Experimental and numerical analysis of two-phase infiltration in a partially saturated soil

The purpose of this study is to analyze the effects of the soil air flow on the process of water infiltration in a 93.5 cm deep vertical column for varied boundary conditions at the surface - positive time constant head; time constant fluxes smaller and greater than saturated soil hydraulic conductivity.Several experiments conducted on a sandy soil column with and without a possible air flow through the wall are presented. Continuous and simultaneous measurements of water content and air and water pressure heads at different depths allow the analysis of the air and water movements within the soil and the determination of the capillary pressure and relative permeability for each phase as functions of the volumetric water content.A numerical solution of the equations describing the simultaneous flow of air and water is compared with the experimental data and with the traditional one-phase flow modeling. The results show that the air movement may significantly affect water flow variables such as infiltration rates, water content profiles, and ponding times.Furthermore, some basic assumptions used in two-phase flow modeling, such as the hydrodynamic stability of the wetting fronts and the pertinence of the relative permeability concept, are discussed in the light of the experimental data.     

THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION

The numerical solution of a singularly perturbed problem for the semilinear parabolicdifferential equation with parabolic boundary layers is discussed.A nonlinear two-leveldifference scheme is constructed on the special non-uniform grids.The uniform convergenceof this scheme is proved and some numerical examples are given.     

A simple approximate solution for horizontal infiltration in a Brooks-Corey medium

A simple approximate solution is derived for the problem of one-dimensional absorption in a porous medium characterized by the Brooks-Corey equations. A piecewise-linear saturation profile, which satisfies flux continuity at the edge of the tension-saturated zone as well as an integrated form of the Richards' equation, is assumed. The predicted sorptivity agrees very well with the results of numerical simulations.     

A mathematical model and numerical solution technique for a novel adjustable hydrodynamic bearing

An analysis model for a novel adjustable hydrodynamic fluid film bearing is described. The principles of hydrodynamic lubrication are outlined together with an expanded version of the governing pressure field equation as related to the novel bearing. Finite difference approximations are given for the pressure field equation and a temperature model, both related to the fluid film thickness. Relationships of viscosity with temperature and pressure are included. A finite element model and an iterative computational process are described, whereby full simultaneously converged field solutions for fluid film thickness, temperature, viscosity and pressure were obtained, together with oil film forces. The model and solution process were developed to apply to a variety of hydrodynamic bearings and an outline is given of its extensive use in the design and simulation of one version of the novel bearing. Observations are given on the operation, success rates and verifications of the computational process. Copyright © 1999 John Wiley & Sons, Ltd.     

Difference scheme and numerical simulation based on mixed finite element method for natural convection problem

ntroductionLetΩ R2 beaboundeddomain .Weconsiderthefollowingnon_stationarynaturalconvectionproblem :Problem (Ⅰ )　Findu =(u1,u2 ) ,p ,andTsuchthat,foranyt1>0 ,ut- μΔu +(u· )u + p=λjT　　 ((x ,y ,t) ∈Ω× (0 ,t1) ) ,divu =0　　　　　　　　　 ((x ,y,t) ∈Ω× (0 ,t1) ) ,Tt-ΔT +λu· T =0　　 ((x,y,t) ∈Ω× (0 ,t1) ) ,u =0 ,T =0　　　　　　 ((x,y,t)∈ Ω× (0 ,t1) ) ,u(x ,y ,0 ) =0 ,　T(x,y,0 ) =f(x,y)　　 ((x,y) ∈Ω) ,whereuisthefluidvelocityvectorfield ,pthepressurefield ,Tthet…     

气体运动论数值算法在微槽道流中的应用研究

简要介绍基于Boltzmann模型方程的气体运动论数值算法基本思想及其对二维微槽道流动问题数值计算的推广,并阐述适用于微尺度流动问题的气体运动论边界条件数值处理方法。通过对压力驱动的二维微槽道流动问题进行数值模拟,将不同Knudsen数下的微槽道流计算结果分别与有关DSMC模拟值和经滑移流理论修正的N—S方程解进行比较分析,表明基于Boltzmann模型方程的气体运动论数值算法对微槽道气体流动问题具有很好的模拟能力。     

Translation of a sphere in a rotating viscous fluid: A numerical study

The translation of a sphere moving along the axis of a rotating viscous fluid is studied by the finite difference method at moderate Reynolds (up to R = 500) and Taylor (up to T = 100) numbers. Suppression of the separation is observed with increasing rotation parameter T. The drag coefficient is also presented. It is observed that the drag coefficient is less than that with no rotation in the range 0<N<0·7, where N = 2T/R is the inverse Rossby number. The same phenomenon was observed experimentally by Maxworthy in the range 0<N<0·75±0·03.     

