共查询到18条相似文献，搜索用时 171 毫秒
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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
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《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
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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
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Richards方程在非饱和渗流模拟及其他相关领域应用广泛。在数值求解过程中,可以采用有限差分方法进行数值离散并迭代求解,为了获得较可靠的数值解,常规的均匀网格空间步长往往是较小的。在一些不利数值条件下,如入渗于干燥土壤,迭代计算费时甚至精度也不能得到很好改善。因此,文章提出Chebyshev空间网格改进方法,结合有限差分方法对Richards方程进行数值离散以获得线性方程组,并通过经典的Picard迭代方法进行迭代求解线性方程组以得到Richards方程的数值解。通过均质土和分层土2个不利情况下的非饱和渗流算例,又结合模型解析解和软件Hydrus-1D,对比研究了改进网格方法与均匀网格方法获得数值解的精度。结果表明,提出的Chebyshev网格方法相较于传统的均匀网格,可以在较少的节点数下获得较高的数值精度,又具有较小的计算开销,有较好的应用前景。 相似文献
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非饱和土中溶质迁移参数反演的HISR方法 总被引：1，自引：0，他引：1
以非饱和土中溶质迁移参数反演问题为背景, 依据正则化方法的思路, 以Itakura Saito距离作为同伦函数中的平凡问题, 将同伦方法引入非线性参数反演问题的求解, 进而提出一种求解非线性参数反演问题的大范围收敛(HomotoyItakura SaitoRegularization, HISR) 方法.为保证迭代稳定性, 并同时削弱观测噪声的影响, 同伦参数的修正采用了连续化修正方法.本文将HISR方法应用于求解带有平衡及非平衡吸附效应的一维非饱和土中溶质迁移参数反演问题, 计算结果表明HISR方法具有大范围收敛性及计算稳健性, 同时有较强的抵抗观测噪声的能力. 相似文献
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非饱和带水气二相渗流动力学模型 总被引：3，自引：0，他引：3
非饱和带地下水运动实质上是一个水气二相渗流过程。本文以多相渗流理论为基础,从水气二相渗流的连续性方程和达西定律出发,推导了非饱和带水气二相渗流的耦合动力学模型,讨论了模型的IMPES和全隐式联立求解方法的原理和步骤,认为IMPES求解方法由于达西系数项的处理,饱和度的计算均采用显式,因此该解法具有稳定性差、精度低且要求计算时间步长小的局限性;而全隐式联立求解方法是联立求解气相、水相方程,同时求出压力和饱和度值,因此压力和饱和度值都是隐式求出,具有较高精度,且无条件稳定,应是今后模型求解的重点研究内容 相似文献
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下限分析有限单元法将下限定理这一数学变分问题转化为一个数学规划问题,克服了人为构造可静应力场的困难,在实际工程中具有广阔的应用前景。通过有限元离散得到的非线性下限规划模型中包含大量的优化变量与约束条件,常规优化算法难以求解。为此,在分析非线性下限规划模型自身特点的基础上,引入可行弧技术和Wolfe非精确搜索技术改进其优化求解效率。算例分析表明,基于可行弧技术和Wolfe非精确搜索技术,下限分析有限单元法优化求解程序的收敛速度和步长搜索效率得到明显的提升,并且其数值稳定性良好、计算精度较高,可以较好地适应实际工程问题的计算。 相似文献
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三维稳定渗流的 p 型自适应有限元分析 总被引：3，自引：2，他引：3
建立了三维稳定渗流的p型自适应有限元分析的误差估计器。充分利用p型有限元前处理少、计算精度高和收敛速度快的优点，分析了p型有限元法求解渗流问题的技术特点，给出了求解三维稳定渗流的自适应升阶策略。通过具体算例，研究了单元阶次及网格尺度对计算结果的影响，验证了三维p型有限元法在求解渗流问题时的可行性。 相似文献
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This paper proposed a numerical formulation for unsaturated flow problems with nonlinear boundaries of seepage face and soil–atmosphere interface via the concept of parabolic variational inequality (PVI) method. A unified unilateral boundary condition was first proposed to represent the conditions on the seepage face and soil–atmosphere interface boundaries within the partial differential equation (PDE) formulation. A PVI formulation mathematically equivalent to the PDE formulation was then proposed, which automatically transforms the flux part of the unified unilateral boundary condition into the natural boundary condition and eliminates the singularity at seepage points. By discretizing the PVI formulation, a finite element procedure together with an iterative algorithm was suggested. An existing experiment of unsaturated flow in a layered hillside and a laboratory test of unsaturated flow through sand flume performed in this study were used to validate the proposed method, with a good agreement between the measured and computed results and a satisfactory balance of mass being maintained during the simulations. The numerical results also indicated that the problem of mesh dependence associated with unsaturated flow simulations is well addressed with the proposed numerical method. Finally, the process of unsaturated flow in a soil slope with layers of horizontal drains subjected to rainfall/evaporation was further examined. The numerical results reveal that the deployment of drains in a soil slope can significantly lower the pore water pressure around the drains, with the bottom layer drains being most effective in controlling the seepage flow. 相似文献
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在进行裂隙岩体非饱和渗流研究中,选用合理的裂隙岩体毛管压力-饱和度关系曲线非常关键。基于裂隙岩体非饱和渗流特点,简述当前国内外非饱和裂隙岩体毛管压力-饱和度关系曲线模型的研究状况。总结出非饱和裂隙渗透具有毛细管流、薄膜流、优先流、裂隙-基质相互作用和沟槽流特点;分析了建立单裂隙岩体非饱和渗流毛管压力-饱和度关系曲线模型的主要方法,包括物模试验法、数值计算法和数学推导法,并归纳这些方法的计算结果;最后,结合渗流特点,对各种曲线模型结果进行比较,进一步分析得出：(1) 目前的曲线关系均建立在毛管理论基础之上,几乎没有反映渗流其他特点的关系曲线;(2) 运用数值计算法和数学推导建立曲线模型较为简便;(2) 在排水曲线初始时段,Brooks-Corey(BC)模型模拟得到的结果比van Genuchten(VG)模型要好些,而在末尾时段VG模型要好些。 相似文献
