海水入侵数值模拟的特征块中心差分法

本文研究二维海水入侵数值模拟的有限差分法．对关于压力的流动方程本文采用块中心差分法,对关于含盐浓度方程的对流扩散方程采用基于完全二次矩形插值的特征差分法,运用先验估计的理论和技巧得到了最佳阶L~2误差估计的结果．     

A characteristic difference method for the transient fractional convection-diffusion equations

A new characteristic finite difference method for solving the two-sided space-fractional convection-diffusion equations is presented, by combining characteristic methods and fractional finite difference methods. Stability, consistency and (therefore) convergence of the new method are discussed in this paper. An error estimate is given. Numerical experiments of this method are carried out and compared with other known methods.     

The characteristic finite difference streamline diffusion method for convection-dominated diffusion problems

In this paper, we consider the characteristic finite difference streamline diffusion method for two-dimensional convection-dominated diffusion problems. The scheme is combined the method of characteristics with the finite difference streamline diffusion (FDSD) method to create the characteristic FDSD (C-FDSD) procedures. Stability analysis and error estimate of the C-FDSD method are deduced. The scheme not only realizes the purpose of lowering the time-truncation error, using larger time step for solving the convection-dominated diffusion problems, but also keeps the favorable stability and high precision of the FDSD method. Finally, numerical experiments are presented to illustrate the availability of the scheme.     

FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.     

非稳态奇异系数微分方程的时间间断时空有限元方法

针对一类二维单轴奇异系数非稳态问题构造了一种时间间断时空有限元格式,利用以Radau点为节点的Lagrange插值多项式的特性,结合有限差分法和有限元法的技巧证明了格式的稳定性和有限元解的时间最大模、空间加权L²（?）-模误差估计.最后列举了一些数值试验结果,验证了理论结果和格式的可行性.     

CABARET scheme for the numerical solution of aeroacoustics problems: Generalization to linearized one-dimensional Euler equations

A generalization of the CABARET finite difference scheme is proposed for linearized one-dimensional Euler equations based on the characteristic decomposition into local Riemann invariants. The new method is compared with several central finite difference schemes that are widely used in computational aeroacoustics. Numerical results for the propagation of an acoustic wave in a homogeneous field and the refraction of this wave through a contact discontinuity obtained on a strongly nonuniform grid are presented.     

Galerkin methods for a model of population dynamics with nonlinear diffusion

A numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro-differential equations describing age-dependent population dynamics with spatial diffusion. We use a finite difference method along the characteristic age-time direction combined with finite elements in the spatial variable. Optimal order error estimates are derived for this approximation. © 1996 John Wiley & Sons, Inc.     

一类非线性反应-扩散方程有限差分格式的稳定性研究

In the article,the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established.Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.The approach used is of a simple characteristic in gaining the stability condition of the scheme.     

THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION

A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced(chemical) oil production in porous media.Some techniques,such as the calculus of variations,energy analysis method,commutativity of the products of difference operators,decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l~2 norm is derived.This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields,and the simulation results are quite interesting and satisfactory.     

基于二次插值的非饱和土壤水流问题的特征差分方法及数值模拟

本文针对一类非饱和土壤水流问题,提出了基于二次插值的特征差分格式,得到了严谨的L2模误差估计.并作了数值试验,指明方法的有效性.     

The construction of high order convergent look-ahead finite difference formulas for Zhang Neural Networks

ABSTRACT

Zhang Neural Networks rely on convergent 1-step ahead finite difference formulas of which very few are known. Those which are known have been constructed in ad-hoc ways and suffer from low truncation error orders. This paper develops a constructive method to find convergent look-ahead finite difference schemes of higher truncation error orders. The method consists of seeding the free variables of a linear system comprised of Taylor expansion coefficients followed by a minimization algorithm for the maximal magnitude root of the formula's characteristic polynomial. This helps us find new convergent 1-step ahead finite difference formulas of any truncation error order. Once a polynomial has been found with roots inside the complex unit circle and no repeated roots on it, the associated look-ahead ZNN discretization formula is convergent and can be used for solving any discretized ZNN based model. Our method recreates and validates the few known convergent formulas, all of which have truncation error orders at most 4. It also creates new convergent 1-step ahead difference formulas with truncation error orders 5 through 8.     

TWO-GRID CHARACTERISTIC FINITE VOLUME METHODS FOR NONLINEAR PARABOLIC PROBLEMS＊

In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.     

