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Corrector Method (corrector + method)
Selected AbstractsSlope stability analysis based on elasto-plastic finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005H. Zheng Abstract The paper deals with two essential and related closely processes involved in the finite element slope stability analysis in two-dimensional problems, i.e. computation of the factors of safety (FOS) and location of the critical slide surfaces. A so-called ,,v inequality, sin ,,1 , 2v is proved for any elasto-plastic material satisfying Mohr,Coulomb's yield criterion. In order to obtain an FOS of high precision with less calculation and a proper distribution of plastic zones in the critical equilibrium state, it is stated that the Poisson's ratio v should be adjusted according to the principle that the ,,v inequality always holds as reducing the strength parameters c and ,. While locating the critical slide surface represented by the critical slide line (CSL) under the plane strain condition, an initial value problem of a system of ordinary differential equations defining the CSL is formulated. A robust numerical solution for the initial value problem based on the predictor,corrector method is given in conjunction with the necessary and sufficient condition ensuring the convergence of solution. A simple example, the kinematic solution of which is available, and a challenging example from a hydraulic project in construction are analysed to demonstrate the effectiveness of the proposed procedures. Copyright © 2005 John Wiley & Sons, Ltd. [source] Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tankINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004J. R. Cho Abstract This paper is concerned with the accurate and stable finite element analysis of large amplitude liquid sloshing in two-dimensional tank under the forced excitation. The sloshing flow is formulated as an initial-boundary-value problem based upon the fully non-linear potential flow theory. The flow velocity field is interpolated from the velocity potential with second-order elements according to least square method, and the free surface conditions are tracked by making use of the direct time differentiation and the predictor,corrector method. Meanwhile, the liquid mesh is adapted such that the incompressibility condition is strictly satisfied. The accuracy and stability of the numerical method introduced are verified from the comparison with the existing reference solutions. As well, the numerical results are compared with those obtained by the linear theory with respect to the liquid fill height and the excitation amplitude. Copyright © 2004 John Wiley & Sons, Ltd. [source] A higher-order predictor,corrector scheme for two-dimensional advection,diffusion equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Chuanjian Man Abstract A higher-order accurate numerical scheme is developed to solve the two-dimensional advection,diffusion equation in a staggered-grid system. The first-order spatial derivatives are approximated by the fourth-order accurate finite-difference scheme, thus all truncation errors are kept to a smaller order of magnitude than those of the diffusion terms. Therefore, there is no need to add an artificial diffusion term to balance the unwanted numerical diffusion. For the time derivative, the fourth-order accurate Adams,Bashforth predictor,corrector method is applied. The stability analysis of the proposed scheme is carried out using the Von Neumann method. It is shown that the proposed algorithm has good stability. This method also shows much less spurious oscillations than current lower-order accurate numerical schemes. As a result, the proposed numerical scheme can provide more accurate results for long-time simulations. The proposed numerical scheme is validated against available analytical and numerical solutions for one- and two-dimensional transport problems. One- and two-dimensional numerical examples are presented in this paper to demonstrate the accuracy and conservative properties of the proposed algorithm by comparing with other numerical schemes. The proposed method is demonstrated to be a useful and accurate modelling tool for a wide range of transport problems. Copyright © 2007 John Wiley & Sons, Ltd. [source] Stability and accuracy of a semi-implicit Godunov scheme for mass transportINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Scott F. Bradford Abstract Semi-implicit, Godunov-type models are adapted for solving the two-dimensional, time-dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor,corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second-order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax-Wendroff, Warming-Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank,Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi-discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi-implicit schemes. Some linear, two-dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source] On the maximum principle and its application to diffusion equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2007T. Stys Abstract In this article, an analog of the maximum principle has been established for an ordinary differential operator associated with a semi-discrete approximation of parabolic equations. In applications, the maximum principle is used to prove O(h2) and O(h4) uniform convergence of the method of lines for the diffusion Equation (1). The system of ordinary differential equations obtained by the method of lines is solved by an implicit predictor corrector method. The method is tested by examples with the use of the enclosed Mathematica module solveDiffusion. The module solveDiffusion gives the solution by O(h2) uniformly convergent discrete scheme or by O(h4) uniformly convergent discrete scheme. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source] On a numerical scheme for curved crack propagation based on configurational forces and maximum dissipationPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Henning Schütte A numerical scheme is presented to predict crack trajectories in two dimensional components. First a relation between the curvature in mixed,mode crack propagation and the corresponding configurational forces is derived, based on the principle of maximum dissipation. With the help of this, a numerical scheme is presented which is based on a predictor,corrector method using the configurational forces acting on the crack together with their derivatives along real and test paths. With the help of this scheme it is possible to take bigger than usual propagation steps, represented by splines. Essential for this approach is the correct numerical determination of the configurational forces acting on the crack tip. The methods used by other authors are shortly reviewed and an approach valid for arbitrary non,homogenous and non,linear materials with mixed,mode cracks is presented. Numerical examples show, that the method is a able to predict the crack paths in components with holes, stiffeners etc. with good accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||