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The 1D consolidation of unsaturated multi-layered soil is studied based on the theory proposed by Fredlund and Hasan, and an analytical solution for a typical boundary condition is obtained by assuming all material parameters remain constant during consolidation. In the derivation of the analytical solution, the eigenfunction and eigenvalue for the multi-layered problem are first derived through the transfer matrix method. Then, by using the method of undetermined coefficients and the orthogonal relation of the eigenfunction, the analytical solution is obtained. The present method is applicable to various types of boundary conditions. Finally, numerical examples are provided to investigate the consolidation behavior of unsaturated multi-layered soil. 相似文献
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The results of a numerical simulation of the observed field-drying behaviour of an unsaturated clay are described. In particular, the simulation of soil drying during the summer of 1983 is addressed. Richards' pressure-based unsaturated flow formulation is adopted. Transient numerical solutions are achieved by making use of the finite element method coupled with a finite difference timestepping scheme. The application of the algorithm to the simulation of the problem in hand is described. The initial moisture content distribution represents saturated conditions as indicated by field-measured data. Boundary conditions are determined from an interpretation of meteorological data. A simple method of representing plant root extraction of soil moisture is proposed. Comparisons of numerical results with field-measured data collected by British Gas are presented. Good correlation is obtained. The numerical simulation is shown to be capable of representing the observed field-drying behaviour. The complexity of modelling soil drying, as opposed to infiltration, is clearly illustrated by the work presented. 相似文献
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Energy piles are bi-functional foundation elements used as structural support as well as ground heat exchangers for shallow geothermal energy systems. Because they are relatively short, energy piles may be partially embedded in unsaturated soils. Saturation conditions influence the thermal properties of the ground and therefore the heat exchange rate, which in turn affects the efficiency of energy piles. This paper combines analytical, experimental and numerical investigations to evaluate the heat exchange rate of energy piles partially or fully embedded in unsaturated soils. The proposed analytical solution is based on the cylindrical heat source theory that treats the soil as a semi-infinite, homogeneous, and isotropic medium. The solution from this theory is multiplied by a function developed analytically in this paper and the outcome is the heat exchange rate for energy piles in unsaturated soils. The proposed function depends on soil saturation, soil and pile thermal properties, and pile geometry. The analytical solution was compared against a finite element solution; which was in turn validated against results from laboratory experiments. Very satisfactory agreements between the analytical, numerical and experimental outputs were observed. The proposed method can be used for a quick and simple evaluation of the efficiency of energy piles in unsaturated conditions. The proposed analytical solution can also be a useful tool for the verification of numerical codes developed for the design of energy piles in unsaturated soils. 相似文献
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半无限含水层中带衬砌隧洞渗流解析研究 总被引：3，自引：0，他引：3
现有关于半无限含水层中隧洞渗流的解析解不能考虑衬砌部分排水的特性。假定土体和衬砌均为饱和均匀连续介质,采用土体与衬砌分算;利用复变函数解决孔口问题基本方法,对土体采用共形映射坐标变换,将土体中的渗流方程转换为与衬砌部分类似的二维Laplace方程圆环域的Dirichlet问题;通过Fourier解法,根据边界条件并利用流量连续条件,求得半无限空间中带衬砌隧洞渗流量和衬砌周边水头解析解答。分析了径深比、土体与衬砌渗透系数相对值、内壁水压力等因素对渗流量和衬砌周边水头的影响,并与数值算例进行了比较。结果表明,对浅埋隧洞该解析解仍具有较好的精度,是简便、实用的计算方法。 相似文献
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在非饱和多孔介质渗流分析中,近饱和条件下物理模型与数值模型之间的差异会导致数值不稳定问题。为解决这一问题,并保证模拟结果的可靠性,提出了3种方法,并在有限元分析程序U-DYSAC2中分别进行了程序代码的实施。通过数值试验与试验数据的比较,证实了在近饱和条件下土-水特征曲线和水力传导函数的高非线性可引起数值收敛性、稳定性和精度问题,而且在不同条件下含水率和基质吸力的预测结果差异明显。在3种方法中,修正的Van Genuchten模型（MVGM）方法对含水率的预测较为准确,而Line方法对基质吸力的预测较为合理。因此,解决在分析近饱和条件下非饱和多孔介质渗流问题时,为获得接近真实的模拟结果,采用合适的数值方法进行预测是非常关键的。 相似文献