CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.

AN IMPLICIT ALGORITHM OF THIN LAYER EQUATIONS IN VISCOUS，TRANSONIC，TWO－PHASE NOZZLE FLOW

Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to solve the gas-phase governing equ-ations and the characteristic method to follow the tracks of particles, we then obtainedthe full coupled numerical method of two-phase.transonic, turbulent flow. Here, par- ticle size may be grouped, the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow. These methods are applied in viscous two-phase flow. calculation of ro-cket nozzle and in the prediciton of thrust and specific impulse for solid propellant ro-cket motor. The calculation results are in good agreement with the measurerment va-lues. Moreover, the influences of different particle radius, different particle mass frac-tion and particle size grouped on flow field have been discussed, and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time. More important, the effect is more obvious for the calculation of particle size being grouped.

An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids

A Newton/LU-SGS(lower-upper symmetric Gauss-Seidel)iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids.The Newton iteration was employed to solve the nonlinear system,while the linear system was solved with LU-SGS iteration.The effect of several parameters in the implicit scheme,such as the CFL number,the Newton sub-iteration steps,and the update frequency of Jacobian matrix,was investigated to evaluate the performance of convergence history.Several typical test cases were simulated,and compared with the traditional explicit Runge-Kutta(RK)scheme.Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes.Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also.Finally,the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity.The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently.Choosing proper parameters would improve the efficiency of the implicit scheme.Moreover,in the same framework,the DG/FV hybrid schemes are more efficient than the same order DG schemes.

A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations

This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.

PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS

A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings

EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERAL MULTIVALUED MIXED IMPLICIT QUASI-VARIATIONAL INEQUALITIES

A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational inequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative answer to the open question raised by M. A . Noor, and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementarity problems involving the single-valued and set- valued mappings in the recent literature .

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.

Existence and Algorithm of Solutions for Generalized Mixed Implicit Quasi-Variational-Like Inequalities

By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow

The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.

考虑小应变刚度特性的软土边界面模型与应用

基坑开挖导致周边土体经历复杂的加卸载应力路径,传统的本构模型难以同时反映此过程中土体的超固结和小应变刚度特性。在现有的边界面模型中,引入土体小应变刚度特性,提出软土边界面模型小应变刚度修正方法。基于一种高效的半隐式应力更新算法,将改进后的边界面模型采用UMAT子程序二次开发嵌入有限元软件ABAQUS中,并应用于某地铁车站深基坑开挖工程的数值模拟。分析结果表明,采用改进模型准确地反映了上海地区典型土层的小应变状态本构关系和土体的应变刚度相关性;由于改进的边界面模型能够同时反映土体超固结和小应变刚度特性,计算的围护结构变形与现场监测数据吻合较好。

ON A CLASS OF GENERALIZED NONLINEAR IMPLICIT QUASIVARIATIONAL INCLUSIONS

In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is Proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given, As special cases, some known results in this field are also discussed.

A Genetic Algorithm Approach to Optimize Parameters in Infrared Guidance System

In the infrared guidance system, the gray level threshold is key for target recognition. After thresholding, a target in the binary image is distinguished from the complex background by three recognition features. Using a genetic algorithm, this paper seeks to find the optimal parameters varied with different sub images to compute the adaptive segmentation threshold.The experimental results reveal that the GA paradigm is an efficient and effective method of search.

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented, An iterative algorithm for approximating the solutions of generalized implicit wriational- like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved,

