共查询到20条相似文献，搜索用时 15 毫秒
1.
Yu‐Hong Dai Jinyun Yuan 《International journal for numerical methods in engineering》2004,60(8):1383-1399
Some theoretical problems and implementation problems are studied here for the semi‐conjugate direction method established by Yuan, Golub, Plemmons and Cecilio (2002). The existence of semi‐conjugate directions is proved for almost all matrices except skew‐symmetric matrices. A new technique is proposed to overcome the breakdown problem appeared in the semi‐conjugate direction method. In the implementation of the semi‐conjugate direction method, the generation of the semi‐conjugate direction is very important and necessary, but very expensive. The technique of limited‐memory is introduced to economize the cost of the generation of the semi‐conjugate direction in the Yuan–Golub– Plemmons–Cecilio algorithm. Finally, some numerical experiments are given to confirm our theoretical results. Our results illustrate that the semi‐conjugate direction method is very nice alternative for solving non‐symmetric systems, and the limited‐memory left conjugate direction method is a good improvement of the left conjugate direction method. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
2.
A framework for the construction of node-centred schemes to solve the compressible Euler and Navier–Stokes equations is presented. The metric quantities are derived by exploiting some properties of C0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated. 相似文献
3.
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
4.
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
5.
L. P. Franca A. Nesliturk 《International journal for numerical methods in engineering》2001,52(4):433-453
We consider the Galerkin finite element method for the incompressible Navier–Stokes equations in two dimensions, where the finite‐dimensional space(s) employed consist of piecewise polynomials enriched with residual‐free bubble functions. To find the bubble part of the solution, a two‐level finite element method (TLFEM) is described and its application to the Navier–Stokes equation is displayed. Numerical solutions employing the TLFEM are presented for three benchmark problems. We compare the numerical solutions using the TLFEM with the numerical solutions using a stabilized method. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
6.
《International journal for numerical methods in engineering》2018,115(8):913-955
We present a computational framework for the simulation of J2‐elastic/plastic materials in complex geometries based on simple piecewise linear finite elements on tetrahedral grids. We avoid spurious numerical instabilities by means of a specific stabilization method of the variational multiscale kind. Specifically, we introduce the concept of subgrid‐scale displacements, velocities, and pressures, approximated as functions of the governing equation residuals. The subgrid‐scale displacements/velocities are scaled using an effective (tangent) elastoplastic shear modulus, and we demonstrate the beneficial effects of introducing a subgrid‐scale pressure in the plastic regime. We provide proofs of stability and convergence of the proposed algorithms. These methods are initially presented in the context of static computations and then extended to the case of dynamics, where we demonstrate that, in general, naïve extensions of stabilized methods developed initially for static computations seem not effective. We conclude by proposing a dynamic version of the stabilizing mechanisms, which obviates this problematic issue. In its final form, the proposed approach is simple and efficient, as it requires only minimal additional computational and storage cost with respect to a standard finite element relying on a piecewise linear approximation of the displacement field. 相似文献
7.
将虚拟介质方法推广到应力波与流固界面的相互作用,基于修正虚拟流体方法(MGFM)思想提出一种适用于流固界面应力波折射问题的界面状态计算法则.以此为基础,用Zwas格式和WENO格式分别离散固体和流体控制方程,数值模拟应力波穿透水舱.数值测试表明:虚拟介质方法推广到模拟流固界面上的应力波时,数值误差具有很好的收敛性;该研... 相似文献
8.
William John Trevor Daniel Ted Belytschko 《International journal for numerical methods in engineering》2005,64(3):335-353
Solutions employing perturbation stiffness or viscous hourglass control with one‐point quadrature finite elements often exhibit spurious modes in the intermediate frequency range. These spurious frequencies are demonstrated in several examples and their origin is explained. Then it is shown that by critically damping the hourglass modes, these spurious mid‐range frequency modes can be suppressed. Estimates of the hourglass frequency and damping coefficients are provided for the plane 4‐node quadrilateral and a 4‐node shell element. Results are presented that show almost complete annihilation of spurious intermediate frequency modes for both linear and non‐linear problems. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
A. Truty 《International journal for numerical methods in engineering》2001,52(8):763-786
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. 相似文献
10.
H. T. Banks Malcolm J Birch Mark P Brewin Stephen E Greenwald Shuhua Hu Zackary R Kenz Carola Kruse Matthias Maischak Simon Shaw John R Whiteman 《International journal for numerical methods in engineering》2014,98(2):131-156
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space‐time coupling matrices are diagonalizable over for r ?100, and this means that the time‐coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG‐in‐time methodology, for the first time, to second‐order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high‐order (up to degree 7) temporal and spatio‐temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. 相似文献
11.
