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1.
三维溶质运移问题的分步广义迎风解法 总被引：1，自引：0，他引：1
姚磊华 《长春地质学院学报》1997,27(4):424-428
对对流占优的三维溶质运移问题提出了分步广义的迎风解法，首先利用Ｎ，Ｎ，Ｙａｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节眯速度 相似文献
2.
姚磊华 《吉林大学学报(地球科学版)》1997,(4)
对对流占优的三维溶质运移问题提出了分步广义迎风解法，首先利用Ｎ．Ｎ．Ｙａ－ｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节点速度这一步，节省运算步骤，对井点的浓度变化给出了更合适的求解方法。 相似文献
3.
探讨了孔隙与单裂隙双重介质中的一类核素迁移数学模型及其反演问题。该核素迁移模型是一个耦合的抛物型方程组定解问题。若已知排污点的核素浓度变化规律,利用Laplace变换及其逆变换方法,求得了核素迁移模型正问题的解析解;反之,由下游裂隙中某个点的实测核素浓度,利用偏微分方程的叠加原理和反问题的拟解法,反求出核素迁移模型反问题的解,即排污点的核素状态。最后,给出核素迁移模型的正问题和反问题的数值模拟。数值结果表明,正问题的解析解能够刻画核素的迁移规律,也显示出所提反问题方法能有效地反演核素污染源。 相似文献
4.
根据汉口新业大厦水文地质与工程地质条件,建立开采地下水非稳定流定解问题三维数学模型,利用现有承压含水层非稳定流定解问题数值方案求解,重点讨论了源汇项的具体数学表达式。又简介根据达西定律和水均衡原理,建立了三维有限差分数值方程及其解法。根据土的有效应力原理和压密原理推导出了抽水沉降非线性压密方程,并研制了相应的三维有限元和有限差分计算程序。最后,对该环境岩土工程问题进行了分析和评价,计算结果与实测结果符合较好。 相似文献
5.
一、前言解线性方程组 A~Tx=b (1) 是地质数学中经常遇到的问题,其中 A∈R~(n×m),b∈R~m,x∈R~n,m≥n。在趋势分析中最后归结为解超定方程组A~Tx=b的问题。这里直接影响其效果的主要有两方面:一是趋势函数的选择;二是超定方程组解的精确度。在这里,我们仅讨论第二个问题。因为趋势分析是按最小二乘原则进行曲线拟合,而曲线拟合特别是多项式拟合导出的线性方程组,往往条件很坏。对于这样的问题,若用直接法求解,则精确度很差,有时甚至完全失真;若用迭代法求解,收敛速度很慢,有时甚至根本不收敛。故坏条件问题给数值计算带来了很大的困难。因此,讨论坏条件线性方程组的有效 相似文献
6.
考虑用GMRES方法求解多右端非对称位移方程组(A-σjI)x^(j)=b^(j)，1≤j≤p。基于Smith的求解多右端方程组的种子投影思想，提出了求解上述位移方程组的GMRES种子投影方法，利用种子方程组产生的Krylov子空间来求近似解。本文给出了近似解的误差界，最后数值结果显示了该方法的有效性。 相似文献
7.
考虑方位漂移因素的设计约束方程组是一个具有3个独立未知数、多个隐含未知数的非线性方程组,需要使用数值迭代法才能求出其数值解。给出了解析形式的垂深增量公式,利用约束方程组中的垂深方程,将3个独立未知数中的一个未知数表示成其他2个未知数的函数,并用之对设计约束方程组进行降维处理。剖析了隐含未知数的计算细节,给出了隐含未知数的递推算法。提出了降维后的约束方程组的数值求解算法——缩半网格法,该算法可以快速、可靠地求出设计问题的数值解,适用于在开发计算机软件时编程实现。 相似文献
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作者根据在计算机数值计算中的经验,提出了在解地球物理反演中常见的病态方程组时,如何确定所用求解方法中的参数问题,取得较好效果。最后用算例作了说明。 相似文献
10.
谢承迪 《华东地质学院学报》1995,18(2):169-178
在无压含水层流动计算中，对自由表面变动边界的处理是迄今尚未解决的难题，以往只能 按定边界求解，本文运用泛函原理，将该变域问题归结为微分－积分方程组的求解，采用解析一有限元一次迭代法获得了变边界下的理论解。经验证，其精度较定边界解有明显改善，文末并分析了两种边界条件下解的差别。 相似文献
11.
Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential
equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations.
The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained
minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system
of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments
are presented and discussed.
This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431. 相似文献
12.
