共查询到18条相似文献，搜索用时 171 毫秒
1.
Richards方程常用于非饱和土渗流问题,并且应用广泛。在数值求解中,对Richards方程线性化,进而采用有限差分法进行数值离散以及迭代计算。其中传统的迭代法比如Jacobi迭代、Gauss-Seidel迭代法（GS）和连续超松驰迭代法（successive over-relaxation method,简称SOR）迭代收敛率较慢,尤其在离散空间步长较小以及离散时间步长较大时。因此,采用整体校正法以及多步预处理法对传统迭代法进行改进,提出一种基于整体校正法的多步预处理Gauss-Seidel迭代法（improved Gauss-Seidel iterative method with multistep preconditioner based on the integral correction method,简称ICMP(m)-GS）求解Richards方程导出的线性方程组。通过非饱和渗流算例,并与传统迭代法和解析解对比,对改进算法的收敛率和加速效果进行了验证。结果表明,提出的ICMP(m)-GS可以很大程度地改善线性方程组的病态性,相较于常规方法GS,SOR以及单一改进方法,ICMP(m)-GS具有更快的收敛率,更高的计算效率和计算精度。该方法可以为非饱和土渗流的数值模拟提供一定参考。 相似文献
2.
非饱和渗流Richards方程数值求解的欠松弛方法 总被引：1，自引：0，他引：1
非饱和土渗流理论是岩土工程问题的基础理论,在土石坝渗流、污染物传输、冻土渗流相变和边坡稳定分析等领域有着广泛的应用。非饱和土渗流Richards方程的数值求解过程中,某些参数如水力传导系数计算不当可能引起非线性方法,如Picard方法或Newton方法的迭代收敛震荡,从而导致非线性迭代方法收敛缓慢和精度降低。为了消除或降低迭代收敛震荡对求解精度和计算性能的影响,目前主要采用欠松弛方法。通过一维入渗算例和二维非均质土坝渗流算例演示已有欠松弛方法的局限性,进而提出新的短项混合欠松弛法,并对其实用性和可靠性进行验证。 相似文献
3.
《岩土力学》2017,(11):3332-3340
针对裂隙岩体的非饱和渗流问题,基于离散裂隙网络模型并结合非饱和Darcy定律、Richards方程、非饱和本构模型以及Signorini型饱和-非饱和互补溢出边界,提出了离散裂隙网络非饱和渗流问题的数学模型。采用有限单元法建立了裂隙网络非饱和渗流模型的数值求解格式和对应的迭代算法。通过与矩形坝稳定渗流、一维竖直裂隙非饱和入渗以及室内二维瞬态排水渗流的试验、数值及理论结果对比分析,验证了文中算法的有效性;根据流量等效原则,指出了裂隙网络模型应用于求解连续介质非饱和渗流问题的有效性。验证了该算法对于求解裂隙边坡降雨入渗问题的可靠性,揭示了降雨入渗过程裂隙网络流量分布的非均匀性及裂隙产状对降雨入渗流动具有重要的控制作用。 相似文献
4.
在使用有限元方法求解非饱和土渗流问题时,土-水特征曲线和渗透率函数的强烈非线性经常会造成计算中出现迭代不收敛、计算误差大等问题。基于变量变换的思想,结合时间步长自适应技术提出了一种求解非饱和渗流问题的新方法--欠松弛RFT变换方法（ATUR1）。ATUR1方法通过变量变换,大大降低了Richards方程中未知数在空间和时间上的非线性程度,从而改善这种非线性所带来的计算收敛困难和精度差等问题。欠松弛技术的引入减少了迭代过程中的振荡现象,进一步提高了非线性迭代计算的效率。时间步长自适应技术则有效地控制整个计算过程的误差。数值算例结果说明,ATUR1可以有效地提高计算效率和精度,是一种准确有效的计算方法。 相似文献
5.
《岩土力学》2016,(1):256-262
有效地模拟非饱和渗流过程对土质边坡稳定性分析、土石坝渗流、污染物迁移等众多领域有着重要的意义。描述非饱和渗流的Richards方程是具有强烈非线性的偏微分方程,通常需要采用有限元等数值方法并结合有效的迭代方法进行求解。Picard迭代法是实用的非线性计算方法,在非饱和渗流领域应用广泛,但经常会出现收敛震荡、速度缓慢和精度降低的问题。为提高计算性能,结合有限元法提出了一种高效的自适应松弛Picard法。通过模拟一维和二维渗流算例,并与传统方法的结果进行对比,对算法和程序的准确性、高效性和鲁棒性进行了验证。测试结果表明,该方法可以在保证计算精度的同时有效地减少数值震荡,提高收敛速度。研究成果对非饱和渗流有限元程序的开发和应用有一定的参考价值。 相似文献
6.
