共查询到20条相似文献,搜索用时 62 毫秒
1.
B. Nath 《国际地质力学数值与分析法杂志》1981,5(2):139-163
A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately. The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically. 相似文献
2.
Michael D. Tocci C.T. Kelley Cass T. Miller Christopher E. Kees 《Computational Geosciences》1998,2(4):291-309
Richards' equation (RE) is often used to model flow in unsaturated porous media. This model captures physical effects, such as sharp fronts in fluid pressures and saturations, which are present in more complex models of multiphase flow. The numerical solution of RE is difficult not only because of these physical effects but also because of the mathematical problems that arise in dealing with the nonlinearities. The method of lines has been shown to be very effective for solving RE in one space dimension. When solving RE in two space dimensions, direct methods for solving the linearized problem for the Newton step are impractical. In this work, we show how the method of lines and Newton-iterative methods, which solve linear equations with iterative methods, can be applied to RE in two space dimensions. We present theoretical results on convergence and use that theory to design an adaptive method for computation of the linear tolerance. Numerical results show the method to be effective and robust compared with an existing approach. 相似文献
3.
4.
Preissmann窄缝法模拟明满流过渡过程方法简单,但存在明显的非物理振荡,抑制非物理振荡是该方法应用的关键。基于Godunov格式和精确Riemann求解器对明满流过渡过程进行模拟,针对Riemann问题代数恒等式在明满流交界处不光滑问题,提出了三阶收敛方法与二分法结合的迭代求解方法,保证迭代收敛至真实解;针对由于变量空间重构方法不能准确表达变量在空间中真实物理状态而导致的非物理振荡,提出了基于精确Riemann解的变量空间重构方法,准确表达激波间断在单元内的空间分布状态,从机理上抑制了非物理振荡。实例研究表明,数值计算结果与解析解或实测值吻合良好,研究成果为明满流过渡过程的高精度数值模拟提供了新的方法。 相似文献
5.
Preissmann窄缝法模拟明满流过渡过程方法简单,但存在明显的非物理振荡,抑制非物理振荡是该方法应用的关键。基于Godunov格式和精确Riemann求解器对明满流过渡过程进行模拟,针对Riemann问题代数恒等式在明满流交界处不光滑问题,提出了三阶收敛方法与二分法结合的迭代求解方法,保证迭代收敛至真实解;针对由于变量空间重构方法不能准确表达变量在空间中真实物理状态而导致的非物理振荡,提出了基于精确Riemann解的变量空间重构方法,准确表达激波间断在单元内的空间分布状态,从机理上抑制了非物理振荡。实例研究表明,数值计算结果与解析解或实测值吻合良好,研究成果为明满流过渡过程的高精度数值模拟提供了新的方法。 相似文献
6.
In this study, the dynamic response of a poroelastic half‐space to a point fluid sink is investigated using Biot's dynamic theory of poroelasticity. Based on Biot's theory, the governing field equations are re‐formulated in frequency domain with solid displacement and pore pressure. In a cylindrical coordinate system, a method of displacement potentials for axisymmetric displacement field is proposed to decouple the Biot's field equations to three scalar Helmholtz equations, and then the general solution to axisymmetric problems are obtained. The full‐space fundamental singular solution for a point sink is also derived using potential methods. The mirror‐image method is finally applied to construct the fundamental solution for a point sink buried in a poroelastic half‐space. Furthermore, a numerical study is conducted for a rock, that is, Berea sandstone, as a representative example. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
7.
A simple and efficient method for the solution of uncoupled transient thermoelastic problems using boundary integral techniques is presented. The method employs a Laplace transformation to remove temporarily the time dependence of the governing equations. Numerical analysis is then carried out in the transform space, and results in the time-position space are found by numerical inversion of the Laplace transform. The method has the advantage that it avoids time-stepping and the costly evaluation of domain integrals. Boundary element and analytic solutions are compared, and the effect of cooling on the stresses around a deep underground opening is examined. 相似文献
8.
A numericl method for solving consolidation problems of layered soils is developed. Starting from the governing differential equations for the coupled poro-elastic medium, the governing partial differential equations are reduced to ordinary differential equations by means of the appropriate displacement functions and Laplace-Fourier transformation. Once the fundamental solution in the transformed domain has been found, the solution in the physical domain is obtained by numerically inverting the transformations. A series of soil consolidation problems have been solved and validated against existing solutions in order to compare the feasibility and the accuracy of the present technique. 相似文献
9.