H. Hajinezhad Ali R. Soheili Mohammad R. Rasaei F. Toutounian 《Computational Geosciences》2018,22(6):1433-1444
In this paper, the numerical methods for solving the problem of steam injection in the heavy oil reservoirs are presented. We consider a 3-dimensional model of 3-phase flow, oil, water, and steam, with the effect of 3-phase relative permeability. Interphase mass transfer of water and steam is considered; oil is assumed nonvolatile. We apply the simultaneous solution approach to solve the corresponding nonlinear discretized partial differential equation in the fully implicit form. The convergence of finite difference scheme is proved by the Rosinger theorem. The heuristic Jacobian-Free-Newton-Krylov (HJFNK) method is proposed for solving the system of algebraic equations. The result of this proposed numerical method is well compared with some experimental results. Our numerical results show that the first iteration of the full approximation scheme (FAS) provides a good initial guess for the Newton method. Therefore, we propose a new hybrid-FAS-HJFNK method while there is no steam in the reservoir. The numerical results show that the hybrid-FAS-HJFNK method converges faster than the HJFNK method. 相似文献
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A number of phenomena and processes in geosciences can be summarized by second order partial differential equations. The major numerical methods for their solution include the classical finite difference method and the finite element method newly developed in the last two or three decades. Since 1977 the author has proved that for the Laplace and Poisson equations, these two methods are identical and are different only in the process of formulation. For transient problems, such as heat conduction in the earth and the groundwater and oil-gas unsteady flow in porous media, there are some differences in resulting linear algebraic euqations. In general, two methods give similar results, but when the time step is decreased to some extent, the resulting algebraic equation will be consistent with the anti-heat conduction equation rather than the original heat conduction equation. This is the reason why unrealistic potentials are produced by the finite element method. Such a problem can be overcome by using the 相似文献
15.
A novel RANSAC robust estimation technique is presented as an effiecient method for solving the seven-parameter datum transformation problem in the presence of outliers. RANSAC method, which is frequently employed in geodesy, has two sensitive features: (i) the user adjusts some parameters of the algorithm, making it subjective and a rather difficult procedure, and (ii) in its shell, a nonlinear system of equation should be solved repeatedly. In this contribution, we suggest an automatic adjustment strategy for the most important parameter, ‘the threshold value’, based on the ‘early stopping’ principle of the machine-learning technology. Instead of using iterative numerical methods, we propose the use of an algebraic polynomial system developed via a dual-quaternion technique and solved by a non-iterative homotophy method, thereby reducing the computation time considerably. The novelty of the proposed approach lies in three major contributions: (i) the provision for automatically finding the proper error limit parameter for RANSAC method, which has until now been a trial-and-error technique; (ii) employing the algebraic polynomial form of the dual-quaternion solution in the RANSAC shell, thereby accelerating the repeatedly requested solution process; and (iii) avoiding iterations via a heuristic approach of the scaling parameter. To illustrate the proposed method, the transformation parameters of the Western Australian Geodetic Datum (AGD 84) to Geocentric Datum Australia (GDA 94) are computed. 相似文献
16.
岩土体的渗透破坏、地下工程的防渗设计等无不与渗流计算有关。针对渗流自由面问题,提出一种重心拉格朗日插值的配点型无网格方法。由于渗流自由面问题的求解区域是不规则区域,该方法通过将不规则求解区域嵌入一个正则矩形区域,在正则区域上采用重心拉格朗日插值近似未知函数,利用配点法离散渗流问题的控制方程,将重心拉格朗日插值的微分矩阵离散成代数方程表达的矩阵形式。将自由面上的边界条件通过重心拉格朗日插值离散,通过置换方程法和附加方程法施加边界条件,利用正则区域上的重心插值配点法,通过迭代确定最终自由面的位置。数值算例表明所提出的无网格方法对于求解渗流自由面问题的正确性和高精度。 相似文献
17.
探地雷达时域有限差分法正演模拟 总被引：2，自引：0，他引：2
在以往雷达波的正演模拟中,借鉴地震波中成熟的正演模拟方法,均采用模拟声波方程的方法,精度不够高。因此从麦克思韦方程组出发,采用目前电磁场理论中最常用的时域有限差分法,对探地雷达进行了正演模拟。为了进一步说明其正确性,对正演模拟的结果又进行了偏移处理,从结果看出该方法的正确性及可行性。 相似文献
18.
一般条分法的安全系数显示解 总被引：2，自引：1，他引：2
对于边坡稳定性分析中的安全系数方案,根据条底法向力方程,对条底法向力进行假定,使得假定后的条底法向力具有两个待定参数.与传统的条间力假定相比,该假定理论根据更充分,物理意义更明确.通过假定后的条底法向力,化简三个整体极限平衡方程(水平方向、垂直方向力的平衡及力矩平衡),得到安全系数Fs的三次代数方程,其有意义的根为严格满足可能滑动体整体平衡条件的一般条分法的安全系数Fs的显示解.参与计算的有关参数尽管偏多,但都是简单的代数求和.因此,在不损失计算精度的同时,大大简化了一般条分法计算安全系数Fs的过程.算例分析表明,所给一般条分法的安全系数显示解是正确的. 相似文献
19.
The paper presents some numerical results of the problem on contact of stratified elastic half‐spaces possessing unevenness of their surface layers. The approach of the Jacobi polynomials is used to reduce the singular integral equation of the problem to a system of linear algebraic equations. On the basis of the system's solution the dependence of gaps' geometric characteristics on external load and friction is investigated for two types of initial boundary disturbances, namely a local symmetric recess and a periodic set of recesses at a flat boundary. Numerical results are presented in figures for a few elastic and geometric parameters of joint components. The analysis shows that elastic properties and geometric structure of a laminated half‐space have a significant influence on the shape of interface gaps and their location. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
20.
将质量作用方程和质量均衡方程组成平衡化学模型,用Newton-Raphon迭代法并辅以曲线逼近法求解多组分系统中全部物种的平衡浓度和活度,本文计算了一套10组分的淡地下水中59种物种的浓度。 相似文献