Marcelo H. Kobayashi Jos Manuel C. Pereira 《International journal for numerical methods in engineering》2005,62(14):1950-1981
This work concerns the development of a numerical method based on the stream function formulation of the Navier–Stokes equations to simulate two‐dimensional—plane or axisymmetric—viscous flows. The main features of the proposed method are: the use of the high order finite‐difference compact method for the discretization of the stream function equation, the implicit pseudo‐transient Newton–Krylov‐multigrid matrix free method for the stationary stream function equation and the fourth order Runge–Kutta method for the integration of non‐stationary flows. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
13.
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
14.
Hong Luo Joseph D. Baum Rainald Löhner 《International journal for numerical methods in engineering》2008,73(5):597-623
Computation of compressible steady‐state flows using a high‐order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics‐based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low‐storage p‐multigrid method is used for solving the governing compressible Euler equations to obtain steady‐state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady‐state flows. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
15.
Mardoche Magolu Monga Made 《International journal for numerical methods in engineering》2001,50(5):1077-1101
Preconditioning techniques based on incomplete factorization of matrices are investigated, to solve highly indefinite complex‐symmetric linear systems. A novel preconditioning is introduced. The real part of the matrix is made positive definite, or less indefinite, by adding properly defined perturbations to the diagonal entries, while the imaginary part is unaltered. The resulting preconditioning matrix, which is obtained by applying standard methods to the perturbed complex matrix, turns out to perform significantly better than classical incomplete factorization schemes. For realistic values of the GMRES restart parameter, spectacular reduction of iteration counts is observed. A theoretical spectral analysis is provided, in which the spectrum of the preconditioner applied to indefinite matrix is related to the spectrum of the same preconditioner applied to a Stieltjes matrix extracted from the indefinite matrix. Results of numerical experiments are reported, which display the efficiency of the new preconditioning. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
16.
B. Boroomand A. A. Tabatabaei E. Oate 《International journal for numerical methods in engineering》2005,63(3):351-379
A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill‐conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non‐monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
17.
Lucia Catabriga Alvaro L. G. A. Coutinho Tayfun E. Tezduyar 《Computational Mechanics》2006,38(4-5):334-343
We present, for the SUPG formulation of inviscid compressible flows, stabilization parameters defined based on the degree-of-freedom submatrices of the element-level matrices. With 2D steady-state test problems involving supersonic flows and shocks, we compare these stabilization parameters with the ones defined based on the full element-level matrices. We also compare them to the stabilization parameters introduced in the earlier development stages of the SUPG formulation of compressible flows. In all cases the formulation includes a shock-capturing term involving a shock-capturing parameter. We investigate the difference between updating the stabilization and shock-capturing parameters at the end of every time step and at the end of every nonlinear iteration within a time step. The formulation includes, as an option, an algorithmic feature that is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected. 相似文献
18.
D. Dreyer O. von Estorff 《International journal for numerical methods in engineering》2003,58(6):933-953
An optimized version of the so‐called mapped wave envelope elements, also known as Astley–Leis elements, is introduced. These elements extend to infinity in one dimension and therefore provide an approach to the simulation of exterior acoustical problems in both frequency and time domains. Their formulation is improved significantly through the proper choice of polynomial bases in the direction of radiation. In particular, certain Jacobi polynomials are identified which behave well with respect to conditioning of the system matrices. As a consequence, the size of the finite element discretization may reduce considerably without any loss of accuracy. In addition, the new polynomial bases lead to superior performance of the infinite elements in conjunction with iterative solvers. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
19.
Two finite element formulations are proposed to analyse the dynamic conditions of saturated porous media at large strains with compressible solid and fluid constituents. Unlike similar works published in the literature, the proposed formulations are based on a recently proposed hyperelastic framework in which the compressibility of the solid and fluid constituents is fully taken into account when geometrical non‐linear effects are relevant on both micro‐ and macroscales. The first formulation leads to a three‐field finite element method (FEM), which is suitable for analysing high‐frequency dynamic problems, whereas the second is a simplification of the first, leading to a two‐field FEM, in which some inertial effects of the pore fluid are disregarded, hence the second formulation is suitable for studying low‐frequency problems. A fully Lagrangian approach is considered, hence all terms are expressed with reference to the material setting; the balance equations for the pore fluid are also expressed in terms of the chemical potential and the mass flux of the pore fluid in order to take the compressibility of the fluid into account. To improve the numerical response in the case of wave propagation, a discontinuous Galerkin FEM in the time domain is applied to the three‐field formulation. The results are compared with analytical and semi‐analytical solutions, highlighting the different effects of the discontinuous Galerkin method on the longitudinal waves of the first and second kind. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
20.
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