共查询到20条相似文献，搜索用时 125 毫秒
1.
沿海岸分布的承压含水屡中成—淡移动界面的近似解析解,是通过解一个非线性一阶偏微分方程获得的。假定接近界面的水流量随时间从一恒定值不连续地变为另一恒定值,则近似解析值与由t=0和t=∞的Dupuit 近似法所得到的稳定流精确解相吻合。近似解析解与数值解相比较表明:在各时间介值的界面前缘位置上出现约百分之十的最大误差。并且这种近似解获得的界面前缘推进和后退速度的估算值均趋于偏高。近似解非常简便,与数解值相比,更易于运算。除此之外,与数值解对比还表明,仅当在距界面前缘不太远的部位接近水流速度的突变时,无疑可以把解析近似法应用于非承压水流。这是因为自由水面的储存效应在实际到达界面前缘所能影响的下游之前,这种效应减缓了水流速度的变化。 相似文献
2.
库水位升降联合降雨作用下库岸边坡中的浸润线研究 总被引：6，自引：1，他引：5
库岸边坡中的地下水对其稳定性有重大影响,目前还没有统一的公式用来计算岸坡中的浸润线。为此,建立隔水底板呈缓倾角的均质岸坡模型,采用稳定渗流情况下的浸润线作为非稳定渗流的初始值,推导出库水位升降联合降雨作用下该模型中浸润线的近似解析解。利用Geo-Slope中的SEEP/W程序,对浸润线的近似解析解进行验证分析,结果表明,在不同库水位升降和降雨的组合条件下,由近似解析解确定的浸润线与数值模拟结果基本一致。对库水位升降联合降雨作用下赵树岭滑坡中的浸润线进行研究,利用实测浸润线验证了近似解析解的正确性,并预测了赵树岭滑坡在快速蓄水、快速蓄水＋暴雨、快速泄水及快速泄水＋暴雨4种工况下（库水位波动范围为145～175 m）浸润线的变化情况。最后,从解析解的适用条件出发剖析了近似解析解误差产生的原因,为应用浸润线解析解解决实际问题提供依据。 相似文献
3.
拟解析近似方法是一种求解积分方程的一种近似方法,它可以处理强散射或者大扰动的电磁散射问题,在计算过程中避免了传统微分数值方法解决问题时所遇到的大型矩阵或大型代数方程组的求解。孙建国[5]将其引入直流电场的积分方程中,并给出了求解异常电场积分方程的标量拟解析近似公式。在以前的研究中,已经验证了均匀场中异常球体的拟解析近似解的精度,这里对均匀场中的立方体异常体进行数值模拟,得到了直流电场中异常立方体模型的标量拟解析近似解。由于复杂地电模型可以用立方体的组合进行模拟,因此对立方体异常电场拟解析近似解的研究,为三维直流电场中复杂地电模型的快速正反演模拟打下了基础。 相似文献
4.
拟解析近似方法是一种可以处理强散射或大扰动问题的求解积分方程的近似方法,该方法可以避免用传统数值方法解决问题时,所遇到的大型矩阵或大型代数方程组问题。根据孙建国在文章[14]中的求解异常电场积分方程的标量拟解析近似理论公式,对标量拟解析近似进行研究。对均匀场中的异常球体标量拟解析近似解进行计算,并与理论解进行了对比,验证了其精度,证明拟解析近似方法求解直流电场积分方程是可行的。通过对标量拟解析近似方法在直流电场数值模拟的研究,为三维直流电场快速正反演模拟打下了基础。 相似文献
5.
针对目前国内外竖井地基非线性固结计算大多均采用近似等效法求解的不足,根据软土固结理论及数学理论推导,基于塑料排水板椭圆柱假定,推导了考虑地基土水平渗透系数、压缩模量随固结过程非线性变化影响下的排水板处理地基非线性固结控制方程,并利用数学中非线性微分方程理论,给出了非线性固结解析解。通过与Indraratna等非线性固结近似解对比分析,认为理想井下预压荷载越大（Nu越大）,则Indraratna等近似法成果误差越大;且在Cc/Ck = 1.8、Nu = 5时Indraratna等近似解与该理想井非线性固结精确解析解误差高达16%,而解析解与精确数值解基本一致。最后通过Indraratna等典型工程案例验证分析,认为所得理论更符合工程实际,具有较好的工程应用价值。 相似文献
6.
本文阐述了布西涅斯克方程的近似解析解,文中假定具有不变的初始条件,并且边界上的测压水头成阶梯函数增加。利用波尔兹曼变换将这祥的一维问题简化为常微分方程问题,并利用精确解的一些基本特性的方法导出这种问题多项式的近似解。这种方法也适用于一维非线性弥散问题。文中表示了与精确解的一些解析性质有关的数值过程。论文中进行了讨论和推断。 相似文献
7.
