FINITE DIFFERENCE METHOD OF TRANSINET NONLINEAR FREE SURFACE WAVE PROBLEMS

A finite difference method is developed for computing the two-dimensional trantsientpotential flow generated by an impulse on the free surface.Both the dynamic and kinematicfree surface conditions are considered in nonlinear version.the primary features of thepresent paper include the use of special coordinates transformations so that the geometry ofthe flow field is transformed into a time-invariant region,presents an iteration process.bywhich the velocity potential is computed as the solution of a Poisson equation.theapplication of fast Fourier transform(FFT)technique results in a tri-diagonal system ofequations which can be readily solved by the Thomas algorithm,the computing time issignificantly reduced.Thus an efficient technique for handling the transient potentialproblems is well justified.The feasibility of the present method has been verified by twoexamples including different initial disturbances respectively.     

非线性自由表面波问题的差分解法

本文提出计算二维非定常位势流动的有限差分法,流动是因自由表面任意瞬间扰动所产生的.自由表面上同时满足动力和运动的非线性条件.本方法的基本特征是利用坐标变换将时间相关的物理计算域变换为固定域;建立迭代格式解Poisson方程以求速度势;通过快速富氏变换化为三对角型代数方程组计算未知量,因而大量节省计算机时.为解非定常自由表面波浪问题提供了一个有效的方法.引用了两个例题验证方法的可行性.     

稠油松散岩心相对渗透率曲线的最优化算法

针对稠油松散岩心的相对渗透率曲线计算问题，根据渗流力学及最优化理论，给出了描述岩心内部油、水两相渗流的简化方程，并利用约束变尺度法求解最优化问题，基本解决了岩心堵塞以及结果对初值的敏感性问题。通过实例计算，说明了本方法的可靠性和可行性。     

浅水环流问题的有限元分析

考虑涡流粘性,底部摩擦,Coriolis力和重力作用,以单层模型的竖直向积分建立二维流动的环流控制方程.用Galerkin加权余量法建立环流边值问题的弱形式.用有限元法和分裂时间法分别离散空间和时间进行数值近似计算.采用线性内插的“人工光滑”处理以消除短波长噪音干扰,而避免已有的大阻尼系数方法等缺陷.为节省计算内存容量,程序中建立稀疏矩阵的一维紧凑存贮格式,排除了全部“零”元素的容量要求.     

THE MATHEMATICAL MODELLING OF NEAR COAST SHALLOW WATER CIRCULATION

This paper presents a finite element method to solve the shallow water circulation problem numerically. Considering the Coriolis effect, bottom friction and eddy viscosity, the continuity equation and momentum equation are integrated vertically. Using Galerkin weighted residual method, the weak variational formulation is derived for the finite element analysis. The split-time method is applied for the numerical integration instead of iteration for nonlinear terms. Moreover, an artificial smooth approach is proposed to suppress the short wavelength noise. In order to save Computer storage units, a densed storage scheme is set up, where all the zero elements in large scaled and sparse matrices are excluded.     

Finite difference method of transinet nonlinear free surface wave problems

A finite difference method is developed for computing the two-dimensional transient potential flow generated by an impulse on the free surface. Both the dynamic and kinematic free surface conditions are considered in nonlinear version. the primary features of the present paper include the use of special coordinates transformations so that the geometry of the flow field is transformed into a time-invariant region, presents an iteration process, by which the velocity potential is computed as the solution of a Poisson equation, the application of fast Fourier transform (FFT) technique results in a tri-diagonal system of equations which can be readily solved by the Thomas algorithm, the computing time is significantly reduced. Thus an efficient technique for handling the transient potential problems is well justified. The feasibility of the present method has been verified by two examples including different initial disturbances respectively.