不锈钢板式热沉传热特性的实验与模拟研究

目的 研究流量、胀高及焊点排布方式对不锈钢板式热沉传热特性的影响。方法 搭建实验平台,加工出结构参数不同的板式热沉实验件,同时采用静力隐式算法建立相应的几何模型,通过实验与数值模拟相结合的方法,研究流量、胀高和焊点排布方式的变化对板式热沉热阻的影响规律,并分析热沉流道内部流场状态。结果 首先计算了6个工况下的热阻,发现实际换热量为540 W时,数值模拟与实验结果的最大相对误差不大于25%。然后分析了误差来源,最后得到了热沉全流道速度场与温度场的分布情况。结论 实验与模拟结果有较好的符合程度,证明了数值模拟方法的可靠性。在换热量相同时,板式热沉的热阻随流量与胀高的增大而减小,焊点为菱形排布的热沉传热性能相对更好。板式热沉内部的流场具有周期性,焊点使流体扰动增强,并形成射流和旋涡,起到了强化传热的效果。

A Class of Parallel Implicit Runge-Kutta Formulas

A class of parallel implicit Runge-Kutta formulas is constructed for multiprocessor system. A family of parallel implicit two-stage fourth order Runge-Kutta formulas is given. For these formulas, the convergence is proved and the stability analysis is given. The numerical examples demonstrate that these formulas can solve an extensive class of initial value problems for the ordinary differential equations.

An Implicitly Restarted Block Arnoldi Method in a Vector-Wise Fashion

In this paper, we develop an implicitly restarted block Arnoldi algorithm in a vector-wise fashion. The vector-wise construction greatly simplifies both the detection of necessary deflation and the actual deflation itself, so it is preferable to the block-wise construction. The numerical experiment shows that our algorithm is effective.

基于隐式偏好的多目标推荐算法研究

推荐的准确性(accuracy)和多样性(diversity)是推荐算法研究的二个重要指标,能够最大程度地满足用户的喜好.然而,基于准确性的推荐将导致推荐结果过于聚焦集中在某类特征上,使得多样性降低,导致用户选择的广度不足而整体效果不佳.针对推荐算法的两个指标之间的平衡以满足用户的需求,本文采用最大预测评分和最大内部相似度差异的两目标模型,选取极值点和膝点为隐式偏好,利用隐式偏好改进推荐方案搜索优化策略,提出了一种基于隐式偏好的多目标推荐算法.该算法利用切比雪夫距离在迭代过程中对偏好点动态标定,以引导个体收敛于隐式偏好区域,得到具有不同偏好的推荐方案.在Movielens和Netflix数据集上实验结果表明,与Item-based协同过滤推荐算法相比,该算法的推荐结果在确保准确率性能情况下多样性平均提升了38%和33.4%,新颖度平均提升了58.6%和125.4%,降低了多目标推荐算法的复杂度,有效解决了实际应用问题.

基于因素空间理论的扫类连环多分类算法

为解决多分类问题,基于因素空间理论中因素显隐的思想,在扫类连环分类算法基础上,定义类别的合并,提出因素显隐的合并扫类连环分类方法,给出算法步骤,并用数值算例进行分析;定义类别的两两组合,提出因素显隐的两两扫类连环分类方法,给出算法步骤,并用数值算例进行分析。提出采用因素显隐的差额绝对值方法解决两个算法执行过程中出现的决策类别分不开的问题;对UCI数据集中3个实例与支持向量机作了算法对比分析,研究结果表明:提出的合并扫类连环分类方法、两两扫类连环分类方法实现了因素显隐,分类算法的精确度优于支持向量机。多分类学习的因素显隐研究结论拓展了因素空间的理论及应用研究。

基于Hoek-Brown准则的岩体高温-荷载耦合损伤模型及其验证

针对隧道岩体在高温和荷载共同作用下产生的耦合损伤问题,基于连续损伤力学理论,引入高温-荷载耦合损伤因子,建立了考虑高温作用的广义Hoek-Brown(H-B)准则的弹塑性损伤本构模型,解决了模型在数值积分过程中的奇异点问题,并利用Fortran语言编写了模型的有限元程序。结果表明:模型计算的应力-应变曲线与试验所得到的曲线趋势一致且计算结果误差在5%以内,温度作用下隧洞围岩损伤逐渐加剧,验证了模型的准确性和程序的稳健性,可为火灾作用下隧道围岩安全稳定性评价提供一种有效计算方法。