This study concerns the identification of constitutive models from geotechnical measurements by inverse analysis. Soil parameters are identified from measured horizontal displacements of sheet pile walls and from a measured pressuremeter curve. An optimization method based on a genetic algorithm (GA) and a principal component analysis (PCA), developed and tested on synthetic data in a previous paper, is applied. These applications show that the conclusions deduced from synthetic problems can be extrapolated to real problems. The GA is a robust optimization method that is able to deal with the non‐uniqueness of the solution in identifying a set of solutions for a given uncertainty on the measurements. This set is then characterized by a PCA that gives a first‐order approximation of the solution as an ellipsoid. When the solution set is not too curved in the research space, this ellipsoid characterizes the soil properties considering the measured data and the tolerate margins for the response of the numerical model. Besides, optimizations from different measurements provide solution sets with a common area in the research space. This intersection gives a more relevant and accurate identification of parameters. Finally, we show that these identified parameters permit to reproduce geotechnical measurements not used in the identification process. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
G. Beer 《国际地质力学数值与分析法杂志》1983,7(1):1-7
The Finite Element Method is frequently used to analyse problems involving an ‘infinite domain’. A typical problem is an underground excavation in prestressed infinite medium in either tunnelling or mining operations or a foundation in an infinite half space. This paper examines the implications of mesh truncation on the accuracy of the accuracy of the solution. At the same time, a more economical and accurate method of analysing these problems using special ‘infinite domain’ Finite Elements is presented. 相似文献
11.
A. A. Boyarchuk B. M. Shustov I. S. Savanov M. E. Sachkov D. V. Bisikalo L. I. Mashonkina D. Z. Wiebe V. I. Shematovich Yu. A. Shchekinov T. A. Ryabchikova N. N. Chugai P. B. Ivanov N. V. Voshchinnikov A. I. Gomez de Castro S. A. Lamzin N. Piskunov T. Ayres K. G. Strassmeier S. Jeffrey S. K. Zwintz D. Shulyak J.-C. Gérard B. Hubert L. Fossati H. Lammer K. Werner A. G. Zhilkin P. V. Kaigorodov S. G. Sichevskii S. Ustamuich E. N. Kanev E. Yu. Kil’pio 《Astronomy Reports》2016,60(1):1-42
The article presents a review of scientific problems and methods of ultraviolet astronomy, focusing on perspective scientific problems (directions) whose solution requires UV space observatories. These include reionization and the history of star formation in the Universe, searches for dark baryonic matter, physical and chemical processes in the interstellar medium and protoplanetary disks, the physics of accretion and outflows in astrophysical objects, from Active Galactic Nuclei to close binary stars, stellar activity (for both low-mass and high-mass stars), and processes occurring in the atmospheres of both planets in the solar system and exoplanets. Technological progress in UV astronomy achieved in recent years is also considered. The well advanced, international, Russian-led Spektr-UV (World Space Observatory—Ultraviolet) project is described in more detail. This project is directed at creating a major space observatory operational in the ultraviolet (115–310 nm). This observatory will provide an effective, and possibly the only, powerful means of observing in this spectral range over the next ten years, and will be an powerful tool for resolving many topical scientific problems. 相似文献
12.
A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information 总被引:1,自引:1,他引:0
Katrine Lange Jan Frydendall Knud Skou Cordua Thomas Mejer Hansen Yulia Melnikova Klaus Mosegaard 《Mathematical Geosciences》2012,44(7):783-803
The frequency matching method defines a closed form expression for a complex prior that quantifies the higher order statistics of a proposed solution model to an inverse problem. While existing solution methods to inverse problems are capable of sampling the solution space while taking into account arbitrarily complex a priori information defined by sample algorithms, it is not possible to directly compute the maximum a posteriori model, as the prior probability of a solution model cannot be expressed. We demonstrate how the frequency matching method enables us to compute the maximum a posteriori solution model to an inverse problem by using a priori information based on multiple point statistics learned from training images. We demonstrate the applicability of the suggested method on a synthetic tomographic crosshole inverse problem. 相似文献
13.
In this paper, we present a computational framework for the simulation of coupled flow and reservoir geomechanics. The physical
model is restricted to Biot’s theory of single-phase flow and linear poroelasticity, but is sufficiently general to be extended
to multiphase flow problems and inelastic behavior. The distinctive technical aspects of our approach are: (1) the space discretization
of the equations. The unknown variables are the pressure, the fluid velocity, and the rock displacements. We recognize that
these variables are of very different nature, and need to be discretized differently. We propose a mixed finite element space
discretization, which is stable, convergent, locally mass conservative, and employs a single computational grid. To ensure
stability and robustness, we perform an implicit time integration of the fluid flow equations. (2) The strategies for the
solution of the coupled system. We compare different solution strategies, including the fully coupled approach, the usual
(conditionally stable) iteratively coupled approach, and a less common unconditionally stable sequential scheme. We show that
the latter scheme corresponds to a modified block Jacobi method, which also enjoys improved convergence properties. This computational
model has been implemented in an object-oriented reservoir simulator, whose modular design allows for further extensions and
enhancements. We show several representative numerical simulations that illustrate the effectiveness of the approach. 相似文献
14.
