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Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems

PHYSICS OF THE EARTH AND PLANETARY INTERIORS 2007年第1-4期163卷 83-105页

作者： Gerya, Taras V. Yuen, David A. ETH Swiss Fed Inst Technol Inst Geophys Dept GeosciGeophys Fluid Grp CH-8093 Zurich Switzerland Univ Minnesota Dept Geol & Geophys Minnesota Supercomp Inst Minneapolis MN 55455 USA

We have extended our previous 2D method [Gerya, T.V., Yuen, D.A., 2003. Characteristics-based marker-in-cell method with conservative finite-differences schemes for modeling geological flows with strongly variable transport properties. Phys. Earth Planet. Interiors 140, 295-320], which is a combination of conservative finite-differences with marker-in-cell techniques to include the effects of visco-elasto-plastic rheology, self-gravitation and a self-consistently derived evolving curvilinear planetary surface. This code is called 12ELVIS and can solve a new class of computationally challenging problems in geodynamics, such as shear localization with large strains, crustal intrusion emplacement of magmas, bending of realistic visco-elasto-plastic plates and core-formation by vigorous shell tectonics activities related to a global Rayleigh-Taylor instability of a metal layer formed around silicate-rich lower density (primordial) core during planetary accretion. We discuss in detail the computational strategy required the rheological constraints to be satisfied at each time step and spatial location. We show analytical benchmarks and examples drawn from comparing between numerical and analogue experiments in structural geology, subducting slab bending with a visco-elasto-plastic rheology and equilibrium spherical configurations from self-gravitation. We have also tested possibilities of future applications by addressing 3D geometries based on multigrid method and including inertial effects in the momentum equation with tracers in order to simulate meteoritic impact events and eventually earthquake instabilities. (c) 2007 Elsevier B.V. All rights reserved.

关键词： numerical algorithm visco-elasto-plasticity self-gravitation free curvilinear surface inertial effects

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A Hybrid Adaptive Phase Space Method for Reflection Traveltime Tomography

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SIAM JOURNAL ON IMAGING SCIENCES 2019年第1期12卷 28-53页

作者： Zhao, Hongkai Zhong, Yimin Univ Calif Irvine Dept Math Irvine CA 92697 USA

We present a hybrid imaging method for a challenging traveltime tomography problem which includes both unknown medium and unknown scatterers in a bounded domain. The goal is to recover both the medium and the boundary of the scatterers from the scattering relation data on the domain boundary. Our method is composed of three steps: (1) preprocess the data to classify them into three different categories of measurements corresponding to nonbroken rays, broken-once rays, and others, respectively, (2) use the the nonbroken ray data and an effective data-driven layer stripping strategy-an optimization based iterative imaging method-to recover the medium velocity outside the convex hull of the scatterers, and (3) use selected broken-once ray data to recover the boundary of the scatterers-a direct imaging method. By numerical tests, we show that our hybrid method can recover both the unknown medium and the not-too-concave scatterers efficiently and robustly.

关键词： traveltime tomography inverse problem numerical algorithm Hamilton's equations inverse scattering phase space method

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Improved prediction of springback on final formed components

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JOURNAL OF MATERIALS PROCESSING TECHNOLOGY 2004年第153-154期153卷 464-471页

作者： Mullan, HB Univ Coll Swansea EPSRC Engn Doctorate Ctr Automot Appl Corus RD&T Swansea SA2 8PP W Glam Wales

This paper investigates the major difficulty associated with the bending of sheet steel products, namely that of material elastic recovery (springback). Key material, and loading factors that influence springback have been assessed from an experimental study of this phenomenon, using a variety of forming methods. The results of which, in conjunction with previously published data are used to derive an expression for predicting springback using a numerical algorithm method. In addition, comparison is made between the best performing analytical model and that of the numerical algorithm derived in this study. (C) 2004 Published by Elsevier B.V.

关键词： elastic recovery springback forming sheet steel numerical algorithm

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A conservative algorithm for parabolic problems in domains with moving boundaries

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JOURNAL OF COMPUTATIONAL PHYSICS 2014年 270卷 203-213页

作者： Novak, Igor L. Slepchenko, Boris M. Univ Connecticut Ctr Hlth Dept Cell Biol Richard D Berlin Ctr Cell Anal & Modeling Farmington CT 06030 USA

We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior. Consequently, our algorithm is free of the CFL stability issue due to moving interfaces and does not involve cell-merging or mass redistribution. Local mass conservation is ensured by finite-volume discretization and natural-neighbor interpolation. numerical experiments with two-dimensional geometries demonstrate exact mass conservation and indicate an order of convergence in space between one and two. The use of standard meshing techniques makes extension of the method to three dimensions conceptually straightforward. Published by Elsevier Inc.

