurately represent the intricate microarchitectural structure of bone; hence, the resulting µFE models possess a very large number of degrees of freedom. In order to be solved quickly and reliably on state‐of‐the‐art parallel computers, the µFE analyses require advanced solution techniques. In this paper, we investigate the solution of the resulting systems of linear equations by the conjugate gradient algorithm, preconditioned by aggregation‐based multigrid methods. We introduce a variant of the preconditioner that does not need assembling the system matrix but uses element‐by‐element techniques to build the multilevel hierarchy. The preconditioner exploits the voxel approach that is common in bone structure analysis, and it has modest memory requirements, at the same time robust and scalable. Using the proposed methods, we have solved in 12min a model of trabecular bone composed of 247 734 272 elements, yielding a matrix with 1 178 736 360 rows, using 1024 CRAY XT3 processors. The ability to solve, for the first time, large biomedical problems with over 1 billion degrees of freedom on a routine basis will help us improve our understanding of the influence of densitometric, morphological, and loading factors in the etiology of osteoporotic fractures such as commonly experienced at the hip, spine, and wrist. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
13.
E. Shapiro D. Drikakis 《International journal for numerical methods in engineering》2006,66(9):1466-1482
An investigation of characteristics‐based (CB) schemes for solving the incompressible Navier–Stokes equations in conjunction with the artificial‐compressibility approach, is presented. Both non‐conservative and conservative CB numerical reconstructions are derived and their accuracy and convergence properties are assessed analytically and numerically. We demonstrate by means of eigenvalue analysis that there are differences in the spectral characteristics of these formulations that result in different convergence properties. Numerical tests for two‐ and three‐dimensional flows reveal that the two formulations provide similar accuracy but the non‐conservative formulation converges faster. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
14.
P. Nithiarasu 《International journal for numerical methods in engineering》2003,56(13):1815-1845
In this paper, an artificial compressibility scheme using the finite element method is introduced. 2002 Zienkiewicz Silver Medal and Prize winning paper. The multi‐purpose CBS scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems. It is important to note that the scheme developed here includes split and velocity correction. The proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes. Unlike many other artificial compressibility schemes, the proposed one works on a variety of grids and gives results for a wide range of Reynold's numbers. The paper presents some bench mark two‐ and three‐dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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16.
E. Hachem S. Feghali R. Codina T. Coupez 《International journal for numerical methods in engineering》2013,94(9):805-825
This paper presents advancements toward a monolithic solution procedure and anisotropic mesh adaptation for the numerical solution of fluid–structure interaction with complex geometry. First, a new stabilized three‐field stress, velocity, and pressure finite element formulation is presented for modeling the interaction between the fluid (laminar or turbulent) and the rigid body. The presence of the structure will be taken into account by means of an extra stress in the Navier–Stokes equations. The system is solved using a finite element variational multiscale method. We combine this method with anisotropic mesh adaptation to ensure an accurate capturing of the discontinuities at the fluid–solid interface. We assess the behavior and accuracy of the proposed formulation in the simulation of 2D and 3D time‐dependent numerical examples such as the flow past a circular cylinder and turbulent flows behind an immersed helicopter in a forward flight. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
17.
Nicholas Zabaras Deep Samanta 《International journal for numerical methods in engineering》2004,60(6):1103-1138
A stabilized equal‐order velocity–pressure finite element algorithm is presented for the analysis of flow in porous media and in the solidification of binary alloys. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. The analysis is performed in a single domain with a fixed numerical grid. The fluid flow scheme developed includes SUPG (streamline‐upwind/Petrov–Galerkin), PSPG (pressure stabilizing/Petrov–Galerkin) and DSPG (Darcy stabilizing/Petrov–Galerkin) stabilization terms in a variable porosity medium. For the energy and species equations a classical SUPG‐based finite element method is employed. The developed algorithms were tested extensively with bilinear elements and were shown to perform stably and with nearly quadratic convergence in high Rayleigh number flows in varying porosity media. Examples are shown in natural and double diffusive convection in porous media and in the directional solidification of a binary‐alloy. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
18.
A three‐dimensional microstructure‐based finite element framework is presented for modeling the mechanical response of rubber composites in the microscopic level. This framework introduces a novel finite element formulation, the meshfree‐enriched FEM, to overcome the volumetric locking and pressure oscillation problems that normally arise in the numerical simulation of rubber composites using conventional displacement‐based FEM. The three‐dimensional meshfree‐enriched FEM is composed of five‐noded tetrahedral elements with a volume‐weighted smoothing of deformation gradient between neighboring elements. The L2‐orthogonality property of the smoothing operator enables the employed Hu–Washizu–de Veubeke functional to be degenerated to an assumed strain method, which leads to a displacement‐based formulation that is easily incorporated with the periodic boundary conditions imposed on the unit cell. Two numerical examples are analyzed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
19.
Carl Sandström Fredrik Larsson 《International journal for numerical methods in engineering》2017,109(3):307-325
By separation of scales and the homogenization of a flow through porous media, a two‐scale problem arises where a Darcy‐type flow is present on the macroscale and a Stokes flow on the subscale. In this paper, the problem is given as the minimization of a potential. Additional constraints imposing periodicity in a weak sense are added using Lagrange multipliers. In particular, the upper and lower energy bounds for the corresponding strongly periodic problem are produced, quantifying the accuracy of the weakly periodic boundary conditions. A numerical example demonstrates the evaluation of energy bounds and the performance of weakly periodic boundary conditions on a representative volume element. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd 相似文献
20.
C.T. Wu W. Hu J.S. Chen 《International journal for numerical methods in engineering》2012,90(7):882-914
In this paper, a two‐dimensional displacement‐based meshfree‐enriched FEM (ME‐FEM) is presented for the linear analysis of compressible and near‐incompressible planar elasticity. The ME‐FEM element is established by injecting a first‐order convex meshfree approximation into a low‐order finite element with an additional node. The convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the Kronecker‐delta property on the element boundaries. The gradient matrix of ME‐FEM element satisfies the integration constraint for nodal integration and the resultant ME‐FEM formulation is shown to pass the constant stress test for the compressible media. The ME‐FEM interpolation is an element‐wise meshfree interpolation and is proven to be discrete divergence‐free in the incompressible limit. To prevent possible pressure oscillation in the near‐incompressible problems, an area‐weighted strain smoothing scheme incorporated with the divergence‐free ME‐FEM interpolation is introduced to provide the smoothing on strains and pressure. With this smoothed strain field, the discrete equations are derived based on a modified Hu–Washizu variational principle. Several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near‐incompressible problems. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献