一维河流水质方程解析解性态的初步分析 总被引：1，自引：1，他引：0
采用较为简单的数学方法,建立了一维时投源河流水质方程解析解计算结果的统计参数与原始数据的统计参数间的近似关系,推导出描述该解析解计算问题性态的条件数,通过讨论,指明了计算问题属于“病态”和“良态”的条件。从而为正确使用该解析解解决实际水质问题提出了相应的建议。 相似文献
8.
从各向同性非均匀介质中弹性波波动方程出发，导出了在弱不均匀条件下，频率－波数域衍射场方程，给出了格林函数解析解。在电磁波地球物理层析成像数据合成的基础上，用类“体电流法”，将解析解线性化，得到未作Ｂｏｒｎ近似或Ｒｙｔｏｖ近似的衍射场数值解，便于计算合成数据。采用迭代法进行反演，每步迭代中，采用等比Ｎｅｕｍａｎｎ级数解；反问题用ＳＶＤ法求解，探讨了阻尼因子的取法。数值模型试验表明，这种算法是有效和成 相似文献
9.
一类断层效应反演问题的条件稳定性和数值算法 总被引：2，自引：2，他引：2
徐定华 《华东地质学院学报》2003,26(2):101-103
考虑一类垂直断层效应反演问题，其数学模型是具有解析核的第一类积分方程。因其不适定性，获得它的稳定解非常困难。为获得其数值解，有必要先揭示它的条件稳定性。由积分方程方法、解析延拓方法和积分变换性质，获得了它的条件稳定性。基于条件稳定性设计了一种正则化算法，获得了近似解的误差估计。 相似文献
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An approximate analytical solution is presented for the coupled seepage and deformation problem of unsaturated soils. Because of the matric suction dependence of both saturation and permeability coefficient, the coupled governing equations are strongly nonlinear. To obtain an analytical solution, these coupled governing equations are linearized and analytically solved for a specified saturation using the eigenfunction method. Then, the obtained analytical solutions are extended to the entire saturation range. Comparison between the current solution and the previous theoretical solution indicates that the proposed solution yields excellent results. Due to its analytical nature, the proposed procedure can be effectively used to obtain the solution of the coupled seepage and deformation of unsaturated soils. 相似文献
12.
This paper focuses on the derivation of an approximate analytical solution to predict ground surface settlements along the centre-line perpendicular to a slurry-supported diaphragm wall panel. An analytical model of trench excavation is constructed by applying linearly-distributed total earth pressure changes on the sidewalls and the base of the trench in a homogeneous, isotropic, elastic half-space. By applying the principle of superposition appropriately, an explicit solution to calculate ground surface settlements is derived by integrating Mindlin’s displacement formulae. The validity of the solution is verified by three-dimensional finite-element analyses and case studies. Based on the results obtained from a parametric study using the newly derived solution, an algebraic formula is obtained as a first approximation for calculating ground surface settlements. 相似文献
13.
采用简化的k-σ′和mv-σ′分段模型,通过把结构性土一维固结问题转化为上、下层土体厚度不断变化的双层地基一维固结问题,得出了变荷载下结构性土一维固结近似解,并与数值解对比验证了解的合理性。分析结构破坏后渗透系数和体积压缩系数的变化分别对结构性土固结特性的影响表明,在固结系数减小程度相同的情况下,渗透系数减小程度增加则按孔压定义的固结度减小程度加大,而体积压缩系数不断增加则按变形定义的固结度减小程度加大;固结过程中按孔压定义的固结度大于按变形定义的固结度,且随着体积压缩系数增加程度加大,二者的差距加大。 相似文献
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This paper presents a new numerical tool to model the two-dimensional contaminant transport through saturated porous media
using a meshfree method, called radial point interpolation method (RPIM) with polynomial reproduction. In RPIM, an approximate
solution is constructed entirely in terms of a set of nodes and no characterisation of the interrelationship of the nodes
is needed. The advection–dispersion equation with sorption is considered to illustrate the applicability of the RPIM. The
Galerkin weak form of the governing equation is formulated using 2D meshfree shape functions constructed using thin plate
spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Three numerical examples are presented
and the results are compared with those obtained from the finite element method and analytical solutions. In order to test
the practical applicability and performance of the RPIM, two case studies of contaminant transport through landfill liners
are presented. A good agreement is obtained between the results of the RPIM and the field investigation data. 相似文献
16.
