共查询到20条相似文献，搜索用时 218 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.
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
3.
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
4.
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
5.
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
6.
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
7.
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8.
This work concerns linearization methods for efficiently solving the Richards equation, a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media. The discretization of Richards’ equation is based on backward Euler in time and Galerkin finite elements in space. The most valuable linearization schemes for Richards’ equation, i.e. the Newton method, the Picard method, the Picard/Newton method and the L-scheme are presented and their performance is comparatively studied. The convergence, the computational time and the condition numbers for the underlying linear systems are recorded. The convergence of the L-scheme is theoretically proved and the convergence of the other methods is discussed. A new scheme is proposed, the L-scheme/Newton method which is more robust and quadratically convergent. The linearization methods are tested on illustrative numerical examples. 相似文献
9.
A method is presented to estimate actual evapotranspiration (ETA) from potential evapotranspiration (ETP) by numerical modeling of water flow in the unsaturated zone. Water flow is described by the Richards equation with a sink term representing the root water uptake. Evaporation is included in the model as a Neumann boundary condition at the soil surface. The Richards equation is solved in a one-dimensional domain using a mixed finite element method. The values of ETA are obtained by applying a water stress factor to ETP to account for soil moisture changes during the simulation period. The proposed numerical model is used to estimate ETA in an experimental plot located in a flatland area in Buenos Aires (Argentina). Numerical results show that the proposed model is a useful tool for evaluating evapotranspiration under different scenarios. 相似文献
10.
Solution of Laplace’s equation can be done by iteration methods likes Jacobi, Gauss–Seidel, and successive over-relaxation (SOR). There is no new knowledge about the relaxation coefficient (ω) in SOR method. In this paper, we used SOR for solving Laplace’s differential equation with emphasis to obtaining the optimum (minimum) number of iterations with variations of the relaxation coefficient (ω). For this purpose, a code in FORTRAN language has been written to show the solution of a set of equations and its number of iterations. The results demonstrate that the optimum value of ω with minimum iterations is achieved between 1.7 and 1.9. Also, with increasing β?=??x/?y from 0.25 to 10, the number of iterations reduced and the optimum value is obtained for β?=?2. 相似文献
11.
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
12.
Cheng-Yu Ku Chih-Yu Liu Yan Su Jing-En Xiao Chi-Chao Huang 《Environmental Earth Sciences》2017,76(16):570
This study investigates the transient modeling of regional rainfall-triggered shallow landslides in unsaturated soil using the Richards equation. To model shallow landslides within a distributed regional-scale framework, infinite slope stability analysis coupled with the hydrological model with consideration of the fluctuation of time-dependent pore water pressure and the soil–water characteristic curve proposed by van Genuchten was developed. The validity of the proposed model is established through several test problems by comparing the numerical results with the analytical solutions. A new procedure to set up wide-range shallow landslide analysis and to integrate regional distribution variations for input data such as geology, groundwater level, hydrogeological characteristics, and rainfall intensity and duration was presented. The results obtained demonstrate that the computed distribution of the safety factor is consistent with the distribution of actual landslides. In addition, the fluctuation of pore water pressure in unsaturated soil dominates the stability of landslides during typhoons accompanied by heavy rainfall. The findings observed in this study are a fundamental contribution to environmental effects for landslides in areas with higher occurrence and vulnerability to extreme precipitation. 相似文献
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14.
Theoretical study and simulation of moisture transport in unsaturated porous media by periodic homogenization 
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下载免费PDF全文 In this work, the macroscopic Richards equation for moisture transport is established in unsaturated porous media using periodic homogenization. By performing dimensional analysis on microscopic equations of moisture transfer, dimensional numbers characterizing moisture transport appear. The application of the asymptotic homogenization leads to the classical Richards equation, which is justified rigorously this way. Moreover, we obtain an accurate definition of the homogenized diffusion tensor of moisture involving the geometric properties of the microstructure and known transport properties of the material. A different behavior for the transport of water vapor between hygroscopic and super‐hygroscopic region is revealed. Finally, a simple 2D example where an analytical solution exists is addressed. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
15.
