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Corrector Scheme (corrector + scheme)
Selected AbstractsA predictor,corrector scheme for the optimization of 3D crack front shapesFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 1-2 2005K. KOLK ABSTRACT A predictor,corrector scheme is presented to improve the shape of 3D crack fronts within the 3D simulation of fatigue crack growth. This concept is fully functional for mode-I, and an extension for mixed-mode problems is presented. The whole procedure is embedded in an automatic incremental crack growth algorithm for arbitrary 3D problems with linear elastic material behaviour. The numerical simulation is based on the 3D dual boundary element method (Dual BEM) and on an optimized evaluation of very accurate stress intensity factors (SIFs) and T-stresses. As part of the proposed predictor,corrector scheme, 3D singularities along the crack front especially in the vicinity of the intersection of the crack front and the boundary are considered. The knowledge of these singularities allows the specification of crack front shapes with bounded energy release rate. Numerical examples with complex cross-sections are presented to show the efficiency of the proposed crack growth algorithm. The obtained results are in good agreement with recent experimental results. [source] Micromechanical viscoelasto-plastic models and finite element implementation for rate-independent and rate-dependent permanent deformation of stone-based materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2010Qingli Dai Abstract This paper presents parallel and serial viscoelasto-plastic models to simulate the rate-independent and the rate-dependent permanent deformation of stone-based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto-plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement-based incremental formulation for the viscoelastic part and an elastic predictor,plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto-plastic model employed a viscoelastic predictor,plastic corrector algorithm. The stone-based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto-plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto-plastic matrix models. The simulation results showed that the serial viscoelasto-plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto-plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate-independent and rate-dependent viscoelasto-plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto-plastic behaviors of the stone-based materials. Copyright © 2009 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] An efficient finite difference scheme for free-surface flows in narrow rivers and estuariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003XinJian ChenArticle first published online: 13 MAY 200 Abstract This paper presents a free-surface correction (FSC) method for solving laterally averaged, 2-D momentum and continuity equations. The FSC method is a predictor,corrector scheme, in which an intermediate free surface elevation is first calculated from the vertically integrated continuity equation after an intermediate, longitudinal velocity distribution is determined from the momentum equation. In the finite difference equation for the intermediate velocity, the vertical eddy viscosity term and the bottom- and sidewall friction terms are discretized implicitly, while the pressure gradient term, convection terms, and the horizontal eddy viscosity term are discretized explicitly. The intermediate free surface elevation is then adjusted by solving a FSC equation before the intermediate velocity field is corrected. The finite difference scheme is simple and can be easily implemented in existing laterally averaged 2-D models. It is unconditionally stable with respect to gravitational waves, shear stresses on the bottom and side walls, and the vertical eddy viscosity term. It has been tested and validated with analytical solutions and field data measured in a narrow, riverine estuary in southwest Florida. Model simulations show that this numerical scheme is very efficient and normally can be run with a Courant number larger than 10. It can be used for rivers where the upstream bed elevation is higher than the downstream water surface elevation without any problem. Copyright © 2003 John Wiley & Sons, Ltd. [source] The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2008Mehdi Dehghan Abstract This article describes a numerical method based on the boundary integral equation and dual reciprocity method for solving the one-dimensional Sine-Gordon (SG) equation. The time derivative is approximated by the time-stepping method and a predictor,corrector scheme is employed to deal with the nonlinearity which appears in the problem. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. In addition, the conservation of energy in SG equation is investigated. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source] Pressure segregation methods based on a discrete pressure Poisson equation.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008An algebraic approach Abstract In this paper, we introduce some pressure segregation methods obtained from a non-standard version of the discrete monolithic system, where the continuity equation has been replaced by a pressure Poisson equation obtained at the discrete level. In these methods it is the velocity instead of the pressure the extrapolated unknown. Moreover, predictor,corrector schemes are suggested, again motivated by the new monolithic system. Key implementation aspects are discussed, and a complete stability analysis is performed. We end with a set of numerical examples in order to compare these methods with classical pressure-correction schemes. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||