The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential char...The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential characteristics of mesoscale eddies ascertained through each approach,and attempting to identify factors influencing eddy lifetime.The findings suggest that eddies identified via the sea surface height(SSH)method in the Eulerian framework typically have larger spatial extents compared to those identified using the Lagrangian Average Vorticity Deviation(LAVD)method.The latter is characterized by a greater number of vortices with smaller average values of characteristic parameters.SSH eddies exhibited more remarked seasonal variations than LAVD vortices,and the seasonal variations of their respective cyclonic and anticyclonic eddies showed opposite trends.Analysis in both frameworks indicates that eddy lifetime is positively correlated with various eddy characteristic parameters,including radius,vorticity,kinetic energy,amplitude,EKE/MKE(ratio of boundary to spatial mean kinetic energy),and U/c(max rotation speed to mean propagation speed ratio).A subsequent comparison between SSH eddies with LAVD cores(SSH eddy with LAVD vortex inside)and those without reveals a greater likelihood of extended lifetime in the former.Compared to the characteristic parameters of eddies,the presence of LAVD cores emerges as a critical factor in determining the lifetime of SSH eddies.展开更多
In this paper,we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems(cMOP).Specifically,we reviewed two types of sufficie...In this paper,we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems(cMOP).Specifically,we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral functions.Under a mild quadratic growth condition on the dual of cMOP,we further discussed the R-superlinear convergence of the Karush-Kuhn-Tucker(KKT)residuals of the sequence generated by the augmented Lagrangian methods(ALM)for solving convex matrix optimization problems.Implementation details of the ALM for solving core convex matrix optimization problems are also provided.展开更多
Transports of air particulate matters(PM) from face sources in the atmospheric boundary layer(ABL) are investigated by the Eulerian single fluid model and the Lagrangian trajectory method,respectively.Large eddy simul...Transports of air particulate matters(PM) from face sources in the atmospheric boundary layer(ABL) are investigated by the Eulerian single fluid model and the Lagrangian trajectory method,respectively.Large eddy simulation is used to simulate the fluid phase for high accuracy in both two approaches.The mean and fluctuating PM concentrations,as well as instantaneous PM distributions at different downstream and height positions,are presented.Higher mean and fluctuating particle concentrations are predicted by the Eulerian approach than the Lagrangian one.For the Lagrangian method,PM distributions cluster near the ground-wall because of the preferential dispersion of inertial particles by turbulence structures in the ABL,while it cannot be obtained by the Eulerian single fluid method,because the two-phase velocity differences are neglected in the Eulerian method.展开更多
In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),...In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions.展开更多
The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present st...The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.展开更多
In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are t...In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.展开更多
To predict the effect of the liquid rocket engine combustion chamber conditions on the impingement spray, the conventional uncoupled spray model for impinging injectors is extended by considering the coupling of the j...To predict the effect of the liquid rocket engine combustion chamber conditions on the impingement spray, the conventional uncoupled spray model for impinging injectors is extended by considering the coupling of the jet impingement process and the ambient gas field. The new coupled model consists of the plain-orifice sub-model, the jet-jet impingement sub-model and the droplet collision sub-model. The parameters of the child droplet are determined with the jet-jet impingement sub-model using correlations about the liquid jet parameters and the chamber conditions.The overall model is benchmarked under various impingement angles, jet momentum and offcenter ratios. Agreement with the published experimental data validates the ability of the model to predict the key spray characteristics, such as the mass flux and mixture ratio distributions in quiescent air. Besides, impinging sprays under changing ambient pressure and non-uniform gas flow are investigated to explore the effect of liquid rocket engine chamber conditions. First, a transient impingement spray during engine start-up phase is simulated with prescribed pressure profile. The minimum average droplet diameter is achieved when the orifices work in cavitation state, and is about 30% smaller than the steady single phase state. Second, the effect of non-uniform gas flow produces off-center impingement and the rotated spray fan by 38°. The proposed model suggests more reasonable impingement spray characteristics than the uncoupled one and can be used as the first step in the complex simulation of coupling impingement spray and combustion in liquid rocket engines.展开更多
In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian co...In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.展开更多
Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide ra...Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRPCA problem by an alternation minimization algorithm along with two adaptive rankadjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor,a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.展开更多
