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耦合拉格朗日-欧拉方法及其在海洋工程中的应用
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作者 钱志浩 杨腾茂 刘谋斌 《哈尔滨工程大学学报(英文版)》 CSCD 2024年第2期366-397,共32页
Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in o... Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized. 展开更多
关键词 Coupled Lagrangian–Eulerian description Ocean engineering Wave–structure interaction Particle methods Arbitrary Lagrangian–Eulerian(ALE)methods Particle-in-cell(PIC) Material point method(MPM) Lagrangian–Eulerian stabilized collocation method(LESCM)
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Stabilization meshless method for convection-dominated problems
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作者 张小华 欧阳洁 王建瑜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第8期1067-1075,共9页
It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY iss... It is weN-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instabilitY issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all. 展开更多
关键词 meshless method convection-diffusion problem stability method
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Evaluation of embankment foundation creep in conditions of deep bedding of roof in permafrost soils
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作者 Evgeny Ashpiz Lev Khrustalev 《Research in Cold and Arid Regions》 CSCD 2013年第5期534-539,共6页
Railroad operating experience in permafrost conditions has shown that deformations of embankments on thawing foun- dations last for a long time. After an initial period of heat settlement due to permafrost degradation... Railroad operating experience in permafrost conditions has shown that deformations of embankments on thawing foun- dations last for a long time. After an initial period of heat settlement due to permafrost degradation, the determining factor is the plastic flow of seasonal thawed soils of the foundation upper layer under the embankment. This paper provides a method to evaluate these deformations, and calculation examples using data from line sections of the Chum-Labytnangi Railway in northwestern Russia. It also discusses several methods of embankment stabilization, including the use of ver- tical thermosiphons. 展开更多
关键词 PERMAFROST RAILWAY plastic flow embankment stabilization methods thermosiphons
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Direct discontinuous Galerkin method for the generalized Burgers-Fisher equation 被引量:3
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作者 张荣培 张立伟 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第9期72-75,共4页
In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cell... In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method. 展开更多
关键词 direct discontinuous Galerkin method Burgers Fisher equation strong stability pre-serving Runge-Kutta method
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Intra-layer synchronization in duplex networks 被引量:1
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作者 沈洁 汤龙坤 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第10期245-251,共7页
This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability ... This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly,for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results. 展开更多
关键词 multi-layer network intra-layer synchronization Lyapunov stability method
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Two-level stabilized finite element method for Stokes eigenvalue problem 被引量:1
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作者 黄鹏展 何银年 冯新龙 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第5期621-630,共10页
A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh si... A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O(H2), which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method. 展开更多
关键词 Stokes eigenvalue problem stabilized method lowest equal-order pair two-level method
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Seismic stability evaluation of embankment slope based on catastrophe theory 被引量:5
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作者 Hongwei Zhu Lingkan Yao Yuan Luo 《Journal of Modern Transportation》 2013年第2期111-116,共6页
An evaluation method for the seismic stability of embankment slope was presented based on catastrophe theory. Seven control factors, including internal frictional angle, cohesion force, slope height, slope angle, surf... An evaluation method for the seismic stability of embankment slope was presented based on catastrophe theory. Seven control factors, including internal frictional angle, cohesion force, slope height, slope angle, surface gradients, peak acceleration, and distance to fault were selected for analysis of multi-level objective decomposition. According to the normalization formula and the fuzzy subject function produced by combination of catastrophe theory and fuzzy math, a recursive calculation was carried out to obtain a catastrophic affiliated functional value, which can be used to evaluate the seismic stability of embankment slope. Fifteen samples were used to verify the effectiveness of this method. The results show that compared with the traditional quantitative method, the catastrophe progression owns higher accuracy and good application potential in predicting the seismic stability of embankment slope. 展开更多
关键词 Embankment slope Seismic stability -Catastrophe progression method - Comprehensiveevaluation
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Design and operation problems related to water curtain system forunderground water-sealed oil storage caverns 被引量:4
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作者 Zhongkui Li Baoqi Lu +2 位作者 Jing Zou Bin Xu Zhizeng Zhang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2016年第5期689-696,共8页