稀薄流非线性模型方程离散速度坐标法有限差分解

从一般非线性Bo ltzm ann方程出发,发展并实现了一套适于大范围K nudsen数稀薄流问题数值模拟的统一算法。采用BGK模型和Shakov模型近似碰撞项,进而引入两个二速度无量纲简化分布函数,通过关于分子速度第三分量取矩积分,将三速度单一模型方程变换为二速度微分方程组。基于G auss-H erm ite积分公式和正交多项式G auss积分公式,借助离散速度坐标法消除简化模型方程对分子速度空间的连续依赖性,从相空间到物理空间得到一组带源项双曲守恒离散方程,并给出其显式和隐式二阶迎风TVD有限差分解。以二维圆柱A r气体超声速绕流算例,验证了数值算法的有效性,比较分析了漫反射和镜面反射两种气体分子壁面反射模型的计算结果。     

ON THE NUMERICAL SOLUTION OF QUASILINEAR WAVE EQUATION WITH STRONG DISSIPATIVE TERM

The numerical solution for a type of quasilinear wave equation is studied. The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved. The error of the difference solution is estimated. The theoretical results are controlled on a numerical example.     

水力机组制动过程的分段递推数值解法

水力机组制动过程的数学模型为非线性一阶常微分方程,目前尚不法得到该方程的精确解析解.本文提出的分段递推法通过对该方程在小分段内进行合理的线性化处理,用拉普拉斯数学变换求出小分段内的近似解析解,得到递推算式,利用递推算式得到全部数值解.使用分段递推法对XAJ水力机组在各种制动方式下进行数值求解,得到了制动过程,并分析了各种制动方式的特点.同时,在自由制动和飞逸过程时与龙格—库塔法进行了比较,并在电气制动时用实验数据进行了验证.结果显示分段递推法是精确的,能满足科学研究和工程应用需要,是求解类似方程的一种简便通用方法.     

An iterative stabilized fractional step algorithm for numerical solution of incompressible N–S equations

Stabilized fractional step algorithm has been widely employed for numerical solution of incompressible Navier–Stokes equations. However, smaller time step sizes are required to use for existing explicit and semi‐implicit versions of the algorithm due to their fully or partially explicit nature particularly for highly viscous flow problems. The purpose of this paper is to present two modified versions of the fractional step algorithm using characteristic based split and Taylor–Galerkin like based split. The proposed modified versions of the algorithm are based on introducing an iterative procedure into the algorithm and allow much larger time step sizes than those required to the preceding ones. A numerical study of stability at acceptable convergence rate and accuracy as well as capability in circumventing the restriction imposed by the LBB condition for the proposed iterative versions of the algorithm is carried out with the plane Poisseuille flow problem under different Reynolds numbers ranging from low to high viscosities. Numerical experiments in the plane Poisseuille flow and the lid‐driven cavity flow problems demonstrate the improved performance of the proposed versions of the algorithm, which are further applied to numerical simulation of the polymer injection moulding process. Copyright © 2005 John Wiley & Sons, Ltd.     

用差分法与超松弛迭代法求高维平稳FPK方程的解

用不同精度的差分格式将高维平稳FPK方程离散化为线性代数方程组,然后用超松弛迭代法求解该线性代数方程组得到平稳FPK方程的近似解。讨论了不同的差分格式、网格密度及超松弛因子对解精度及收敛速度的影响,并与其他方法的计算精度进行比较,提出用多重网格算法提高计算效率。研究了典型的二维及四维随机系统的稳态响应,算例表明,该算法具有简洁、节省存储量且精度高的特点,是求解高维平稳FPK方程解的有效算法。     

Numerical solution of a nonlinear reaction-diffusion equation

A nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkinfinite element method,which has been proved to be2nd-order accurate in time and4th-orderin space.The comparison between the exact and numerical solutions of progressive wavesshows that this numerical scheme is quite accurate,stable and efficient.It is also shown thatany local disturbance will spread,have a full growth and finally form two progressive wavespropagating in both directions.The shape and the speed of the long term progressive wavesare determined by the system itself,and do not depend on the details of the initial values.     