The targeted drug delivery and targeted drug therapy transport a drug directly to the center of the disease under various conditions and thereby treat it deliber- ately without effects on the body. This paper studies ...The targeted drug delivery and targeted drug therapy transport a drug directly to the center of the disease under various conditions and thereby treat it deliber- ately without effects on the body. This paper studies the magnetic drug targeting （MDT） technique by particle tracking in the presence of magnetic field in bifurcation vessels of a healthy person and a diabetes patient. The Lagrangian particle tracking is performed to estimate particle behavior under effects of imposed magnetic field gradients along the bifurcation. The results show that the magnetic field increases the volume fraction of particle in the target region, and the efficiency of MDT on a patient with the diabetes disease is better than a healthy person. Also, for the higher magnetic numbers, the flow in the upper branch is strongly affected by the magnetic field.展开更多
A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution functi...A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law. The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.展开更多
The classical Lagrangian particle tracing method is widely used in the evaluation of the ocean annual subduction rate.However,our analysis indicates that in addition to neglecting the effect of mixing,there are two po...The classical Lagrangian particle tracing method is widely used in the evaluation of the ocean annual subduction rate.However,our analysis indicates that in addition to neglecting the effect of mixing,there are two possible deviations in the method:one is an overestimation due to not considering that the amount of subducted water at the source location may be inadequate during the late winter of the first year when the mixed layer becomes shallow;the other one is an underestimation due to the neglect of the effective subduction caused by strong vertical pumping.Quantitative analysis shows that these two deviations mainly exist in the low-latitude subduction areas of the South Pacific and South Atlantic.The two deviations have very similar distribution areas and can partially off set each other.However,the overall deviation is still large,and the maximum relative deviation ratio can reach 50%;therefore,it cannot be ignored.展开更多
This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving t...This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.展开更多
Vehicular Edge Computing(VEC)is a promising technique to accommodate the computation-intensive and delaysensitive tasks through offloading the tasks to the RoadSide-Unit(RSU)equipped with edge computing servers or nei...Vehicular Edge Computing(VEC)is a promising technique to accommodate the computation-intensive and delaysensitive tasks through offloading the tasks to the RoadSide-Unit(RSU)equipped with edge computing servers or neighboring vehicles.Nevertheless,the limited computation resources of edge computing servers and the mobility of vehicles make the offloading policy design very challenging.In this context,through considering the potential transmission gains brought by the mobility of vehicles,we propose an efficient computation offloading and resource allocation scheme in VEC networks with two kinds of offloading modes,i.e.,Vehicle to Vehicle(V2V)and Vehicle to RSU(V2R).We define a new cost function for vehicular users by incorporating the vehicles’offloading delay,energy consumption,and expenses with a differentiated pricing strategy,as well as the transmission gain.An optimization problem is formulated to minimize the average cost of all the task vehicles under the latency and computation capacity constraints.A distributed iterative algorithm is proposed by decoupling the problem into two subproblems for the offloading mode selection and the resource allocation.Matching theorybased and Lagrangian-based algorithms are proposed to solve the two subproblems,respectively.Simulation results show the proposed algorithm achieves low complexity and significantly improves the system performance compared with three benchmark schemes.展开更多
This paper presents theoretical investigations of lattice Boltzmann method(LBM)to develop a completed LBM theory.Based on H-theorem with Lagrangian multiplier method,an amended theoretical equilibrium distribution fun...This paper presents theoretical investigations of lattice Boltzmann method(LBM)to develop a completed LBM theory.Based on H-theorem with Lagrangian multiplier method,an amended theoretical equilibrium distribution function(EDF)is derived,which modifies the current Maxwell–Boltzmann distribution(MBD)to include the total internal energy as its parameter.This modification allows the three conservation laws derived directly from lattice Boltzmann equation(LBE)without additional small-parameter expansions adopted in references.From this amended theoretical EDF,an improved LBM is developed,in which the total internal energy like the mass density and mean velocity is a new macroscopic variable to be updated for different times and cells during simulations.The developed method provides a means to consider external forces and energy generation sources as generalised forces in LBM simulations.The corresponding model and implementation process of the improved LBM are presented with its performance theoretically investigated.Analytically hand-workable examples are given to illustrate its applications and to confirm its validity.The paper will excite more researchers and scientists of this area to numerically practice the new theory and method dealing with complex physical problems,from which it is expected to further advance LBM benefiting science and engineering.展开更多
