Finite element formulation for transport equations in a mixed co-ordinate system: An application to determine temperature effects on the single-well chemical tracer test

Heterogeneous equation systems in a pair of coupled co-ordinate systems are solved by a finite element method. The specific physical application studied is the effect of temperature on single-well chemical tracer (SWCT) tests to measure residual oil saturation (volume fraction of immobile oil phase) remaining after waterflooding of an oil reservoir. Since temperature effects are caused by injecting cooler surface fluid down a well into a warm reservoir, the vertical temperature profile in the wellbore as well as the temperature distribution in the porous oil-bearing layer must be considered. The entire system is modelled to account for the different transport mechanisms. However, it is expedient to divide the connected geometrical region into two model domains. The equations for each submodel are expressed in an appropriate set of co-ordinates. The variational formulation of each model is then discussed. A significant temperature effect on the estimation of residual oil saturation occurs when the radial temperature and concentration wave propagation speeds in the porous formation are about the same. In this case the temperature gradient is located across the chemical tracer bank, causing the chemical reaction rate to vary radially. The temperature effects are demonstrated for two actual field tests in complex reservoirs.     

多目标规划在条件微分方程组中的应用

从工程实际出发,借助最佳逼近论和总体极值的思想,运用常微分方程组的求解理论,最优化理论与数值方法,为在最优控制中的一类条件微分方程组的求解,开辟了一条新的求解途径,并用多个计算实例,证明了算法的有效性和可行性。     

On pricing and reserving with-profits life insurance contracts

As a first approximation, asset and liability management issues faced by life insurance companies originate from the sale of with-profits contracts. These contracts are bond-type products with several rate guarantees and other interestsensitive embedded options. Benefits paid out to policyholders mostly depend on the investment performance of a given asset portfolio in which premiums are invested. Thus, guarantees and options granted to policyholders may become effective when the investment performance of the asset portfolio is poor. Issuing a with-profits contract is therefore not equivalent to issuing plain-vanilla debt. The purpose of this paper is to value with-profits liabilities in a consistent option-pricing framework and to develop efficient asset or liability strategies to manage profitability and variability of shareholder value.     

Integral-functional equations for optimal renovation problems

The integral-functional equations with the unknown variable in the upper limit of integration are introduced and studied. They arise in the optimization problems for integral dynamical models and allow to analyze the variable aftereffect duration of dynamical system     

流体力学基本方程组(BEFM)的层次结构理论和简化Navier-Stokes方程组(SNSE)

本文从流场中空间和时间的尺度分析及流体力学基本方程组(BEFM)中诸项的量级分析出发,提出了BEFM的层次结构理论,表明:当特征雷诺数Re>l、且一坐标方向的长度尺度大于其它坐标方向的长度尺度吋,按照BEFM中诸项的量级关系,形成从Euler方程到 BEFM 和从边界层方程到 BEFM 的两支层次结构,文中以二维可压缩流动和不可压缩轴对称射流为例说明了两支层次结构的关系和特点,分析了诸层次方程组的特征、次特征(Subcharacteristics)以及它们的数学性质,并把诸层次方程组与已有的诸简化Navier-Stakes方程组(SNSE)作了对照比较。     

From “You have to have three numbers and a plus sign” to “It’s the exact same thing”: K–1 students learn to think relationally about equations

This research shares progressions in thinking about equations and the equal sign observed in ten students who took part in an early algebra classroom intervention across Kindergarten and first grade. We report on data from task-based interviews conducted prior to the intervention and at the conclusion of each school year that elicited students’ interpretations of the equal sign and equations of various forms. We found at the beginning of the intervention that most students viewed the equal sign as an operational symbol and did not accept many equations forms as valid. By the end of first grade, almost all students described the symbol as indicating the equivalence of two amounts and were much more successful interpreting and working with equations in a variety of forms. The progressions we observed align with those of other researchers and provide evidence that very young students can learn to reason flexibly about equations.     

Efficient ADI and spline ADI methods for the steady-state Navier-Stokes equations

The present paper provides an improved alternating direction implicit (ADI) technique as well as high-order-accurate spline ADI method for the numerical solution of steady two-dimensional incompressible viscous flow problems. The vorticity-stream function Navier-Stokes equations are considered in a general curvilinear coordinate system, which maps an arbitrary two-dimensional flow domain in the physical plane into a rectangle in the computational plane. The stream function equation is parabolized in time by means of a relaxation-like time derivative and the steady state solution is obtained by a time-marching ADI method requiring to solve only 2 × 2 block-tridiagonal linear systems. The difference equations are written in incremental form; upwind differences are used for the incremental variables, for stability, whereas central differences approximate the non-incremental terms, for accuracy, so that, at convergence, the solution is free of numerical viscosity and second-order accurate. The high-order-accurate spline ADI technique proceeds in the same manner; in addition, at the end of each two-sweep ADI cycle, the solution is corrected by means of a fifth-order spline interpolating polynomial along each row and column of the computational grid, explicitly. The validity and the efficiency of the present methods are demonstrated by means of three test problems.     

Numerical simulation of swirling flow in diffusers

A reduced form of Navier–Stokes equations is developed which does not have the usual minimum axial step size restriction. The equations are able to predict accurately turbulent swirling flow in diffusers. An efficient single sweep implicit scheme is developed in conjunction with a variable grid size domain-conforming co-ordinate system. The present scheme indicates good agreement with experimental results for (1) turbulent pipe flow, (2) turbulent diffuser flow, (3) turbulent swirling diffuser flow. The strong coupling between the swirl and the axial velocity profiles outside of the boundary layer region is demonstrated.     

解线性方程组的一种预处理方法

用迭代法求解线性代数方程组时,由于收敛条件较严,只能对一些特殊矩阵(如对角占优、对称正定矩阵等)构造迭代公式.针对一般的线性代数方程组,本文采用预处理的手段. Gauss-Seidel迭代法做出了改进,可以将Gauss-Seidel迭代法不收敛的线性方程组,选取适当的预处理因子,使得线性方程组预处理迭代收敛.