共查询到20条相似文献，搜索用时 203 毫秒
1.
Luz Angélica Caudillo-Mata Eldad Haber Christoph Schwarzbach 《Computational Geosciences》2017,21(5-6):963-980
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static Maxwell’s equations in the frequency domain. We assume a coarse mesh nested within a fine mesh that accurately discretizes the problem. For each coarse cell, we independently solve a local version of the original Maxwell’s system subject to linear boundary conditions on an extended domain, which includes the coarse cell and a neighborhood of fine cells around it. The local Maxwell’s system is solved using the fine mesh contained in the extended domain and the mimetic finite volume method. Next, these local solutions (basis functions) together with a weak-continuity condition are used to construct a coarse-mesh version of the global problem. The basis functions can be used to obtain the fine-mesh details from the solution of the coarse-mesh problem. Our approach leads to a significant reduction in the size of the final system of equations and the computational time, while accurately approximating the behavior of the fine-mesh solutions. We demonstrate the performance of our method using two 3D synthetic models: one with a mineral deposit in a geologically complex medium and one with random isotropic heterogeneous media. Both models are discretized using an adaptive mesh refinement technique. 相似文献
2.
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
3.
V.P. Gubatenko 《Russian Geology and Geophysics》2013,54(1):102-109
We propose a heuristic method for the analytical solution of electrical-prospecting problems for direct currents and 3D isotropic media. The corresponding parameters of the medium (conductivity, magnetic permeability) are determined from Maxwell’s equations by the assignment of electric- or magnetic-field intensity in the analytical form. The application of this method is illustrated with examples. 相似文献
4.
裂隙岩体因含有发育程度不同的裂隙、节理和断层等不连续面,致其渗透性具有各向异性、不连续性等特点,因此传统的有限元法对分布密集的裂隙岩体渗流场求解有一定的难度。本文提出了采用无单元Glaerkin法求解有自由面裂隙渗流问题,并推导了无单元法求解渗流场的基本方程和积分格式,给出了应用罚函数法处理渗流边界条件和自由面处理方法。采用IDL语言编制了二维无单元法计算软件LIDAREFM。文中以北京怀柔桥梓镇某裂隙岩体边坡渗流场计算为例,研究了复杂裂隙共同作用下渗流场特性和自由面分布,讨论了不同开度、不同连通程度的裂隙对渗流场的影响。研究结果表明:无单元法可以较好地解决有密集裂隙的岩体渗流场的求解问题,实现了裂隙处结点任意加密以及积分网格的独立布置,避免了对有自由面和裂隙穿越的子域的重新处理,简化了渗流问题的求解过程。 相似文献
5.
S. Sadiku 《国际地质力学数值与分析法杂志》2013,37(16):2789-2800
One‐dimensional consolidation analysis of layered soils conventionally entails solving a system of differential equations subject to the flow conditions at the bounding upper and lower surfaces, as well as the continuity conditions at the interface of every pair of contiguous layers. Formidable computational efforts are required to solve the ensuing transcendental equations expressing the matching conditions at the interfaces, using this method. In this paper, the jump discontinuities in the flow parameters upon crossing from one layer to the other have been systematically built into a single partial differential equation governing the space–time variation of the excess pore pressure in the entire composite medium, by the use of the Heaviside distribution. Despite the presence of the discontinuities in the coefficients of the differential equation, a closed‐form solution in the sense of an infinite generalized Fourier series is obtained, in addition to which is the development of a Green's function for the differential problem. The eigenfunctions of the composite medium are the coordinate functions of the series, obtained computationally through the application of the extended equations of Galerkin. The analysis has been illustrated by solving the consolidation problem of a four‐layer composite, and the results obtained agree very well with the results obtained by previous researchers. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
6.