Analysis of the electromagneto-mechanical coupling effect contributes greatly to the high accuracy estimation of the EM load of many EM devices, such as a tokamak structure during plasma disruption. This paper present...Analysis of the electromagneto-mechanical coupling effect contributes greatly to the high accuracy estimation of the EM load of many EM devices, such as a tokamak structure during plasma disruption. This paper presents a method for the numerical analysis of the electromagnetomechanical coupling effect on the basis of Maxwell＇s equations in the Lagrangian description and staggered load transfer scheme, which can treat the coupled behaviors of magnetic damping and magnetic stiffness effects at the same time. Codes were developed based on the ANSYS development platform and were applied to solve two typical numerical examples： the TEAM Problem 16 and dynamic behavior analysis of a shallow arch under electromagnetic force. The good consistency of numerical results and experimental data demonstrates the validity and accuracy of the proposed method and the related numerical codes.展开更多
In this paper, Lagrangian method is applied to discuss the problem of the hydrodynamic pressure on a suddenly starting vessel. The free surface profile and the coefficients of the hydrodynamic pressure im the vessel w...In this paper, Lagrangian method is applied to discuss the problem of the hydrodynamic pressure on a suddenly starting vessel. The free surface profile and the coefficients of the hydrodynamic pressure im the vessel wall are obtained. And it is verified that the singularity of the pressure near the free surface is only logarithmic.展开更多
A massive bloom of the giant jellyfi sh Nemopilema nomurai occurred in waters off Qinhuangdao,a port city in Hebei Province,in July 2013.However,jellyfi sh larvae were not found in this location during the previous wi...A massive bloom of the giant jellyfi sh Nemopilema nomurai occurred in waters off Qinhuangdao,a port city in Hebei Province,in July 2013.However,jellyfi sh larvae were not found in this location during the previous winter and spring.To determine the possible origin of the giant jellyfi sh medusa in the Bohai Sea,we developed a backward particle-tracking model and a series of numerical simulations were conducted by using the hydrodynamic,three-dimensional Regional Ocean Modeling System(ROMS)results.The simulated results showed that passive particles,representing jellyfi sh medusae,released in surface waters at diff erent dates during the summer had consistent trajectories.Particles released at the sea surface on August1 and 15 could be traced back to the center of the Bohai Sea and to waters between Feiyan Shoal and the new Huanghe(Yellow)River estuary.Particles released on July 1 and 15 could also be traced back to the center of the Bohai Sea and to waters between Feiyan Shoal and only to Zhuangxi tide station.However,none of the particles released in the middle and bottom water layers could be traced back to those areas.Based on the results of the numerical simulations,the distribution characteristics of seafl oor sediments,and observational data for giant jellyfi sh in the region,we suggest that waters between Feiyan Shoal and the new Huanghe River estuary are the likely origin of giant jellyfi sh observed near Qinhuangdao in summer.展开更多
This paper presents a case study on incidents of offshore pile running in layered soils.The study provides a detailed description of the seabed soil data,pile driving records,and field surveillance video observations....This paper presents a case study on incidents of offshore pile running in layered soils.The study provides a detailed description of the seabed soil data,pile driving records,and field surveillance video observations.Three-dimensional large deformation finite element(LDFE)analyses were conducted to retrospectively analyze the incidents,considering the remoulding of seabed soil and degradation of the pile-soil interface in the LDFE modeling.By comparing the field observations with the LDFE analysis,the mechanism of pile running was discussed,with a focus on investigating the pile penetration resistance in each layer.The study revealed that pile running in layered soils primarily resulted from a significant reduction in pile base resistance when transitioning from a strong layer to an adjacent weak layer.To further investigate the pile running mechanism in layered soils,a parametric study on the strength variation of adjacent soil layers and its influence on pile base resistance was conducted.Lastly,a simplified prediction model of pile base resistance,suitable for assessing the risk of pile running in layered soils,was proposed.展开更多
Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motiva...Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.展开更多
基金Supported by the National Natural Science Foundation of China(No.41906021)the Guangdong Ocean University Scientific Research Start-up Fund(No.060302112312)。
文摘The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential characteristics of mesoscale eddies ascertained through each approach,and attempting to identify factors influencing eddy lifetime.The findings suggest that eddies identified via the sea surface height(SSH)method in the Eulerian framework typically have larger spatial extents compared to those identified using the Lagrangian Average Vorticity Deviation(LAVD)method.The latter is characterized by a greater number of vortices with smaller average values of characteristic parameters.SSH eddies exhibited more remarked seasonal variations than LAVD vortices,and the seasonal variations of their respective cyclonic and anticyclonic eddies showed opposite trends.Analysis in both frameworks indicates that eddy lifetime is positively correlated with various eddy characteristic parameters,including radius,vorticity,kinetic energy,amplitude,EKE/MKE(ratio of boundary to spatial mean kinetic energy),and U/c(max rotation speed to mean propagation speed ratio).A subsequent comparison between SSH eddies with LAVD cores(SSH eddy with LAVD vortex inside)and those without reveals a greater likelihood of extended lifetime in the former.Compared to the characteristic parameters of eddies,the presence of LAVD cores emerges as a critical factor in determining the lifetime of SSH eddies.