基于一维的Richards方程,考虑van Genuchten提出的土-水特征曲线和水力传导系数的表达式,采用差分方法进行求解,研究该土-水特征曲线对孔隙水压力分布的影响,分析该模型四个参数θs、θr、α和n对孔隙水压力分布的作用特征。结果表明经验参数α和n对孔隙水压力分布产生显著的影响。α影响土-水特征曲线的位置和水力传导系数斜率,其值越大,基质吸力越滞后,孔隙水压力分布弯曲度随着α值的增大而明显;n决定土-水特征曲线的斜率,其值大意味着基质吸力易消散。计算分析显示θr值变化引起孔隙水压力分布微弱的差异,这差异随着时间的增长而增大;饱和含水量θs对孔隙水压力分布也产生不小的影响,随θs的降低孔隙水压力消散减慢。 相似文献
16.
This paper develops a semi-analytical solution for the transient response of an unsaturated single-layer poroviscoelastic medium with two immiscible fluids by using the Laplace transformation and the state-space method. Using the elastic–viscoelastic correspondence principle, we first introduce the Kelvin–Voigt model into Zienkiewicz’s unsaturated poroelastic model. The vibrational response for unsaturated porous material can be obtained by combining these two models and assuming that the wetting and non-wetting fluids are compressible, the solid skeleton and solid particles are viscoelastic, and the inertial and mechanical couplings are taken into account. The Laplace transformation and state-space method are used to solve the basic equations with the associated initial and boundary conditions, and the analytical solution in the Laplace domain is developed. To evaluate the responses in the time domain, Durbin’s numerical inverse Laplace transform method is used to obtain the semi-analytical solution. There are three compressional waves in porous media with two immiscible fluids. Moreover, to observe the three compressional waves clearly, we assume the two immiscible fluids are water and oil. Finally, several examples are provided to show the validity of the semi-analytical solution and to assess the influences of the viscosity coefficients and dynamic permeability coefficients on the behavior of the three compressional waves. 相似文献
17.
当采用合理的强度参数时,根据常规极限平衡或极限分析方法的计算结果,很难解释一些膨胀土边坡会在极缓的坡度下发生失稳破坏的原因。事实上,由于膨胀土遇水后会发生显著的变形,在饱和区与非饱和区交界面附近会出现很大的剪应力。因此,在膨胀土边坡的稳定分析中,需要考虑这种因素的影响。根据塑性力学的上限定理,严格地导出了考虑膨胀应力作功的功能平衡方程。根据强度储备定义的安全系数即隐含在这一方程中,它可以通过迭代方法求解。边坡稳定的上限分析在数值上是利用了单元集成法来完成的。这不仅能方便地利用应力分析的成果,而且能进行滑裂面的优化,从而找到最小的安全系数。对一个坡度为1:4的膨胀土边坡的稳定计算结果表明,膨胀变形会使边坡的安全系数显著减小。当考虑膨胀时,优化得到的破坏模式是在浅层出现一个局部的滑动,它会牵动其上部的土体也相继出现局部滑动,这正好符合膨胀土滑坡时所常见的牵引性的特征。 相似文献
18.
得到了地下结构在水平地震作用下的动力运动方程,利用拉普拉斯变换和结构的对接条件,得到了求解待定系数的超越方程。利用拉普拉斯逆变换得到了结构的位移表达式和确定拉普拉斯参数极点的方程。进一步研究发现,拉普拉斯变换参数s与结构频率ω之间存在某种特殊的关系:s2=?ω2。为了避免确定待定系数及拉普拉斯参数极点时求解复杂超越方程的困难,建议通过数值的办法先把结构体系的频率求出来,再通过拉普拉斯逆变换留数定理求解结构的位移和内力。 相似文献
19.
A low-dimensional model that describes both saturated and unsaturated flow processes in a single equation is presented. Subsurface flow processes in the groundwater, the vadose zone, and the capillary fringe are accounted for through the computation of aggregated hydrodynamic parameters that result from the integration of the governing flow equations from the bedrock to the land surface. The three-dimensional subsurface flow dynamics are thus described by a two-dimensional equation, allowing for a drastic reduction of model unknowns and simplification of the model parameterizations. This approach is compared with a full resolution of the Richards equation in different synthetic test cases. Because the model reduction stems from the vertical integration of the flow equations, the test cases all use different configurations of heterogeneity for vertical cross-sections of a soil-aquifer system. The low-dimensional flow model shows strong consistency with results from a complete resolution of the Richards equation for both the water table and fluxes. The proposed approach is therefore well suited to the accurate reproduction of complex subsurface flow processes. 相似文献
20.
The paper presents the analytical solution for the steady‐state infiltration from a buried point source into two types of heterogeneous cross‐anisotropic unsaturated half‐spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half‐space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross‐anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献