The numerical solution of a singularly perturbed problem for quasilinear parabolic differential equation

We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L~2 norm is proved and numerical examples are presented.     

New numerical schemes based on a criterion for constructing essentially stable and accurate numerical schemes for convection-dominated equations

In order to obtain stable and accurate numerical solutions for the convection-dominated steady transport equations, we propose a criterion for constructing numerical schemes for the convection term that the roots of the characteristic equation of the resulting difference equation have poles. By imposing this criterion on the difference coefficients of the convection term, we construct two numerical schemes for the convection-dominated equations. One is based on polynomial differencing and the other on locally exact differencing. The former scheme coincides with the QUICK scheme when the mesh Reynolds number (Rm) is $\mathop \[{\textstyle{{\rm 8} \over {\rm 3}}}\] $, which is the critical value for its stability, while it approaches the second-order upwind scheme as Rm goes to infinity. Hence the former scheme interpolates a stable scheme between the QUICK scheme at Rm = $\mathop \[{\textstyle{{\rm 8} \over {\rm 3}}}\] $ and the second-order upwind scheme at Rm = ∞. Numerical solutions with the present new schemes for the one-dimensional, linear, steady convection-diffusion equations showed good results.     

子域精细积分及偏微分方程数值解

对于偏微分方程半解析法的方程，精细时程积分虽然能求出高度准确的解，但往往面临矩阵尺度太大的困难；另一方面差分法虽然有带宽小的优点，但有稳定性及精度方面的问题．本文提出子域精细积分法，既可利用精细积分的数值优点，又有带宽小的好处．数值例题表明了子域精细积分法的效能．     

The solution of viscous incompressible jet flows using non‐staggered boundary fitted co‐ordinate methods

A new approach for the solution of the steady incompressible Navier–Stokes equations in a domain bounded in part by a free surface is presented. The procedure is based on the finite difference technique, with the non‐staggered grid fractional step method used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a numerical mapping technique. In order to design an effective free solution scheme, we distinguish between flows dominated by surface tension and those dominated by inertia and viscosity. When the surface tension effect is insignificant we used the kinematic condition to update the surface; whereas, in the opposite case, we used the normal stress condition to obtain the free surface boundary. Results obtained with the improved boundary conditions for a plane Newtonian jet are found to compare well with the available two‐dimensional numerical solutions for Reynolds numbers, up to Re=100, and Capillary numbers in the range of 0≤Ca<1000. Copyright © 2001 John Wiley & Sons, Ltd.     

A control volume-based discretization of the Reynolds equation for the numerical solution of elastohydrodynamic lubrication problems

This paper deals with the discretization of the one-dimensional Reynolds equation coupled with the film shape equation, that is used for the numerical solution of elastohydrodynamically lubricated contacts. The derivation of the developed discretization formula is based on the control volume approach. To reduce the discretization error caused by the upwind expression of the Couette (velocity) term, non-symmetric control volumes are used for discretization of the Reynolds equation, while for the elasticity equation the standard approach is used. A numerical method for the solution of the pressure and the film thickness profiles of elastohydrodynamically lubricated isothermal line contacts is presented. Results are presented for chosen typical parameters of a highly loaded contact. To show the formula efficiency, the convergence speed of both the presented discretization formula and a chosen comparative discretization formula (A.A. Lubrecht, Ph.D. Thesis, University of Twente, The Netherlands, 1987 and C.H. Venner, Ph.D. Thesis, University of Twente, The Netherlands, 1991) are checked. The results show that the presented formula gives better approximations of film thickness values for a given number of equidistant grid nodes. Moreover, the presented approach is probably suitable for more sophisticated cases, such as transient situations and elliptical contacts. © 1998 John Wiley & Sons, Ltd.     

A wavelet multiscale method for inversion of Maxwell equations

This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.     

An Accurate Solution of the Poisson Equation by the Finite Difference-Chebyshev-Tau Method

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