基金Chao Ding’s research was supported by the National Natural Science Foundation of China(Nos.11671387,11531014,and 11688101)Beijing Natural Science Foundation(No.Z190002)+6 种基金Xu-Dong Li’s research was supported by the National Key R&D Program of China(No.2020YFA0711900)the National Natural Science Foundation of China(No.11901107)the Young Elite Scientists Sponsorship Program by CAST(No.2019QNRC001)the Shanghai Sailing Program(No.19YF1402600)the Science and Technology Commission of Shanghai Municipality Project(No.19511120700)Xin-Yuan Zhao’s research was supported by the National Natural Science Foundation of China(No.11871002)the General Program of Science and Technology of Beijing Municipal Education Commission(No.KM201810005004).
文摘In this paper,we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems(cMOP).Specifically,we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral functions.Under a mild quadratic growth condition on the dual of cMOP,we further discussed the R-superlinear convergence of the Karush-Kuhn-Tucker(KKT)residuals of the sequence generated by the augmented Lagrangian methods(ALM)for solving convex matrix optimization problems.Implementation details of the ALM for solving core convex matrix optimization problems are also provided.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50876053 and 11132005)Opening fund of State of Key Laboratory of Nonlinear Mechanics
文摘Transports of air particulate matters(PM) from face sources in the atmospheric boundary layer(ABL) are investigated by the Eulerian single fluid model and the Lagrangian trajectory method,respectively.Large eddy simulation is used to simulate the fluid phase for high accuracy in both two approaches.The mean and fluctuating PM concentrations,as well as instantaneous PM distributions at different downstream and height positions,are presented.Higher mean and fluctuating particle concentrations are predicted by the Eulerian approach than the Lagrangian one.For the Lagrangian method,PM distributions cluster near the ground-wall because of the preferential dispersion of inertial particles by turbulence structures in the ABL,while it cannot be obtained by the Eulerian single fluid method,because the two-phase velocity differences are neglected in the Eulerian method.
文摘In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.40906044 and 41076048)the Fundamental Research Funds for the Central Universities Project(Grant No.2011B05714)
文摘The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
基金supported by the National Science Foundation of China (Grants 11132007,11272203)
文摘In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.
文摘To predict the effect of the liquid rocket engine combustion chamber conditions on the impingement spray, the conventional uncoupled spray model for impinging injectors is extended by considering the coupling of the jet impingement process and the ambient gas field. The new coupled model consists of the plain-orifice sub-model, the jet-jet impingement sub-model and the droplet collision sub-model. The parameters of the child droplet are determined with the jet-jet impingement sub-model using correlations about the liquid jet parameters and the chamber conditions.The overall model is benchmarked under various impingement angles, jet momentum and offcenter ratios. Agreement with the published experimental data validates the ability of the model to predict the key spray characteristics, such as the mass flux and mixture ratio distributions in quiescent air. Besides, impinging sprays under changing ambient pressure and non-uniform gas flow are investigated to explore the effect of liquid rocket engine chamber conditions. First, a transient impingement spray during engine start-up phase is simulated with prescribed pressure profile. The minimum average droplet diameter is achieved when the orifices work in cavitation state, and is about 30% smaller than the steady single phase state. Second, the effect of non-uniform gas flow produces off-center impingement and the rotated spray fan by 38°. The proposed model suggests more reasonable impingement spray characteristics than the uncoupled one and can be used as the first step in the complex simulation of coupling impingement spray and combustion in liquid rocket engines.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035 and 11171038)the Science Research Foundation of the Institute of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102)
文摘In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.