Crankshaft-bearing evolution indexes investigation and asperity contact identification based on neural network

The dynamic and lubrication characteristic analyses of the crankshaft–bearing system is quite a complex problem, and it is important to avoid asperity contact which may lead to bearing wear and increase of friction loss significantly in dynamic lubrication condition. In this paper, the dynamic characteristic that has an essential impact on lubrication was investigated over an inline six-cylinder engine. Multi-body dynamics method, tribology, finite element method (FEM), finite difference method (FDM) and component mode synthesis method (CMS) were combined to analyze the dynamic characteristic of crankshaft, oil leakage, oil film pressure, asperity contact pressure and friction loss. Then the orthogonal experiment that included 5 levels and 6 factors was conducted to obtain the training sample sets for neural network, and the probabilistic neural network (PNN) was employed to identify weather the asperity contact happened or not according to its nonlinear characteristic. The analyses which can provide the guidance for the design of main bearing, and avoid the asperity contact in the lubrication are significant to the design of the bearing at the development stage of the engine.     

多层非线性渗流耦合系统的特征分数步差分方法

对多层非线性渗流耦合系统提出适合并行计算的特征分数步差分格式, 利用变分形式、能量方法、粗细网格配套、分片双二次插值、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧, 得到收敛性的最佳阶的l₂误差估计. 该方法已成功的应用到多层油资源评估的生产实际中.     

三维热传导型半导体问题的交替方向特征有限元方法

提出交替方向特征有限元方法,对电场位势方程采用混合元格式,对电子,空穴浓度方程采用交替方向特征有限元格式,对温度方程提出交替方向格式.应用向量积计算及先验估计理论和技巧,得到最佳的L2误差估计.     

A Characteristic Finite Volume Element Method for the Air Pollution Model

In this article, a characteristic finite volume element method is presented for solving air pollution models. The convection term is discretized using the characteristic method and diffusion term is approximated by finite volume element method. Compared with standard finite volume element method, our proposed method is more accurate and efficient, especially suitable to solve convection-dominated problems. The proposed numerical schemes are analyzed for convergence in L ₂ norm. Some numerical results are presented to demonstrate the efficiency and accuracy of the method.     

Solution of the advective-dispersive transport equation using a least squares collocation,Eulerian-Lagrangian method

Numerical solution of the advective-dispersive transport equation is difficult when advection dominates. Difficulties arise because of the first-order spatial derivatives which can be elminated by a local coordinate transformation to the characteristic lines of the first order hyperbolic portion of the equation. The resulting differential equation is discretized using a finite difference in time and finite elements in space employing cubic Hermite basis functions. The residuals at individual collocation points are then computed. The sum of the squares of the residuals is minimized to form the necessary set of algebraic equations. The method has performed well in one-dimensional test problems.     

多孔介质可混溶流动问题的混合元与区域分裂特征差分格式

1 引 言 用区域分裂方法求微分方程的数值解,是近年来计算数学领域的—个新方法。这种方法通过分裂区域来减少所处理问题的规模,并实现并行计算,因此,特别适用于大范围的工程技术问题和数学物理问题。本文用这种方法处理平面可混溶不可压缩流动问题其中J=[0.T].u为Darcy速度,p为压力,c为浓度,k为渗透率,μ（c)为流体粘性,c为注入井给定浓度,q为外界源汇项,q~+=max{q,0}.φ为孔隙度。D为扩散矩阵,本文D与u无关。即仅考虑分子扩散,边条件可取为第一或第二类边条件。本文考虑第一类初边值问题     

平面二维水沙模型的特征有限元数值模拟

1引言水流泥沙数学模型是定量预测水沙运动及河床演变的重要手段,常用于模拟三角洲的形成与发展、淤积区的扩展、淤泥和泥沙输运和沉积而引起的河道的变迁等水利水沙问题.这一模型的数值研究已引起了水动力学工程师们的极大关注,对此问题的细致的研     

Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain

A linear singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain is examined. Regularity constraints are imposed on the data in the vicinity of the two characteristic points. The solution is decomposed into a regular and a singular component. A priori parameter-explicit pointwise bounds on the partial derivatives of these components are established. By transforming to polar co-ordinates, a monotone finite difference method is constructed on a piecewise-uniform layer-adapted mesh of Shishkin type. Numerical analysis is presented for this monotone numerical method. The numerical method is shown to be parameter-uniform. Numerical results are presented to illustrate the theoretical error bounds established.