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Improving the numerical stability of the MAGIC model

Journal of Environmental Sciences 2001年第2期13卷 189-191页

作者： DENG Yi- xiang CHEN Ji- ning HU Xue- tao Department of Envi ronment Sciences and Engineering T singhua University Bei jing 100084 China

MAGIC is one of the most widely used models for forecasting long-term acidification. The model's code, however, has been experiencing numerical instability, though this might not be widely known to the public users. The major instability comes from the analytical solution to two cubic equations for calculating SO42- concentration and the exchangeable fraction of Al on the soils. The mathematical algorithm for calculating the concentration of SO42- from a quadratic equation is also found instable. This paper is aimed at improving the instability above through proved numerical algorithms.

关键词： MAGIC model numerical instability

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numerical study via total Lagrangian smoothed particle hydrodynamics on chip formation in micro cutting

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Advances in Manufacturing 2020年第2期8卷 144-159页

作者： Jin-Shi Wang Xiao-Dong Zhang Feng-Zhou Fang State Key Laboratory of Precision Measuring Technology and Instruments Centre of Micro/Nano Manufacturing Technology(MNMT)Tianjin UniversityTianjin 300072People's Republic of China Centre of Micro/Nano Manufacturing Technology(MNMT-Dublin) University College DublinDublinIreland

numerical simulation is an effective approach in studying cutting mechanism.The widely used methods for cutting simulation include finite element analysis and molecular dynamics.However,there exist some intrinsic shortcomings when using a mesh-based formulation,and the capable scale of molecular dynamics is extremely small.In contrast,smoothed particle hydrodynamics(SPH)is a candidate to combine the advantages of them.It is a particle method which is suitable for simulating the large deformation process,and is formulated based on continuum mechanics so that large scale problems can be handled in principle.As a result,SPH has also become a main way for the cutting simulation.Since some issues arise while using conventional SPH to handle solid materials,the total Lagrangian smoothed particle hydrodynamics(TLSPH)is developed.But instabilities would still occur during the cutting,which is a critical issue to resolve.This paper studies the effects of TLSPH settings and cutting model parameters on the numerical instability,as well as the chip formation process.Plastic deformation,stress field and cutting forces are analyzed as well.It shows that the hourglass coefficient,critical pairwise deformation and time step are three important parameters to control the stability of the simulation,and a strategy on how to adjust them is provided.

关键词： Cutting Total Lagrangian smoothed particle hydrodynamics(TLSPH) numerical instability Chip formation

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A high-order SPH method by introducing inverse kernels

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Chinese Journal of Aeronautics 2017年第1期30卷 1-14页

作者： Fang Le Marongiu Jean Christophe Leduc Julien Amicarelli Andrea Caro Joёlleb LMP Ecole centrale de Pekin Beihang University Co-Innovation Center for Advanced Aero-Engine 100083 Beijing China LMFA Ecole centrale de Lyon 69130 Ecully BP 163 France Laboratoire International Associe Beihang University 100083 Beijing China ANDRITZ HYDRO AG Rue des Deux-Gares 6 1800 Vevey Switzerland

The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square（LS） and Moving-Least-Square（MLS） methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.

关键词： Consistency High-order method Inverse method numerical dissipation numerical instability Smoothed particle hydrodynamics

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Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow

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Communications in Computational Physics 2012年第7期12卷 462-478页

作者： Wanda Strychalski Robert D.Guy Department of Mathematics University of CaliforniaDavis CA 95616USA

The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid.For some applications,such as modeling biological materials,capturing internal boundary viscosity is important.We present numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow.We find that the explicit time immersed boundary update is unconditionally unstable above a critical boundary to fluid viscosity ratio for a Kelvin-Voigt material.We also show there is a severe time step restriction when simulating a standard linear boundary with a small relaxation time scale using the same explicit update.A stable implicit method is presented to overcome these computation challenges.

关键词： Stokes flow viscoelastic structures fluid-structure interaction numerical instability

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Method of Lines with Different Discretization on Layers

Method of Lines with Different Discretization on Layers

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2002 3rd International Conference on Microwave and Millimeter Wave Technology

作者： Guo-Lin Li Zheng-He Feng State Key Lab on Microwave and Digital Communications Tsinghua UniversityEE Dept.

＜正＞The behavior and reasons of numerical instability of the Method of Lines（MOL） is discussed. Strategy of different layer different discretization with linear interpolation on the interfaces is adopted.More thic... 详细信息

ISBN: (纸本)078037486X

关键词： method of lines numerical stability interpolation method of lines discretization numerical instability linear interpolation layer interface

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