关键词： numerical algorithm Moving boundaries Parabolic equations Exact mass conservation Cell migration

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A robust implementation of a sequential quadratic programming algorithm with successive error restoration

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OPTIMIZATION LETTERS 2011年第2期5卷 283-296页

作者： Schittkowski, K. Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany

We consider sequential quadratic programming methods for solving constrained nonlinear programming problems. It is generally believed that these methods are sensitive to the accuracy by which partial derivatives are provided. One reason is that differences of gradients of the Lagrangian function are used for updating a quasi-Newton matrix, e.g., by the BFGS formula. The purpose of this paper is to show by numerical experimentation that the method can be stabilized substantially. The algorithm applies non-monotone line search and internal and external restarts in case of errors due to inaccurate derivatives while computing the search direction. Even in case of large random errors leading to partial derivatives with at most one correct digit, termination subject to an accuracy of 10(-7) can be achieved in 90% of 306 problems of a standard test suite. On the other hand, the original version with monotone line search and without restarts solves only 30% of these problems under the same test environment. In addition, we show how initial and periodic scaled restarts improve the efficiency in situations with slow convergence.

关键词： SQP Sequential quadratic programming Nonlinear programming Line search Restart numerical algorithm Noisy functions

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A FAST algorithm FOR ESTIMATING LARGE-SCALE PERMEABILITIES OF CORRELATED ANISOTROPIC MEDIA

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TRANSPORT IN POROUS MEDIA 1993年第1期12卷 55-72页

作者： HINRICHSEN, EL AHARONY, A FEDER, J HANSEN, A JOSSANG, T CONOCO INC DEPT PERDIV PROD R&DPONCA CITYOK 74603

The problem of estimating large-scale permeabilities of reservoirs based on knowledge of the small-scale permeabilities is addressed. We present an accurate and fast algorithm to calculate the global permeabilities of two- or three-dimensional correlated and anisotropic block samples, thus providing a fast algorithm for obtaining grid block permeabilities for reservoir simulators from small scale data. The algorithm is tested on both two- and three-dimensional tube networks generated from real images and fractal forgeries modeling porous media. In almost all cases, the algorithm estimates the correct global permeability (calculated using exact but slow algorithms) of the network to better than 5%. The new algorithm is comparable in speed to conventional averaging techniques, such as the geometric mean, but the obtained estimates are always much better.

关键词： EFFECTIVE PERMEABILITY CORRELATIONS AND ANISOTROPY RENORMALIZATION numerical algorithm

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Computation of the inverse Laplace transform based on a collocation method which uses only real values

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2007年第1期198卷 98-115页

作者： Cuomo, S. D'Amore, L. Murli, A. Rizzardi, M. Univ Naples Federico II I-80126 Naples Italy Univ Naples Parthenope I-80133 Naples Italy

We develop a numerical algorithm for inverting a Laplace transform (I-T), based on Laguerre polynomial series expansion of the inverse function under the assumption that the LT is known on the real axis only. The method belongs to the class of Collocation methods (C-methods), and is applicable when the LT function is regular at infinity. Difficulties associated with these problems are due to their intrinsic ill-posedness. The main contribution of this paper is to provide computable estimates of truncation, discretization, conditioning and roundoff errors introduced by numerical computations. Moreover, we introduce the pseudoaccuracy which will be used by the numerical algorithm in order to provide uniform scaled accuracy of the computed approximation for any x with respect to e(sigma chi). These estimates are then employed to dynamically truncate the series expansion. In other words, the number of the terms of the series acts like the regularization parameter which provides the trade-off between errors. With the aim to validate the reliability and usability of the algorithm experiments were carried out on several test functions. (c) 2005 Elsevier B.V. All rights reserved.

关键词： Laplace transform real inversion collocation methods error analysis numerical algorithm

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Longitudinal maneuvering motions of the supercavitating vehicle

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EUROPEAN JOURNAL OF MECHANICS B-FLUIDS 2020年 81卷 105-113页

作者： Zou, Wang Wang, Benlong Shanghai Jiao Tong Univ Sch Naval Architecture Ocean & Civil Engn Key Lab Hydrodynam Minist Educ Shanghai 200240 Peoples R China

As the supercavitating flows theory and technology developing, to develop a supercavitating vehicle with maneuverability is a significant trend. In order to achieve this goal, it is prerequisite to establish a dynamics model, reflecting the supercavitating flows' unsteady characteristics and the supercavitating vehicle's dynamics characteristics as much as possible, and an effective control method. The maneuvering supercavity model proposed in our previous work, where the gravity effect model is further improved here, is applied to the vehicle dynamics modeling in the longitudinal motions. Based on the dynamics model, a numerical method that integrates the fourth order Runge-Kutta algorithm with the cavitation number correction algorithm, the exactly feedback linearizing control and the linear quadratic regulator methods is proposed to simulate the level flight, climbing and diving of the vehicle. numerical results confirm that the developed dynamics model and numerical method are effective for the vehicle's maneuvering motions and that the method with control laws is robust to velocity perturbation and trajectory mutation. (C) 2019 Elsevier Masson SAS. All rights reserved.