High-Performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method
A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method, which ensures convergent numerical solution. The main features include: (i) memory usage eight times lower compared with analogous IE-based algorithms, without additional restrictions on the background media; (ii) accurate and stable method to compute matrix coefficients corresponding to the IE; and (iii) high degree of parallelism. The solver’s computational efficiency is demonstrated on a problem of magnetotelluric sounding of media with large conductivity contrast, revealing good agreement with results obtained using the second-order finite-element method. Due to the effective approach to parallelization and distributed data storage, the program exhibits perfect scalability on different hardware platforms. 相似文献
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8.
地质雷达数值模拟中有损耗介质吸收边界条件的实现 总被引：5，自引：1，他引：4
利用时间域有限差分(FDTD)法将麦克斯韦方程进行离散化,可以对地质雷达进行数值模拟。利用完全匹配层(PML)作为吸收边界条件可以有效地吸收向外的电磁波,从而大大提高了计算效率。对于有损耗介质的情况,采用扩张坐标系下改正的麦克斯韦方程,只要扩张变量满足一定的关系,同样可有效地吸收向外的电磁波, 这种吸收边界条件称为通用完全匹配层。 相似文献
9.
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
10.
大地电磁法正演中多重网格法求解的广义傅里叶谱分析 总被引：1，自引：0，他引：1
为了准确预测和分析多重网格法用于大地电磁法正演计算的收敛效果,对多重网格法的收敛性进行了广义傅里叶谱分析。通常情况下,系数矩阵的傅里叶谱是复数,为了直观地判断、提取收敛信息,将谱转换到实数域。在实数域内,特征向量谱定量解释了二重网格法收敛慢的原因（最粗网格用Gauss-Seidel法求解）。传统的局部傅里叶谱分析没有考虑边界条件和模型参数的变化,在分析二重网格法求解收敛性时得出的渐进收敛估计与数值解偏差大。针对这一问题提出广义傅里叶谱分析,其结果与数值解接近（比如2-V（0,1）的广义傅里叶谱分析为0.706,真实值为0.710）。对五重网格法求解的高重广义傅里叶谱分析结果表明,随广义傅里叶谱分析分析重数的增加, 所求渐近收敛估计趋于收敛的数值结果。基于此得出高重广义傅里叶谱分析的经验公式。求得低重广义傅里叶谱分析,通过矫正近似得到高重广义傅里叶谱分析,其结果在本文2个例子有效。 相似文献
11.
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
12.
Pierre Horgue Romain Guibert Hervé Gross Patrice Creux Gérald Debenest 《Computational Geosciences》2015,19(6):1159-1169
This work presents a new subdivision method to upscale absolute permeability fields. This process, called two-step method, consists in (i) solving micro-scale equations on subdomains obtained from the full domain regular decomposition and (ii) solve a second upscaling with Darcy’s law on the permeability fields obtained in the first step. The micro-scale equations used depend on the case studied. The two-step upscaling process is validated on randomly generated Darcy-scale permeability fields by measuring the numerical error induced by upscaling. The method is then applied to real domains obtained from sandstone micro-tomographic images. The method specificities due to pore-space structure are discussed. The main advantage of the two-step upscaling method resides in the drastic reduction of computational costs (CPU time and memory usage) while maintaining a numerical error similar to that of other upscaling procedures. This new upscaling method may improve permeability predictions by the use of finer meshes or larger sample volumes. 相似文献
13.
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
14.
Biot's equations of wave propagation through fluid-saturated porous elastic media are discretized spatially using the finite element method in conjunction with Galerkin's procedure. Laplace transformation of the discretized equations is used to suppress the time variable. Introducing Laplace transforms of constituent velocities at nodal points as additional variables, the quadratic set of equations in the Laplace transform parameter is reduced to a linear form. The solution in the Laplace transform space is inverted, term by term, to get the complete time history of the solid and fluid displacements and velocities. Since the solution is exact in the time domain, the error in the calculated response is entirely due to the spatial approximation. The procedure is applied to one-dimensional wave propagation in a linear elastic material and in a fluid-saturated elastic soil layer with ‘weak’, ‘strong’ as well as ‘moderate’ coupling. With refinement of the spatial mesh, convergence to the exact solution is established. The procedure can provide a useful benchmark for validation of approximate temporal discretization schemes and estimation of errors due to spatial discretization. 相似文献
15.