The underground water-sealed storage technique is critically important and generally accepted for the national energy strategy in China. Although several small underground water-sealed oil storage caverns have been bu... The underground water-sealed storage technique is critically important and generally accepted for the national energy strategy in China. Although several small underground water-sealed oil storage caverns have been built in China since the 1970s, there is still a lack of experience for large-volume underground storage in complicated geological conditions. The current design concept of water curtain system and the technical instruction for system operation have limitations in maintaining the stability of surrounding rock mass during the construction of the main storage caverns, as well as the long-term stability. Although several large-scale underground oil storage projects are under construction at present in China, the design concepts and construction methods, especially for the water curtain system, are mainly based on the ideal porosity medium flow theory and the experiences gained from the similar projects overseas. The storage projects currently constructed in China have the specific features such as huge scale, large depth, multiple-level arrangement, high seepage pressure, complicated geological conditions, and high in situ stresses, which are the challenging issues for the stability of the storage caverns. Based on years’ experiences obtained from the first large-scale (millions of cubic meters) underground water-sealed oil storage project in China, some design and operation problems related to water curtain system during project construction are discussed. The drawbacks and merits of the water curtain system are also presented. As an example, the conventional concept of “filling joints with water” is widely used in many cases, as a basic concept for the design of the water curtain system, but it is immature. In this paper, the advantages and disadvantages of the conventional concept are pointed out, with respect to the long-term stability as well as the safety of construction of storage caverns. Finally, new concepts and principles for design and construction of the underground water-sealed oil storage caverns are proposed. 展开更多
关键词 Underground water-sealed oil storage caverns Water curtain system Design concept and method Cavern stability and safety
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Unstable and exact periodic solutions of three-particles time-dependent FPU chains 被引量:1
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作者 刘期怀 邢明燕 +1 位作者 李新祥 王超 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第12期246-252,共7页
For lower dimensional Fermi–Pasta–Ulam(FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of th... For lower dimensional Fermi–Pasta–Ulam(FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α(t) and β(t) with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions. 展开更多
关键词 periodic solution stability method of averaging
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Solution to multiple attribute group decision making problems with two decision makers 被引量:2
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作者 Fangwei Zhang Wei Wang Xuedong Hua 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第2期329-333,共5页
A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this ... A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method. 展开更多
关键词 multiple attribute group decision making(MAGDM) stability theory jackknife method credibility degree traffic engineering
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Application of Arnoldi method to boundary layer instability 被引量:1
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作者 张永明 罗纪生 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第12期379-391,共13页
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e.,... The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory(LST) for two-dimensional(2D) disturbance on one-dimensional(1D) basic flow, comparison with LST for three-dimensional(3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence(FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting(TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous' in secondary instability. 展开更多
关键词 Arnildi method linear stability theory Floquet theory secondary instability
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Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems 被引量:1
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作者 Evgeniy Perevoznikov Olga Mikhailova 《Journal of Applied Mathematics and Physics》 2015年第5期569-576,共8页
Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a... Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems. 展开更多
关键词 Nonlinear Dynamical Systems Stability Analysis methods Dynamical Chaos Lorenz and Rossler Model Problems
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A new stabilized method for quasi-Newtonian flows
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作者 谢春梅 冯民富 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第9期1081-1096,共16页
For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stab... For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r(Ω) norm and that of the pressure in the L r' (Ω) (1/r + 1/r' = 1). The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results. 展开更多
关键词 quasi-Newtonian stabilized method power law model Carreau model residual-based posterior bound
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An efficient Galerkin meshfree formulation for shear deformable beam under finite deformation 被引量:1
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作者 Dongdong Wang,and Yue Sun Department of Civil Engineering,Xiamen University,Xiamen 361005,China 《Theoretical & Applied Mechanics Letters》 CAS 2011年第5期45-50,共6页
This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear a... This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear analysis encompasses the fully geometric nonlinearities due to large deflection,large deformation as well as finite rotation.The incremental equilibrium equation is obtained by the consistent linearization of the nonlinear variational equation.The Lagrangian meshfree shape function is utilized to discretize the variational equation.Subsequently to resolve the shear and membrane locking issues and accelerate the computation,the method of stabilized conforming nodal integration is systematically implemented through the Lagrangian gradient smoothing operation.Numerical results reveal that the present formulation is very effective. 展开更多
