一类高阶KdV类型水波方程的多辛Euler-box格式

高阶KdV类型水波方程作为一类重要的非线性方程有着许多广泛的应用前景．本文主要研究高阶KdV类型水波方程的多辛Euler-box格式．首先,通过正则变换,构造了高阶KdV方程的多辛结构,并得到该系统的多辛守恒律、局部能量守恒律和动量守恒律．然后,我们利用Euler-box格式对高阶KdV方程进行离散,并基于Hamilton空间体系的多辛理论研究了该系统的离散Euler-box格式．我们证明该格式满足离散多辛守恒律,并且给出该格式的向后误差分析．最后,数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性．     

An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model

In this paper, we develop a discontinuous Galerkin method on triangular meshes to solve the reactive dynamic user equilibrium model for pedestrian flows. The pedestrian density in this model is governed by the conservation law in which the flow flux is implicitly dependent on the density through the Eikonal equation. To solve the Eikonal equation efficiently at each time level, we use the fast sweeping method. Two numerical examples are then used to demonstrate the effectiveness of the algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

A FULLY COUPLED,IMPLICIT, NUMERICAL SCHEME FOR LAMINAR AND TURBULENT PARABOLIC FLOWS

A fully coupled, implicit, numerical scheme has been developed for solving highly stiff systems of parabolic conservation equations. The finite-domain equations are formed by integration of the governing conservation equations, expressed in vector notation, over control volumes. The central idea is to put the discretized vector equations as Differential/Algebraic equations (DAE) in the context of numerically solving a system of stiff ordinary differential equations. One of the benefits of the present numerical method is that the Jacobian matrix retains its banded property and thus the problems related to computer storage are eliminated. The mathematical interface that the code employs is a computer program that is most efficient for solving the stiff equations usually found in chemical kinetics. The method has shown good convergence rate and numerical stability. The mathematical formulation is capable of modelling laminar and turbulent flows. Two study cases are considered in this work to illustrate the applicability of the numerical method. Case one corresponds to a numerical simulation of a laminar non-premixed methane–air flame. The chemical processes are described with a four-step reduced mechanism that derives from a larger mechanism with twenty-five reaction steps. The predicted velocity, temperature, and mole fractions of the confined laminar round-jet flame investigated here are compared with experimental data taken from the literature. The versatility of the present solver for predicting high Reynolds number flows is demonstrated by simulating an isothermal turbulent air jet, labelled as case two. A standard two-equation turbulence model is used to simulate the turbulence processes. The analytical velocity distribution for a turbulent submerged jet is used as a benchmark to test the performance of the model for turbulent jets. © 1997 by John Wiley & Sons, Ltd.     

A rarefaction-tracking method for hyperbolic conservation laws

A numerical method for scalar conservation laws in one space dimension is presented. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing; nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. Numerical examples are presented, and specific applications and extensions of the approach outlined.     

弹性力学极坐标辛体系Hamilton函数的守恒律

用弹性力学直角坐标辛体系中类似的形式,定义了极坐标问题径向和环向辛体系的Hamilton函数,对其守恒性进行了研究,由Hamilton对偶方程推出了Hamilton函数的守恒律,同时给出了守恒条件,指出两种极坐标辛体系中Hamilton函数是否守恒均取决于两侧边的荷载和位移情况。在径向和环向辛体系中都给出了算例,验证了Hamilton函数的守恒律。这一守恒律丰富了弹性力学辛体系的理论内容,不仅对于弹性力学极坐标问题的理论分析有所帮助,也为极坐标问题的数值计算分析提供了一个判断依据。     

An implicit potential method for incompressible flows

In this paper, we consider a novel numerical scheme for solving incompressible flows on collocated grids. The implicit potential method utilizes an implicit potential velocity obtained from a Helmholtz decomposition for the mass conservation and employs a modified form of Bernoulli's law for the coupling of the velocity–pressure corrections. It requires the solution only of the momentum equations, does not involve the solution of additional partial differential equations for the pressure, and is applied on a collocated grid. The accuracy of the method is tested through comparison with analytical, experimental, and numerical data from the literature, and its efficiency and robustness are evaluated by solving several benchmark problems such as flow around a circular cylinder and in curved square and circular ducts.Copyright © 2013 John Wiley & Sons, Ltd.     