基金Supported by the National Natural Science Foundation of China(Grant Nos.6157209961320106008+2 种基金91230103)National Science and Technology Major Project(Grant Nos.2013ZX040050212014ZX04001011)
文摘Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRPCA problem by an alternation minimization algorithm along with two adaptive rankadjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor,a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.
文摘The targeted drug delivery and targeted drug therapy transport a drug directly to the center of the disease under various conditions and thereby treat it deliber- ately without effects on the body. This paper studies the magnetic drug targeting （MDT） technique by particle tracking in the presence of magnetic field in bifurcation vessels of a healthy person and a diabetes patient. The Lagrangian particle tracking is performed to estimate particle behavior under effects of imposed magnetic field gradients along the bifurcation. The results show that the magnetic field increases the volume fraction of particle in the target region, and the efficiency of MDT on a patient with the diabetes disease is better than a healthy person. Also, for the higher magnetic numbers, the flow in the upper branch is strongly affected by the magnetic field.
文摘A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law. The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.
基金Supported by the National Natural Science Foundation of China(No.41676009)the National Key R&D Program of China(No.2016YFC0301203)the State Key Program of National Natural Science of China(No.41730534)。
文摘The classical Lagrangian particle tracing method is widely used in the evaluation of the ocean annual subduction rate.However,our analysis indicates that in addition to neglecting the effect of mixing,there are two possible deviations in the method:one is an overestimation due to not considering that the amount of subducted water at the source location may be inadequate during the late winter of the first year when the mixed layer becomes shallow;the other one is an underestimation due to the neglect of the effective subduction caused by strong vertical pumping.Quantitative analysis shows that these two deviations mainly exist in the low-latitude subduction areas of the South Pacific and South Atlantic.The two deviations have very similar distribution areas and can partially off set each other.However,the overall deviation is still large,and the maximum relative deviation ratio can reach 50%;therefore,it cannot be ignored.
基金State Foundstion of Ph.D Units of China(2003-05)under Grant 20020141013the NNSF(10471015)of Liaoning Province,China.
文摘This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.
基金The work was supported in part by the National Natural Science Foundation of China(No.62271295,U22A2003,62201329)Shandong Provincial Natural Science Foundation(ZR2020QF002,ZR2022QF002).
文摘Vehicular Edge Computing(VEC)is a promising technique to accommodate the computation-intensive and delaysensitive tasks through offloading the tasks to the RoadSide-Unit(RSU)equipped with edge computing servers or neighboring vehicles.Nevertheless,the limited computation resources of edge computing servers and the mobility of vehicles make the offloading policy design very challenging.In this context,through considering the potential transmission gains brought by the mobility of vehicles,we propose an efficient computation offloading and resource allocation scheme in VEC networks with two kinds of offloading modes,i.e.,Vehicle to Vehicle(V2V)and Vehicle to RSU(V2R).We define a new cost function for vehicular users by incorporating the vehicles’offloading delay,energy consumption,and expenses with a differentiated pricing strategy,as well as the transmission gain.An optimization problem is formulated to minimize the average cost of all the task vehicles under the latency and computation capacity constraints.A distributed iterative algorithm is proposed by decoupling the problem into two subproblems for the offloading mode selection and the resource allocation.Matching theorybased and Lagrangian-based algorithms are proposed to solve the two subproblems,respectively.Simulation results show the proposed algorithm achieves low complexity and significantly improves the system performance compared with three benchmark schemes.
基金The author acknowledges the School of Naval Architecture and Ocean Engineering,HUST,providing the finance support managed by Guoxiang Hou,enabling author to visit HUST to tackle LBM.Thanks also are given to Yuehong Qian of Soochow University for providing some references involved in the paper.