波动方程数值模拟是研究地震波传播机理的重要工具,有限差分求解波动方程是当前地震波数值模拟的主要方法之一。当地下介质中的地震波速度较低或地震波高频成分丰富时,常规有限差分技术常常产生严重的数值频散误差,这种误差会降低数值模拟的精度,影响对地震波传播机理的分析。为压制地震波数值模拟时产生的数值频散误差,提高波场模拟精度,提出了基于NAD算子的时间四阶精度波动方程差分格式。根据对应的差分格式,分析了该差分格式的数值频散关系。与常规四阶精度差分算法的频散曲线相比,基于NAD时间四阶精度差分方法不但能够实现时间频散的有效压制,同时其基于更多网格点的位移分量和位移梯度分量空间微分求解方法还能够实现空间频散的有效压制。另外在相同模型条件下,基于NAD算法的声波方程时间四阶差分解法可采用大网格对模拟空间进行差分离散,减少网格数,提高计算效率。 相似文献
7.
基于球坐标系下有限差分的地磁测深三维正演 总被引：2，自引：0，他引：2
为了计算全球尺度电磁感应的响应,本文介绍地磁测深频率域三维正演。正演算法采用球坐标系下的交错网格有限差分方法,从Maxwell方程的积分形式出发,采用PARDISO对离散后的方程组求解,避免了迭代求解的散度校正。为了验证本文结果的正确性和精度,与前人的有限元和有限差分方法进行了对比,一维层状模型的三维交错网格有限差分数值结果和解析解相对误差小于5%,双半球模型的计算结果与前人的计算结果完全吻合。三维"棋盘模型"计算表明磁场分量对异常体的大小和位置具有很好的分辨能力。 相似文献
8.
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
9.
非均匀介质中交错网格高阶有限差分数值模拟 总被引：5，自引：0，他引：5
地震波场的数值模拟一直是地球物理学的一个重要的研究领域,而在数值正演模拟方法的研究中,计算精度和计算效率是评价该方法有效性及优越性的二个关键问题。这里从一阶速度—应力弹性波动方程出发,着重介绍如何构造离散化模型的网格,如何求解空间导数,如何选取边界条件等内容,从而更有效地提高数值计算的精度与计算效率。文中构造了不同类型的介质模型,并在交错网格中,利用高阶有限差分模拟非均匀介质的波场传播。模拟结果表明,该方法实现简单,具有很好地稳定性和较高的精度,能够直观、高效地反映出介质中波场的传播规律。 相似文献
10.
在井间地震有限差分数值模拟中,用离散化的高阶差分方程近似连续导数的波动方程时,不可避免地会产生数值频散,而数值频散程度则直接影响到地震波数值模拟精度,因此为了得到清晰准确的地震波场记录,必须尽可能地压制数值频散。这里在一阶速度应力弹性波方程的基础上,利用两个约束条件构造拉格朗日函数获取优化差分系数,与泰勒展开差分系数下的交错网格高阶差分模拟结果比较,发现改进的优化交错网格差分算子的高阶差分数值模拟能更有效地压制数值频散,进一步提高交错网格高阶差分数值模拟的精度,为高精度井间地震数据的波场成像、纵横波联合解释等提供可靠依据。 相似文献
11.
This paper studies the potential of using the successive over-relaxation iteration method with polynomial preconditioner (P(m)-SOR) to solve variably saturated flow problems described by the linearized Richards’ equation. The finite difference method is employed to numerically discretize and produce a system of linear equations. Generally, the traditional Picard method needs to re-evaluate the iterative matrix in each iteration, so it is time-consuming. And under unfavorable conditions such as infiltration into extremely dry soil, the Picard method suffers from numerical non-convergence. For linear iterative methods, the traditional Gauss-Seidel iteration method (GS) has a slow convergence rate, and it is difficult to determine the optimum value of the relaxation factor w in the successive over-relaxation iteration method (SOR). Thus, the approximate optimum value of w is obtained based on the minimum spectral radius of the iterative matrix, and the P(m)-SOR method is extended to model underground water flow in unsaturated soils. The improved method is verified using three test examples. Compared with conventional Picard iteration, GS and SOR methods, numerical results demonstrate that the P(m)-SOR has faster convergence rate, less computation cost, and good error stability. Besides, the results reveal that the convergence rate of the P(m)-SOR method is positively correlated with the parameter m. This method can serve as a reference for numerical simulation of unsaturated flow.
相似文献12.
M. H. Hashemi 《Geomechanics and Geoengineering》2015,10(4):243-248
One of the significant problems in geo-environmental and geotechnical engineering is the unsaturated flow of soil in unsaturated soils. The model of this phenomenon in porous media is governed by the Richards equation. In this paper a new, efficient, iterative method is used to handle the Richards equation. This new technique is obtained from the variational iteration method by a simple reconstruction that is the Laplace iteration method (LIM). In order to evaluate the efficiency and accuracy of the solutions obtained by the proposed method, two representative examples were investigated. The obtained results show that the Laplace iteration method is a very effective method, simplifies the difficulty of classical techniques and is quite accurate for systems of partial differential equations. 相似文献
13.