An alternative numerical procedure for simulating the dynamical response of non-linear elastic rods

In this paper there is presented an alternative numerical procedure for obtaining approximations to non-linear conservation laws like those that describe the dynamical behaviour of elastic rods (composed of materials whose stress–strain relation is non-linear). The above-mentioned procedure consists of approximating the solution of the Riemann problem (associated with the considered conservation law) by a piecewise constant function (satisfying the jump conditions) and using Glimm's scheme for advancing in time, step by step. The proposed numerical approach eliminates the necessity of solving (in a complete way) the associated Riemann problem, easing and cheapening its computational implementation. This procedure is employed for simulating the dynamical response of an elastic-non-linear rod, fixed at its edges, that is left in a non-equilibrium state. There is presented a comparison between results obtained through a classical procedure and through the procedure proposed in this work.     

Applications of conservation integral to indentation with a rigid punch

When a substrate of the brittle material is indented by a relatively rigid, square-ended punch, a singular stress field and K-dominant region will arise at the near-surface adjacent to the punch corners. The singularity of this stress field is identical with the mode I crack. The stress intensity factor in this case represents the intensification of the stress fields induced by indentation. In present article, a new method to determine the stress intensity factors of the indentation problems is developed based on the conservation law. The physical meanings of the proposed method and some numerical analysis have been investigated.     

A wet‐road braking distance estimate utilizing the hydroplaning analysis of patterned tire

A wet‐road braking distance estimate for the vehicles equipped with ABS (anti‐lock brake system) is presented in this paper. The entire speed interval at braking is divided into several uniform sub‐intervals, and the energy conservation law is applied to individual sub‐intervals to predict the intervalwise braking times and the resulting velocity profile at braking and the total braking distance. The proposed method is based on a numerical‐analytical approach such that the frictional energy loss of the patterned tire is computed by 3‐D hydroplaning analysis while the other at the disc pad is analytically derived. The operation of ABS is numerically implemented by controlling the tire angular velocity such that the preset tire slip ratio on the wet road is maintained. The tire hydroplaning is analysed by generally coupling an Eulerian finite volume method and an explicit Lagrangian finite element method. Illustrative numerical experiment is presented to support the validity of the proposed estimate. Copyright © 2006 John Wiley & Sons, Ltd.     

Validation of a novel algorithm for the adaptive calculation of transient stratified flow of gas,oil and water in pipelines

In this paper, a mathematical model for three‐phase flow in pipelines is developed and a novel algorithm for solving the resulting system of partial differential equations is presented. The numerical solution is based on an adaptive mesh refinement technique. Significant gains in the numerical performance have been achieved by using this technique combined with high‐resolution schemes like FCT. This approach is highly beneficial in terms of speed while preserving accuracy. An explicit adaptive numerical solver adaptive conservation law solver (ACLS) has been developed in fortran90 using object‐oriented methods, which give a modular and flexible code. Some numerical tests are performed to show the good behaviour of this solver and to compare the numerical results against the experimental data. Copyright © 2001 John Wiley & Sons, Ltd.     

Interaction between an interface crack and a parallel subinterface crack in dissimilar anisotropic composite materials

In this paper, the pseudo-traction method is combined with the edge-dislocation method (i.e. PTDM) to solve the interaction problem between an interface crack and a parallel subinterface crack in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack loaded by normal or tangential tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface in the lower anisotropic material, the interaction problem is reduced to a system of a singular integral equations by adopting the well-known superposition technique. The equations are then solved numerically with the aid of the Chebyshev numerical integration and the Chebyshev polynomial expansion technique. Several typical examples are calculated and numerical results are shown in figures and tables from which a series of valuable conclusions is obtained. Since the present results should be verified and since no previous results exist to compare them with a consistency check in introduced which starts from the conservation law of the J-integral in anisotropic cases. It is shown that the check provides a powerful tool to examine the results, although it really presents a necessary condition rather than a sufficient way to the crack-tip parameters of the interface crack and the subinterface crack in the dissimilar anisotropic materials.     

系统的稳定性与不稳定性--搅动能守恒律意义和作用的引伸性讨论

讨论了欧阳首承提出的搅动能守恒律意义和作用，并结合曲率空间做了引伸性的讨论，认为搅动能守恒定律是系统稳定性和演化分析的重要原理和方法，它既是解释系统稳定性的原因，也可以作为系统演化分析的方法，并指出了牛顿体系的某些本质性问题。     

Numerical Solution and Experimental Test for Corona Discharge Between Blade and Plate

This paper presents a numerical technique to solve the problem of space charge distribution in a blade-plate electrodes system. The coupled equations are: Poisson equation solved by finite element method (FEM) to determine the distributions of potential, and charge conservation equation solved by the method of characteristics (MOC) to obtain the charge density between the two electrodes. The structured mesh is redefined at each step of the iterative scheme. A simplified injection law at the blade is retained; it allows us to obtain solutions which compare very favorably with experimental results concerning the current density distribution at the plate     