文摘This paper presents theoretical investigations of lattice Boltzmann method(LBM)to develop a completed LBM theory.Based on H-theorem with Lagrangian multiplier method,an amended theoretical equilibrium distribution function(EDF)is derived,which modifies the current Maxwell–Boltzmann distribution(MBD)to include the total internal energy as its parameter.This modification allows the three conservation laws derived directly from lattice Boltzmann equation(LBE)without additional small-parameter expansions adopted in references.From this amended theoretical EDF,an improved LBM is developed,in which the total internal energy like the mass density and mean velocity is a new macroscopic variable to be updated for different times and cells during simulations.The developed method provides a means to consider external forces and energy generation sources as generalised forces in LBM simulations.The corresponding model and implementation process of the improved LBM are presented with its performance theoretically investigated.Analytically hand-workable examples are given to illustrate its applications and to confirm its validity.The paper will excite more researchers and scientists of this area to numerically practice the new theory and method dealing with complex physical problems,from which it is expected to further advance LBM benefiting science and engineering.
基金supported by National Magnetic Confinement Fusion Program of China(No.2013GB113005)the National Natural Science Foundation of China(Nos.51277139,11321062)the National 973 Program of China(No.2011CB610303)
文摘Analysis of the electromagneto-mechanical coupling effect contributes greatly to the high accuracy estimation of the EM load of many EM devices, such as a tokamak structure during plasma disruption. This paper presents a method for the numerical analysis of the electromagnetomechanical coupling effect on the basis of Maxwell＇s equations in the Lagrangian description and staggered load transfer scheme, which can treat the coupled behaviors of magnetic damping and magnetic stiffness effects at the same time. Codes were developed based on the ANSYS development platform and were applied to solve two typical numerical examples： the TEAM Problem 16 and dynamic behavior analysis of a shallow arch under electromagnetic force. The good consistency of numerical results and experimental data demonstrates the validity and accuracy of the proposed method and the related numerical codes.
文摘In this paper, Lagrangian method is applied to discuss the problem of the hydrodynamic pressure on a suddenly starting vessel. The free surface profile and the coefficients of the hydrodynamic pressure im the vessel wall are obtained. And it is verified that the singularity of the pressure near the free surface is only logarithmic.
基金Supported by the National Special Research Fund for Non-Profi t Marine Sector(No.201005018)the Open Fund of Key Laboratory of Ocean Circulation and Waves,Institute of Oceanology,Chinese Academy of Sciences(No.KLOCAW1403)
文摘A massive bloom of the giant jellyfi sh Nemopilema nomurai occurred in waters off Qinhuangdao,a port city in Hebei Province,in July 2013.However,jellyfi sh larvae were not found in this location during the previous winter and spring.To determine the possible origin of the giant jellyfi sh medusa in the Bohai Sea,we developed a backward particle-tracking model and a series of numerical simulations were conducted by using the hydrodynamic,three-dimensional Regional Ocean Modeling System(ROMS)results.The simulated results showed that passive particles,representing jellyfi sh medusae,released in surface waters at diff erent dates during the summer had consistent trajectories.Particles released at the sea surface on August1 and 15 could be traced back to the center of the Bohai Sea and to waters between Feiyan Shoal and the new Huanghe(Yellow)River estuary.Particles released on July 1 and 15 could also be traced back to the center of the Bohai Sea and to waters between Feiyan Shoal and only to Zhuangxi tide station.However,none of the particles released in the middle and bottom water layers could be traced back to those areas.Based on the results of the numerical simulations,the distribution characteristics of seafl oor sediments,and observational data for giant jellyfi sh in the region,we suggest that waters between Feiyan Shoal and the new Huanghe River estuary are the likely origin of giant jellyfi sh observed near Qinhuangdao in summer.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51879183,51890913)Sino-German Mobility Programme(Grant No.M-0045)。
文摘This paper presents a case study on incidents of offshore pile running in layered soils.The study provides a detailed description of the seabed soil data,pile driving records,and field surveillance video observations.Three-dimensional large deformation finite element(LDFE)analyses were conducted to retrospectively analyze the incidents,considering the remoulding of seabed soil and degradation of the pile-soil interface in the LDFE modeling.By comparing the field observations with the LDFE analysis,the mechanism of pile running was discussed,with a focus on investigating the pile penetration resistance in each layer.The study revealed that pile running in layered soils primarily resulted from a significant reduction in pile base resistance when transitioning from a strong layer to an adjacent weak layer.To further investigate the pile running mechanism in layered soils,a parametric study on the strength variation of adjacent soil layers and its influence on pile base resistance was conducted.Lastly,a simplified prediction model of pile base resistance,suitable for assessing the risk of pile running in layered soils,was proposed.
文摘Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.