关键词 meshfree method beam finite deformation stabilized conforming nodal integration
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Analysis of nonlinear stability and post-buckling for Euler-type beam-column structure
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作者 朱媛媛 胡育佳 程昌钧 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第6期719-728,共10页
Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-... Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional (3D) mathematical model for analyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed. One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution, bifurcation points, and bifurcation solutions by the shooting method and the Newton- Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered. 展开更多
关键词 beam-column structure Hamilton variational principle nonlinear stability shooting method Newton-Raphson iterative method POST-BUCKLING
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LAGRANGE'S THEOREM FOR A CLASS OF NONHOLONOMICSYSTEMS AND ITS APPLICATION
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作者 李刚常 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第2期135-146,共12页
The stability problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied is studied in this paper .Based on Liapunov's direct method and the definition of stability , Lagrange&... The stability problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied is studied in this paper .Based on Liapunov's direct method and the definition of stability , Lagrange's theorem of holonomic systems is extended to a class of nonholonomic conservative systems and dissipative systems ,and a new expression is made to the relation between asymptotic stability for the manifold of equilibrium positions of this class of nonholonomic systems and dissipative forces .Twoexamples are finally given to illustrate the application of the theorems . 展开更多
关键词 nonholonomic system Lagrange's theorem. manifold stability Liapunov's direct method
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Quantum Chemical Investigations on the Structures,Stabilities and Decompositions of Trinitrobenzenes and Their Chloro Derivatives
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作者 tGONG Xuedong XIAO Heming DONG Haishan 《Chemical Research in Chinese Universities》 SCIE CAS CSCD 1999年第2期60-65,共6页
IntroductionTrinitrobenzenes(TNBs)havebeenthefocusofanumberofinvestigationsforalongtime.Manyoftheirderivativ... IntroductionTrinitrobenzenes(TNBs)havebeenthefocusofanumberofinvestigationsforalongtime.Manyoftheirderivatives,forexamplemeth... 展开更多
关键词 Trinitrobenzene Molecular orbital method Molecular structure STABILITY Decomposition method Molecular structure Stability Decomposition
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Multiple solutions and stability of the steady transonic small-disturbance equation
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作者 Ya Liu Shijun Luo Feng Liu 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2017年第5期292-300,共9页
Numerical solutions of the steady transonic small-disturbance(TSD) potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number rang... Numerical solutions of the steady transonic small-disturbance(TSD) potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data. 展开更多
关键词 Transonic flow Multiple solutions Flow stability Numerical method Potential flow
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GENERALIZED TRANSFER FUNCTION OF CONTROL SYSTEM AND AN IMPROVEMENT ON THE DECISION METHOD OF MOVEMENT STABILITY
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作者 叶寿桢 沙万乾 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第4期361-371,共11页
In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been... In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems. 展开更多
关键词 link GENERALIZED TRANSFER FUNCTION OF CONTROL SYSTEM AND AN IMPROVEMENT ON THE DECISION METHOD OF MOVEMENT STABILITY
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Velocity plus displacement equivalent force control for real-time substructure testing
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作者 Zhou Huimeng D.Wagg Wang Tao 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2018年第1期87-102,共16页
This paper employs a velocity plus displacement(V+D)-based equivalent force control(EFC) method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 fee... This paper employs a velocity plus displacement(V+D)-based equivalent force control(EFC) method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 feedback control loops to replace mathematical iteration to solve the nonlinear dynamic equation. A spectral radius analysis of the amplification matrix shows that the type 2 EFC-explicit, Newmark-β method has beneficial numerical characteristics for this method. Its stability limit of Ω = 2 remains unchanged regardless of the system damping because the velocity is achieved with very high accuracy during simulation. In contrast, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation are shown to decrease with an increase in system damping. In fact, the EFC-average acceleration method is shown to change from unconditionally stable to conditionally stable. We also show that if an over-damped system with a damping ratio of 1.05 is considered, the stability limit is reduced to Ω =1.45. Finally, the results from an experiment with a single-degree-of-freedom structure installed with a magneto-rheological(MR) damper are presented. The results demonstrate that the proposed method is able to follow both displacement and velocity commands with moderate accuracy, resulting in improved test performance and accuracy for structures that are sensitive to both velocity and displacement inputs. Although the findings of the study are promising, additional test data and several further improvements will be required to draw general conclusions. 展开更多
关键词 real-time substructure test EFC velocity/displacement control newmark-β method stability
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