By using the numerical method to model the ter-rain effect on the magnetotelluric field,few resultshave been obtained. The finite element method(FEM) was used by Chouteau and Bouchard (1988)and Wannamaker et al .(1986) ,andthe boundary el-ement method (BEM) was used by Xu and Zhou(1997) and Xu (1995) to model 2Dtopographyinflu-ences on magnetotelluric surveys . The BEM methodwas also used to model the 3Dtopographic effect onmagnetotelluric deep sounding (Xu et al .,1997 ;Xu,1995) .In t… 相似文献
16.
三维地形大地电磁场的边界元模拟方法 总被引：1，自引：0，他引：1
提出了一种用边界元法计算大地电磁场三维地形影响的数值模拟方法.首先用矢量积分理论和电磁场边界条件, 将上半空间(空气)和下半空间(地下介质)两个区域电磁场边值问题变为仅对地形界面的两个矢量面积分方程, 其中一个计算磁场, 称磁场方程; 另一个计算电场, 称电场方程.然后将对地形界面的积分剖分为一系列的三角单元积分.在三角单元积分中, 假设单元中电磁场为水平均匀大地空间电磁场与地形影响的迭加, 并假设地形影响为常项, 这样既保证了计算精度又使得计算方法简便.通过分解和计算, 每一个矢量面积分方程分解为对应3个坐标方向的3个常量线性方程, 这些线性方程组成了对角占优的线性方程组, 可用SSOR方法求解.文中给出了2个三维地形上大地电磁视电阻率曲线的计算结果. 相似文献
17.
近些年来地下水中多组分反应-运移模型在地球科学及环境领域开始得到应用,但其求解较为复杂,为了提高计算效率,可以采用去耦合化方法处理,从而使模型求解得到简化。针对自然界中广泛存在的非均质地质体,提出该类条件下的去耦合化方法,即根据水-岩间、水溶组分间反应的不同,将整个研究区划分为若干子区域,获得对应的去耦合化矩阵。对化学场中各子区域间相邻边界进行设定,达到简化模型求解的目的。最后,以一维非均质介质中基于热力学平衡的反应-运移问题作为算例,基于以上方法进行求解,并与该算例经PHAST软件所示的结果较为一致。结果表明,基于去耦合化方法获得的各离子浓度随时间演变和沿空间分布特征与PHAST所示的结果较为一致,显示该方法在非均质区域模拟溶质运移等方面具有较好的适用性。 相似文献
18.
This paper investigates the two‐dimensional flow problem through an anisotropic porous medium containing several intersecting curved fractures. First, the governing equations of steady‐state fluid flow in a fractured porous body are summarized. The flow follows Darcy's law in matrix and Poiseuille's law in fractures. An infinite transversal permeability is considered for the fractures. A multi‐region boundary element method is used to derive a general pressure solution as a function of discharge through the fractures and the pressure and the normal flux on the domain boundary. The obtained solution fully accounts for the interaction and the intersection between fractures. A numerical procedure based on collocation method is presented to compute the unknowns on the boundaries and on the fractures. The numerical solution is validated by comparing with finite element solution or the results obtained for an infinite matrix. Pressure fields in the matrix are illustrated for domains containing several interconnected fractures, and mass balance at the intersection points is also checked. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
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
20.
本文给出了瞬变弹性动力问题的一个边界元法。该法是利用威尔逊——θ法的差分公式,把运动方程化为椭圆型微分方程。根据贝蒂定理和动力点荷载的特解,可获得动力问题的边界积分方程。这个解法是在真实时间域内逐步求解的,不需要使用拉氏变换。一个应力波传播的数值算例证实了该方法使用方便,且解答精度较高。 相似文献