A new numerical tool is presented which models the two-dimensional contaminant transport through saturated porous media using a meshfree method called the radial point interpolation method (RPIM) with polynomial reproduction. In RPIM, an approximate solution is constructed entirely in terms of a set of nodes and no characterisation of the interrelationship of the nodes is needed. An advection-dispersion equation with sorption is considered to illustrate the applicability of the RPIM. The Galerkin weak form of the governing equation is formulated using two-dimensional meshfree shape functions constructed using thin plate spline radial basis functions. A computer program is developed for the implementation of the RPIM procedure. Three numerical examples are presented and the results are compared with those obtained from the analytical solution and finite element method. The experimental results are also used to validate the approach. The proposed RPIM has generated results with no oscillations and they are insensitive to Peclet constraints. 相似文献
17.
将降水工程抽取的地下水进行资源性回灌是高渗透性富水地层地下水控制中保护地下水资源的一种有效选择。当回灌场地受限离降水影响区域不够远时,降水与回灌可能存在耦合作用。基于潜水完整降水-回灌井群的浸润线方程,建立了一体化降水回灌井点群系统等流量近似理论解和等效大井近似理论解公式,并进行了误差分析。以北京某基坑工程为例,一体化降水回灌工程的近似理论解、数模分析、流量实测三者结果能互相符合,验证了公式的可靠性。给出了应用公式进行场地受限条件下一体化降水回灌设计问题的求解思路、求解步骤,建立了潜水完整井的一体化降水回灌设计方法。 相似文献
18.
The formulation of viscoelastic solutions from elastic equations using the ‘correspondence principle’ and an inverse Laplace transform has been discussed extensively in the literature. Because this method has been developed, many time-dependent solutions can be obtained from closed form elastic solutions and conditions have been delineated in which the ‘quasi-elastic’ approximation of the viscoelastic solution is within acceptable tolerance. This communication shows the feasibility of the application of these methods to formulate approximate nonlinear viscoelastic solutions with nonlinear stress-strain materials, and for want of a specific nonlinear model to demonstrate this, the hyperbolic model was selected. The ‘power law’ is used to model the relaxation modulus of the viscoelastic materials. There are five related development that are discussed here using a simple numerical example to illustrate each of them and they are: (1) a linear elastic solution, (2) a linear viscoelastic solution, (3) a nonlinear elastic solution, (4) a nonlinear viscoelastic solution and finally, (5) a ‘regression’ approximation of the nonlinear viscoelastic solution which is suggested by the series form of the elastic solution. All of these are related to one another and each provides an acceptably accurate solution of the problem it addresses. The latter is of particular practical interest since it can be used to provide answers to problems involving nonlinear viscoelastic materials while requiring only very small calculation times. The problem used as an example is the calculation of the displacement of a circular hole in an infinite plate made of a material with a nonlinear time-dependent stress-strain relationship. The nonlinear elastic form of the solution was developed by matching results from nonlinear finite element analysis. 相似文献
19.
Analytical solution for a phreatic groundwater fall: the Riesenkampf and Numerov solutions revisited
A. R. Kacimov 《Hydrogeology Journal》2012,20(6):1203-1209
Steady, two-dimensional Darcian flow in a homogeneous isotropic unconfined aquifer, bounded from below by a rectangular wedge representing bedrock, is studied by the theory of holomorphic functions. A triangle of the complex potential domain is mapped onto a circular triangle in the hodograph plane with the help of an auxiliary variable. A full potential theory results in closed-form integral representations for the complex potential and complex velocity, from which the flow rate and free surface are calculated using computer algebra built-in functions. This solution, uniformly valid in the whole flow domain, is compared with simpler approximate ones, retrieved from an analytical archive. Two flow zones are distinguished: a tranquil subdomain where the Dupuit-Forchheimer approximation is suitable and a nappe (a subdomain with a rapidly changing Darcian velocity and steep slope of the phreatic surface) where the Numerov or Polubarinova-Kochina solutions, in terms of the full potential model, are available. Approximations in the two zones are conjugated by matching the positions of the water table and the flow rates, which eventually agree well with the obtained comprehensive solution. 相似文献
20.
An approximate step-by-step procedure is presented for the finite element analysis of transient unconfined flow problems. At each step the free surface is modelled by means of segments coinciding with sides of the elements. This leads to an approximate but extremely simple solution scheme which can be readily incorporated into standard codes for confined analysis. The solutions of some significant problems are presented and compared with other non-approximate solutions. They show that the technique, in spite of its approximation, is capable of giving meaningful results from an engineering viewpoint. 相似文献