Based on Fredlund’s one-dimensional consolidation equation for unsaturated soil, Darcy’s law and Fick’s law, a semi-analytical solution was presented to the free drainage well with a finite thickness under application of uniform vertical loading and the boundary of the top and bottom surfaces impermeable to water and air. According to the polar governing equations of water and air phases and the boundary and initial conditions, the excess pore-air and pore-water pressures and the soil layer settlement in the Laplace transformed domain are obtained by performing the Laplace transform and utilizing the Bessel functions. Crump’s method is used to perform the inversion of Laplace transform in order to obtain numerical solutions in the real time domain. Finally, a typical example is given to illustrate the changes in the excess pore-air and pore-water pressures and soil layer settlement with time factor at different ratios of air–water permeability coefficient and/or different distances from the well. 相似文献
14.
An isogeometric analysis (IGA) is introduced to obtain a head-based solution to Richards equation for unsaturated flow in porous media. IGA uses Non-Uniform Rational B-Spline (NURBS) as shape functions, which provide a higher level of inter-element continuity in comparison with Lagrange shape functions. The semi-discrete nonlinear algebraic equations are solved using a combination of implicit backward-Euler time-integration and Newton-Raphson scheme. The time-step size is adaptively controlled based on the rate of changes in the pore pressure. The results from the proposed formulation are compared and verified against an analytical solution for one-dimensional transient unsaturated flow in a homogenous soil column. The proposed method is then applied to four more complex problems including two-dimensional unsaturated flow in a two-layered soil and a semi-circular furrow. The test cases in two-layered soil system involve sharp variations in the pressure gradient at the intersection of the two media, where the pore water pressure abruptly changes. It is shown that the proposed head-based IGA is able to properly simulate changes in pore pressure at the soils interface using fewer degrees of freedom and higher orders of approximation in comparison with the conventional finite element method. 相似文献
15.
非饱和土路基毛细作用的数值与解析方法研究 总被引：2，自引：0，他引：2
通过建立非饱和土毛细作用的孔隙分布的分形模型,推导获得了非饱和土毛细水的最大上升高度,同时基于Richards水分运动微分方程,引入边界及初始条件,基于Laplace变换,得到了毛细作用下非饱和土路基湿度变化的解析解;同时引入算例,将所提出的解析方法计算结果与未简化参数的数值计算结果进行了对比分析;最后考虑不同因素的影响进行了非饱和土路基毛细作用下的湿度变化分析。分析结果表明：解析求解获得的路基湿度变化趋势和未进行参数简化的数值法求解结果基本一致,证明解析解法是合理可信的;路基填筑的初始含水率越大,填土的初始吸力越小,毛细水上升的高度及湿度变化量也相应越小;透水性能较好的路基填土毛细水上升速度较快,但上升高度较小,毛细水可以在较短时间内上升到最大高度;路基的填土类型不同,路基在毛细作用下的湿度变化状态也不同,需要针对不同的填土路基进行相应的防排水措施。 相似文献
16.
An alternative method of solution for the linearized ‘theta‐based’ form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ξ. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis‐equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi‐analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
17.
Unsaturated flow problems in porous media often described by Richards’ equation are of great importance in many engineering applications. In this contribution, we propose a new numerical flow approach based on isogeometric analysis (IGA) for modeling the unsaturated flow problems. The non-uniform rational B-spline (NURBS) basis is utilized for spatial discretization whereas the stable implicit backward Euler method for time discretization. The nonlinear Richards’ equation is iteratively solved with the aid of the Newton–Raphson scheme. Owing to some desirable features of an efficient numerical flow approach, major advantages of the present formulation involve: (a) numerical oscillation at the wetting front can be avoided or facilitated, simply by using either an h-refinement or a lumped mass matrix technique; (b) higher-order exactness can be obtained due to the nature of the IGA features; (c) the approach is straightforward to implement and it does not need any transformation, e.g., Kirchhoff transformation or filter algorithm; and (d) in contrast to the Picard iteration scheme, which forms linear convergences, the proposed approach can however yield quadratic convergences by using the Newton–Raphson method for solving resultant nonlinear equations. Numerical model validation is analyzed by solving a three-dimensional unsaturated flow problem in soil, and its derived results are verified against analytical solutions. Numerical applications are then studied by considering three extensive examples with simple and complex configurations to further show the accuracy and applicability of the present IGA. 相似文献
18.
经典的Richards入渗控制方程属于偏微分方程,具有强烈的非线性,难以求得解析解。以入渗时间为最小作用量,基于Richards方程建立关于入渗路径的时间泛函,将考虑重力项的非饱和土垂直入渗问题转化为泛函极值问题,并构造等价的Euler-Lagrange方程进行求解。计算结果表明,扩散系数D（?）与概化湿润锋距离具有函数关系,当扩散系数D（?）形式已知时,可求得最优路径下湿润锋处含水率、较远处湿润锋最小含水率、土壤含水率最大熵分布3个问题,并基于最优路径检验了本研究条件下,Boltzmann变换和线性变换求解Richards方程的精度。求解过程未引进新变量化简Richards方程,不改变原方程结构,因此其解具有普遍性,可作为非饱和土力学计算的一个补充。 相似文献