大型原油浮顶储罐非稳态传热过程数值模拟

随着石油储备建设的高速发展,油罐规模正向大型化以及能适应极限工况的方向发展.为了避免油温过低而造成凝罐等安全事故,需要准确掌握罐内油品温度场的变化规律.本文根据能量守恒定律,采用分步式算法求解储罐传热系数,将其代入到由Taylor级数展开法所建立的节点非稳态传热离散方程中,并进行数值求解.对大庆某10×104m3浮顶储罐的应用分析表明:随着环境温度的降低,罐内油品温度降速率逐渐增大,储罐液位越高,容积越大,罐内原油温度就越高,温降速率就越小.研究结果对于优化大型浮顶罐的储存工艺设计,保障油库安全经济运行提供了重要的技术支持.     

Primal and mixed upwind finite element approximations of control advection-diffusion problems

Control advection-diffusion problems are formulated via variational inequalities and effective upwind finite element approximations are studied. The method of local subdifferentials is applied to model and dualize control constraints, as well as to produce global primal and mixed variational formulations. Upwind finite element schemes are derived, satisfying the discrete maximum principle and the conservation of mass law. The numerical resolution methods used are iterative algorithms of the Uzawa type, which are formulated and analyzed. Some numerical experiments are presented for a model discrete problem.     

A numerical upscaling method for an elliptic equation with heterogeneous tensorial coefficients

The aim of this paper is to develop a new numerical method to determine the effective permeability on a coarse scale level of problems with strongly heterogeneous tensorial coefficients defined on a fine scale. This method stems from a primal–dual mixed formulation and the upscaled permeability is obtained by imposing the continuity of the numerical flux across the lines of discontinuities. Moreover, a finite volume scheme is built to numerically solve elliptic equations with this kind of coefficients. Finally, the method is illustrated by several numerical experiments. Copyright © 2002 John Wiley & Sons, Ltd.     

A direct differentiation formulation of electromechanical sensitivity analysis for rough surfaces in contact

In this article, the electromechanical sensitivity analysis of a rough surface contact law with respect to its governing parameters is developed using the direct differentiation method. The numerical accuracy of the method is assessed in two numerical examples. Finally, the identifiability of surface roughness parameters using an inverse method based on numerical optimization is investigated using pseudo-experimental input data.     

分形方法导出改进的牛顿第二定律及万有引力定律

牛顿第二定律及万有引力定律是根据实验结果总结出来的。为了探讨从理论上导出这两个定律的可能性，根据能量守恒定律，给出用变维分形方法针对一个实例（小球沿长斜面滚下）导出改进的牛顿第二定律及万有引力定律的方法。具体给出了适用于实例的常维分形结果：改进的万有引力定律F=-GMm / r199989和改进的牛顿第二定律F=ma101458。     

A flux conserving meshfree method for conservation laws

Lack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate conservation of numerical fluxes. This numerical flux conservation is performed within the usual moving least squares framework. Unlike Finite Volume Methods, it is based on locally defined control cells, rather than a globally defined mesh. We present the application of this method to an advection diffusion equation and the incompressible Navier–Stokes equations. Our simulations show that the introduction of flux conservation significantly reduces the errors in conservation in meshfree GFDMs. Copyright © 2017 John Wiley & Sons, Ltd.     

An Eulerian particle level set method for compressible deforming solids with arbitrary EOS

In this study, an Eulerian, finite‐volume method is developed for the numerical simulation of elastic–plastic response of compressible solid materials with arbitrary equation of state (EOS) under impact loading. The governing equations of mass, momentum, and energy along with evolution equations for deviatoric stresses are solved in Eulerian conservation law form. Since the position of material boundaries is determined implicitly by Eulerian schemes, the solution procedure is split into two separate subproblems, which are solved sequentially at each time step. First, the conserved variables are evolved in time with appropriate boundary conditions at the material interfaces. In the present work a fourth‐order central weighted essentially non‐oscillatory shock‐capturing method that was developed for gas dynamics has been extended to high strain rate solids problems. In this method fluxes are determined on a staggered grid at places where solution is smooth. As a result, the method does not rely on the solution of Riemann problems but enjoys the flexibility of using any type of EOS. Boundary conditions at material interfaces are also treated by a special ghost cell approach. Then in the second subproblem, the position of material interfaces is advanced to the new time using a particle level set method. A fifth‐order Godunov‐type central scheme is used to solve the Hamilton–Jacobi equation of level sets in two space dimensions. The capabilities of the proposed method are evaluated at the end by comparing numerical results with the experimental results and the reported benchmark solutions for the Taylor rod impact, spherical groove jetting, and void collapse problems. Copyright © 2009 John Wiley & Sons, Ltd.