ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.

Direct simulation of MHD flows in dual-coolant liquid metal fusion blanket using a consistent and conservative scheme

Direct simulation of 3-D MHD(magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert(FCI) has been conducted.Two kinds of pressure equilibrium slot (PES) in FCI,which are used to balance the pressure difference between the inside and outside of FCI,are considered with a slot in Hartmann wall or a slot in side wall,respectively.The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects,which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket.The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.

Consistency Problem with Tracer Advection in the Atmospheric Model GAMIL

The radon transport test, which is a widely used test case for atmospheric transport models, is carried out to evaluate the tracer advection schemes in the Grid-Point Atmospheric Model of IAP-LASG （GAMIL）. Two of the three available schemes in the model are found to be associated with significant biases in the polar regions and in the upper part of the atmosphere, which implies potentially large errors in the simulation of ozone-like tracers. Theoretical analyses show that inconsistency exists between the advection schemes and the discrete continuity equation in the dynamical core of GAMIL and consequently leads to spurious sources and sinks in the tracer transport equation. The impact of this type of inconsistency is demonstrated by idealized tests and identified as the cause of the aforementioned biases. Other potential effects of this inconsistency are also discussed. Results of this study provide some hints for choosing suitable advection schemes in the GAMIL model. At least for the polax-region-concentrated atmospheric components and the closely correlated chemical species, the Flux-Form Semi-Lagrangian advection scheme produces more reasonable simulations of the large-scale transport processes without significantly increasing the computational expense.

A microstructure-based analysis of cyclic plasticity of pearlitic steels with Hill's self-consistent scheme incorporating general anisotropic Eshelby tensor

A pearlitic steel is composed of numerous pearlitic colonies with random orientations, and each colony consists of many parallel lamellas of ferrite and cementite. The constitutive behavior of this kind of materials may involve both inherent anisotropy and plastic deformation induced anisotropy. A description of the cyclic plasticity for this kind of dual-phase materials is proposed by use of a microstructure-based constitutive model for a pearlitic colony, and the Hill＇s self-consistent scheme incorporating anisotropic Eshelby tensor for ellipsoidal inclusions. The corresponding numerical algorithm is developed. The responses of pearlitic steel BS 11 and single-phase hard-drawn copper subjected to asymmetrically cyclic loading are analyzed. The analytical results agree very well with experimental ones. Compared with the results using isotropic Eshelby tensor, it is shown that the isotropic approximation can provide acceptable overall responses in a much simpler way.

A Possible New Effect of Self-Consistency in the Relativistic Hartree-Fock Approximation

A new effect of self-consistency in the relativistic Hartree-Fock(HF)approximation suggested previously is con firmed by a renormalized calculation with the on-shell renormalization conditions.Two self-consistency schemes,ne requiring self-consistency in the HF potential(scheme P)and the other in the baryon propagator(scheme BP),are studied.It is pointed out that the on-shell renormalization conditions make the self-consistency require-ment in scheme P automatically satisfied.Our calculated results show that scheme P is a good approximation to scheme BP for the calculation of the baryon propagator and the self-consistency in scheme BP diminishes the continuum part of the spectral representation for the baryon propagator,while scheme P yields a baryon propagator which is the same as the HF result contributed by the single particle part of the above spectral representation alone.Further,it is demonstrated that the region of validity of the quasi-particle approximationmay depend on the renormalization conditions.

AWeighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

In the present paper,the numerical solution of It?type stochastic parabolic equation with a timewhite noise process is imparted based on a stochastic finite difference scheme.At the beginning,an implicit stochastic finite difference scheme is presented for this equation.Some mathematical analyses of the scheme are then discussed.Lastly,to ascertain the efficacy and accuracy of the suggested technique,the numerical results are discussed and compared with the exact solution.