关键词： Supercavitating vehicle Dynamics model numerical algorithm Maneuvering motion

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A nonlinear constitutive model for whole stress-strain behaviors of compressed rocks incorporating crack closure effect

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INTERNATIONAL JOURNAL FOR numerical AND ANALYTICAL METHODS IN GEOMECHANICS 2023年第11期47卷 2003-2026页

作者： Ren, Lu Zhao, Lun-Yang Niu, Fu-Jun Lai, Yuan-Ming Shao, Jian-Fu South China Univ Technol South China Inst Geotech Engn Sch Civil Engn & Transportat Guangzhou Guangdong Peoples R China South China Univ Technol State Key Lab Subtrop Bldg Sci Guangzhou Guangdong Peoples R China Chinese Acad Sci Cold & Arid Reg Environm & Engn Inst State Key Lab Frozen Soil Engn Lanzhou Gansu Peoples R China Univ Lille CNRS Cent Lille UMR 9013LaMcube Lab Mecan Multiphys & Multiechell Lille France South China Univ Technol South China Inst Geotech Engn Sch Civil Engn & Transportat Guangzhou 510641 Peoples R China

This paper is devoted to establishing a nonlinear constitutive model incorporating crack closure effect for capturing the whole process of rock deformation and failure behavior under compression. The model formulated in the framework of irreversible thermodynamics is based on the additive decomposition of the total strain into crack closure strain, elastic, and plastic parts. New specific criteria are proposed for the description of crack closure strain and plastic strain evolution. Notably, analytical solutions of the model under conventional triaxial compression loading conditions are derived. For application, a robust semi-implicit return mapping (SRM) algorithm with a crack closure strain correction and a plastic strain correction is developed. The analytical solutions, herein, are subtly used to calibrate model parameters and as reference results for assessing the accuracy and robustness of the SRM algorithm. Validation of the model conducted by comparing with experimental data from the literature shows that the model can properly describe the nonlinear mechanical behaviors of rocks, including crack closure effect, strain hardening/softening, peak and residual strength, as well as volumetric compaction/dilation transition. In addition, a nonlocal formulation is introduced as an extension of the model to remedy the mesh dependency problem.

关键词： analytical solution constitutive modeling crack closure effect numerical algorithm rock mechanics whole stress-strain curve

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Alternative split-operator approach for solving chemical reaction groundwater transport models

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ADVANCES IN WATER RESOURCES 1996年第5期19卷 261-275页

作者： Barry, DA Bajracharya, K Miller, CT Department of Environmental Engineering University of Western Australia Nedlands Western Australia 6907 Department of Environmental Sciences and Engineering University of North Carolina Chapel Hill North Carolina 27599-7400 USA

Various schemes are available to solve coupled transport/reaction mathematical models, one of the most efficient and easy to apply being the two-step split-operator method in which the transport and reaction steps are performed separately. Operator splitting, however, does not solve exactly the fully coupled numerical model derived from the governing partial differential and algebraic equations describing the transport and reaction processes. An error, proportional to Delta t (the time step used in the numerical solution) is introduced. Thus, small time steps must be used to ensure that accurate solutions result. An alternative scheme is presented, which iterates to the exact solution of the fully coupled numerical model. The new scheme enables accurate solutions to be calculated more efficiently than the two-step method, while maintaining separation of the transport and reaction steps in the calculations. As in the two-step method, the reaction calculations are performed node-wise throughout the computation grid. However, because the scheme relies on LU factorisation of the coefficient matrix in the transport equation solution, the reaction calculations must be performed in sequence, the sequence order being determined by the ordering of the nodes in the grid. Also, because LU factorisation is used, the scheme is limited to solute transport problems for which LU factorisation is a practical solution method. Copyright (C) 1996 Elsevier Science Limited

关键词： numerical algorithm LU factorisation iterative solution Crank-Nicolson scheme nonequilibrium reactions equilibrium reactions multispecies transport fixed-point iteration

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