《Tectonophysics》1987,140(1):93-102
This paper studies the physical and mathematical meaning of the wave migration method. Quantitative discrepancies between migrated and true wavefields are found.The migration method admits only of a heuristic solution in an unknown inhomogeneous medium. In some instances the inverse problems in an inhomogeneous medium can be reduced to wave migration procedures giving not only a seismic section (structure of the field complexity connected with that of the medium) but also medium's physical parameters.Examples are provided of practical uses of the algorithms for solving the inverse dynamic problems by the wave migration procedures. 相似文献
15.
16.
Ángel Rodríguez-Rozas David Pardo Carlos Torres-Verdín 《Computational Geosciences》2018,22(5):1271-1281
We develop a rapid 2.5-dimensional (2.5D) finite element method for simulation of borehole resistivity measurements in transversely isotropic (TI) media. The method combines arbitrary high-order \(H^{1}\)- and \(\mathbf {H}\)(curl)-conforming spatial discretizations. It solves problems where material properties remain constant along one spatial direction, over which we consider a Fourier series expansion and each Fourier mode is solved independently. We propose a novel a priori method to construct quasi-optimal discretizations in physical and Fourier space. This construction is based on examining the analytical (fundamental) solution of the 2.5D formulation over multiple homogeneous spaces and assuming that some of its properties still hold for the 2.5D problem over a spatially heterogeneous formation. In addition, a simple parallelization scheme over multiple measurement positions provides efficient scalability. Our method yields accurate borehole logging simulations for realistic synthetic examples, delivering simulations of borehole resistivity measurements at a rate faster than 0.05 s per measurement location along the well trajectory on a 96-core computer. 相似文献
17.
E.F. Kaasschieter 《Computational Geosciences》1999,3(1):23-48
Immiscible two‐phase flow in porous media can be described by the fractional flow model. If capillary forces are neglected,
then the saturation equation is a non‐linear hyperbolic conservation law, known as the Buckley–Leverett equation. This equation
can be numerically solved by the method of Godunov, in which the saturation is computed from the solution of Riemann problems
at cell interfaces. At a discontinuity of permeability this solution has to be constructed from two flux functions. In order
to determine a unique solution an entropy inequality is needed. In this article an entropy inequality is derived from a regularisation
procedure, where the physical capillary pressure term is added to the Buckley‐Leverett equation. This entropy inequality determines
unique solutions of Riemann problems for all initial conditions. It leads to a simple recipe for the computation of interface
fluxes for the method of Godunov.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
A procedure for numerical approximation to two-dimensional, hydraulically-driven fracture propagation in a poroelastic material is described. The method uses a partitioned solution procedurè to solve a finite element approximation to problems described by the theory of poroelasticity, in conjunction with a finite difference approximation for modelling fluid flow along the fracture. An equilibrium fracture model based on a generalized, Dugdale–Barenblatt concept is used to determine the fracture dimensions. An important feature is that the fracture length is a natural product of the solution algorithm. Two example problems verify the accuracy of the numerical procedure and a third example illustrates a fully-coupled simulation of fracture propagation. Photographs taken from a high-performance engineering workstation provide insight into the nature of the coupling among the physical phenomena. 相似文献
19.
空间物理学的回顾和展望 总被引:5,自引:1,他引:5
空间物理学是一门重要的迅速发展的学科。回顾了过去百年中发生的重大空间物理学事件。空间物理学已成功地迈过了探索阶段 ,未来是要搞清一些基本的科学问题。这些问题的解决需要观测研究、理论分析、数值模拟和环境预报的紧密合作 ,才能促成空间物理学的飞跃发展。 相似文献
20.
A boundary integral equation approach is presented for the two-dimensional plane strain analysis of horizontally layered elastic systems resting on a rough and rigid base. The validity of Somigliana identity for unbounded layers is discussed and an Infinite Boundary Element is proposed in order to take into account the lateral unboundedness of the physical problem in the discretized equations. This element is implemented in a computer code based on a successive stiffness solution procedure. A series of numerical tests concerning single- and multi-layered problems is illustrated, and the performance of the proposed solution method is compared with that of more traditional boundary element and finite element techniques. 相似文献