二维扩散方程的Du Fort-Frankel差分格式

文章对水质污染分析模型的数值求解技术展开研究,深入细致地探索扩散方程的新型差分格式,应用Du Fort-Frankel差分格式对二维扩散方程进行离散,使用泰勒展开式,提出该类差分格式具有二阶精度,指出该类差分格式与原二维扩散方程是相容的,并验证了该类差分格式的收敛性和绝对稳定性。

基于层次分析法的石材生产线布局优化

采用层次分析法对石材生产线的3种布局方案进行了评估。建立石材生产线布局方案的评价结构模型,计算不同层次评价指标的权重,对石材生产线布局方案进行评估,为实际生产线的建设提供依据。结果表明,基于层次分析法确定各评价指标权重的方法具有一定的实用价值,且能够为类似生产线优化布局的研究提供借鉴。

A CLASS OF EXPLICIT FORWARD TIME-DIFFERENCE SQUARE CONSERVATIVE SCHEMES

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications.

DISSIPATION-BASED CONSISTENT RATE-DEPENDENT MODEL FOR CONCRETE

An energy-dissipation based viscoplastic consistency model is presented to describe the performance of concrete under dynamic loading. The development of plasticity is started with the thermodynamic hypotheses in order that the model may have a sound theoretical background. Independent hardening and softening and the rate dependence of concrete are described separately for tension and compression. A modified implicit backward Euler integration scheme is adopted for the numerical computation. Static and dynamic behavior of the material is illustrated with certain numerical examples at material point level and structural level, and compared with existing experimental data. Results validate the effectiveness of the model.

Random Crank-Nicolson Scheme for Random Heat Equation in Mean Square Sense

The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.

Computational Modeling of Reaction-Diffusion COVID-19 Model Having Isolated Compartment

Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.

A Nonstandard Computational Investigation of SEIR Model with Fuzzy Transmission, Recovery and Death Rates

In this article,a Susceptible-Exposed-Infectious-Recovered(SEIR)epidemic model is considered.The equilibrium analysis and reproduction number are studied.The conventional models have made assumptions of homogeneity in disease transmission that contradict the actual reality.However,it is crucial to consider the heterogeneity of the transmission rate when modeling disease dynamics.Describing the heterogeneity of disease transmission mathematically can be achieved by incorporating fuzzy theory.A numerical scheme nonstandard,finite difference(NSFD)approach is developed for the studied model and the results of numerical simulations are presented.Simulations of the constructed scheme are presented.The positivity,convergence and consistency of the developed technique are investigated using mathematical induction,Jacobean matrix and Taylor series expansions respectively.The suggested scheme preserves all these essential characteristics of the disease dynamical models.The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease.Moreover,the obtained method generates plausible predictions that can be used by regulators to support the decision-making process to design and develop control strategies.Effects of the natural immunity on the infected class are studied which reveals that an increase in natural immunity can decrease the infection and vice versa.

基于结构化变形驱动的非局部宏-微观损伤模型的真Ⅱ型裂纹模拟

Ⅱ型载荷作用下裂纹变形模式也为Ⅱ型的破坏问题称为真Ⅱ型破坏.准确定量地把握真Ⅱ型破坏的全过程是具有挑战性的问题.本文采用结构化变形驱动的非局部宏-微观损伤模型对真Ⅱ型破坏问题进行了模拟.根据结构化变形理论将点偶的非局部应变分解为弹性应变与结构化应变两部分,进而利用Cauchy-Born准则与结构化应变计算点偶的结构化正伸长量.在本文中,结构化应变取为非局部应变的偏量部分.当点偶的结构化正伸长量超过临界伸长量时,微细观损伤开始在点偶层次发展.将微细观损伤在作用域中进行加权求和得到拓扑损伤,并通过能量退化函数将其嵌入到连续介质-损伤力学框架中进行数值求解.进一步地,本文采用Gauss-Lobatto积分格式计算点偶的非局部应变,将积分点数目降低到4个,显著降低了前处理和非线性分析的计算成本.通过对Ⅱ型加载下裂尖应变场的分析揭示了采用偏应变作为结构化应变的原因.对两个典型真Ⅱ型破坏问题的模拟结果表明,本文方法不仅可以把握Ⅱ型加载下的真Ⅱ型裂纹扩展模式,同时可以定量刻画加载过程中的载荷-变形曲线,且不具有网格敏感性.最后指出了需要进一步研究的问题.

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

The first major outbreak of the severely complicated hand,foot and mouth disease(HFMD),primarily caused by enterovirus 71,was reported in Taiwan in 1998.HFMD surveillance is needed to assess the spread of HFMD.The parameters we use in mathematical models are usually classical mathematical parameters,called crisp parameters,which are taken for granted.But any biological or physical phenomenon is best explained by uncertainty.To represent a realistic situation in any mathematical model,fuzzy parameters can be very useful.Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling.However,few works use fuzzy theory in building models to simulateHFMDdynamics.In this context,we examined anHFMD model with fuzzy parameters.A Non Standard Finite Difference(NSFD)scheme is developed to solve the model.The developed technique retains essential properties such as positivity and dynamic consistency.Numerical simulations are presented to support the analytical results.The convergence and consistency of the proposed method are also discussed.The proposed method converges unconditionally while the many classical methods in the literature do not possess this property.In this regard,our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation

In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard equation.The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.

求解Allen-Cahn方程的半隐配点格式

本文首先对Allen-Cahn方程在空间方向基于重心Lagrange插值配点法进行离散,在时间方向分别采用向后欧拉格式(BDF)和Crank-Nicolson(CN)格式进行离散,对其非线性项采用显格式处理,建立半隐配点格式并导出相应的离散线性方程组.然后,对空间一维半离散格式以及二维全离散格式进行相容性分析.最后,通过数值算例验证半隐配点格式的高精度性以及能量随时间递减的性质.与经典的两种差分离散格式进行比较,数值结果表明本文所建立的格式可以用较少的节点达到较高的精度.

IGCC机组厂级监控信息系统搭建方案及数据一致性研究

近几年来随着厂级信息监控系统(SIS)研究的不断深入,SIS系统在企业的应用越来越广泛。SIS系统能够对生产过程中产生的数据进行采集与处理,并建立实时、历史数据库,为电厂管理信息系统(MIS)提供过程数据、计算分析结果,实现了设备运行情况在线监视与分析、机组经济性能指标分析、各类报表自动生成等功能,真正做到检修、运行、生产各部门之间的数据共享,满足了电厂对生产过程管控一体化需求,为机组安全、高效运行提供强大支撑。介绍了一种基于IGCC(整体煤气化联合循环)机组厂级信息监控系统搭建方案,并对DCS与SIS的数据一致性进行研究,给类似机组或工程提供参考。

中文文献引文情感语料库构建

基于内容的引文情感分析克服了传统基于引用频次的引用同一化问题,是引文内容分析领域一个重要的研究热点。然而引文情感分析依赖于带标注的数据集,目前大规模高质量的引文情感语料资源匮乏,严重制约了该领域的研究。因此,本文在分析引文情感表达方式的基础上提出了一套适用于引文情感表示的标注体系,并详细阐述了语料库建设的技术和方法。采用人机结合的标注策略,借助完善的引文标注系统,构建了规模较大的中文文献的引文情感语料库。统计结果显示,在中文信息处理和科技管理领域情感褒义和贬义总的引用的占比分别为22%和6%,引文情感标注kappa值达到0.852,表明该语料库能够客观地反映作者的情感倾向性,可为论文评价、引文网络分析和情感分析等相关领域的研究提供数据支撑。

改进模糊层次分析法及其对任务方案的评价

对于复杂环境中任务方案的评价,由于涉及的因素众多使得评价指标不易全面,文中给出了一种层次化的指标体系,通过准则层细化出子准则层使评价指标全面化。加之对模糊层次分析法的改进,使得上述指标体系层次数目可以不受限制,层次数增加而相应计算量增加却不大;并且通过改换算法中常用的计算因素权值的公式,提高了方案评价的分辨率,增加了对方案优选结果的可信程度。